formulate statistical hypothesis

DEFINITION 1 Bayesian Statistical Inference. Assume the prior probability P ( h θ ) assigned to hypotheses h θ ∈ H , with θ ∈ Θ, the space of parameter values. Further assume P ( s t | h θ ), the probability assigned to the data s t conditional on the hypotheses, called the likelihoods. Bayes' theorem determines that (6) P ( h θ | s t ) = P ( h θ ) P ( s t | h θ ) P ( s t ) .

Bayesian statistics outputs a posterior probability assignment, P ( h θ | s t ).

I refer to [ Barnett, 1999 ] and [ Press, 2003 ] for a detailed discussion. The further results form a Bayesian inference, such as estimations and measures for the accuracy of the estimations, can all be derived from the posterior distribution over the statistical hypotheses.

In this definition the probability of the data P ( s t ) is not presupposed, because it can be computed from the prior and the likelihoods by the law of total probability,

The result of a Bayesian statistical inference is not always a complete posterior probability. Often the interest is only in comparing the ratio of the posteriors of two hypotheses. By Bayes' theorem we have

and if we assume equal priors P ( h θ ) = P ( h θ ′ ), we can use the ratio of the likelihoods of the hypotheses, the so-called Bayes factor, to compare the hypotheses.

Let me give an example of a Bayesian procedure. Say that we are interested in the colour composition of pears from Emma's farm, and that her pears are red, q i 0 , or green, q i 1 . Any ratio between these two kinds of pears is possible, so we have a set of so-called multinomial hypotheses h θ for which

where θ is parameter in the interval [0,1]. The hypothesis h θ fixes the portion of green pears at θ, and therefore, independently of what pears we saw before, the probability that a randomly drawn pear from Emma's farm is green is θ. The type of distribution over Q that is induced by these hypotheses is sometimes called a Bernoulli distribution, or a multinomial distribution.

We now define a Bayesian statistical inference over these hypotheses. Instead of directly choosing among the hypotheses on the basis of the data, as classical statistics advises, we assign a probability distribution over the hypotheses, expressing our epistemic uncertainty. For example, we may choose a so-called Beta distribution,

with θ ∈ Θ = [0,1] and Norm a normalisation factor. For λ = 2, this function is uniform over the domain. Now say that we observe a sequence of pears s t = s k 1 … k t , and that we write t 1 as the number of green pears, or 1's, in the sequence s t , and t 0 for the number of 0's, so t 0 + t 1 = t . The probability of this sequence s t given the hypothesis h θ is

Note that the probability of the data only depends on the number of 0's and the number of 1's in the sequence. Applying Bayes' theorem then yields, omitting a normalisation constant,

This is the posterior distribution over the hypotheses. It is derived from the choice of hypotheses, the prior distribution over them, and the data by means of the axioms of probability theory, specifically by Bayes' theorem.

Most of the controversy over the Bayesian method concerns the determination and interpretation of the probability assignment over hypotheses. As will become apparent in the following, classical statistics objects to the whole idea of assigning probabilities to hypotheses. The data have a well-defined probability, because they consist of repeatable events, and so we can interpret the probabilities as frequencies, or as some other kind of objective probability. But the probability assigned to a hypothesis cannot be understood in this way, and instead expresses an epistemic state of uncertainty. One of the distinctive features of classical statistics is that it rejects such an epistemic interpretation of the probability assignment, and that it restricts itself to a straightforward interpretation of probability as relative frequency.

Even if we buy into this interpretation of probability as epistemic uncertainty, how do we determine a prior probability? At the outset we do not have any idea of which hypothesis is right, or even which hypothesis is a good candidate. So how are we supposed to assign a prior probability to the hypotheses? The literature proposes several objective criteria for filling in the priors, for instance by maximum entropy or by other versions of the principle of indifference, but something of the subjectivity of the starting point remains. The strength of classical statistical procedures is that they do not need any such subjective prior probability.

Nonparametric Hypotheses Tests

In this chapter we learned how to test a statistical hypothesis without making any assumptions about the form of the underlying probability distributions. Such tests are called nonparametric .

Sign Test The sign test can be used to test hypotheses concerning the median of a distribution. Suppose that for a specified value m we want to test

where η is the median of the population distribution. To obtain a test, choose a sample of elements of the population, discarding any data values exactly equal to m . Suppose n data values remain. The test statistic of the sign test is the number of remaining values that are less than m . If there are i such values, then the p value of the sign test is given by

where N is a binomial random variable with parameters n and p = 1 / 2 . The computation of the binomial probability can be done either by running Program 5-1 or by using the normal approximation to the binomial.

The sign test can also be used to test the one-sided hypothesis

It uses the same test statistic as earlier, namely, the number of data values that are less than m . If the value of the test statistic is i , then the p value is given by

where again N is binomial with parameters n and p = 1 / 2 .

If the one-sided hypothesis to be tested is

then the p value, when there are i values less than m , is

where N is binomial with parameters n and p = 1 / 2 .

As in all hypothesis testing, the null hypothesis is rejected at any significance level greater than or equal to the p value.

Signed-Rank Test The signed-rank test is used to test the hypothesis that a population distribution is symmetric about the value 0. In applications, the population often consists of the differences of paired data. The signed-rank test calls for choosing a random sample from the population, discarding any data values equal to 0. It then ranks the remaining nonzero values, say there are n of them, in increasing order of their absolute values. The test statistic is equal to the sum of the rankings of the negative data values. If the value of the test statistic TS is equal to t , then the p value is

where the probabilities are to be computed under the assumption that the null hypothesis is true. The p value can be found either by using Program 14-1 or by using the fact that TS will have approximately, when the null hypothesis is true and n is of least moderate size, a normal distribution with mean and variance, respectively, given by

Rank-Sum Test The rank-sum test can be used to test the null hypothesis that two population distributions are identical, when the data consist of independent samples from these populations. Arbitrarily designate one of the samples as the first sample. Suppose that the size of this sample is n and that of the other sample is m . Now rank the combined samples. The test statistic TS of the rank-sum test is the sum of the ranks of the first sample. The rank-sum test calls for rejecting the null hypothesis when the value of the test statistic is either significantly large or significantly small.

When n and m are both greater than 7, the test statistic TS will, when H 0 is true, have an approximately normal distribution with mean and variance given by, respectively,

This enables us to approximate the p value, which when TS = t is given by

For values of t near n ( n + m + 1 ) / 2 , the p value is close to 1, and so the null hypothesis would not be rejected (and the preceding probability need not be calculated).

For small values of n and m the exact p value can be obtained by running Program 14-2.

Runs Test The runs test can be used to test the null hypothesis that a given sequence of data constitutes a random sample from some population. It supposes that each datum is either a 0 or a 1. Any consecutive sequence of either 0s or 1s is called a run . The test statistic for the runs test is R , the total number of runs. If the observed value of R is r , then the p value of the runs test is given by

The probabilities here are to be computed under the assumption that the null hypothesis is true.

Program 14-3 can be used to determine this p value. If Program 14-3 is not available, we can approximate the p value by making use of the fact that when the null hypothesis is true, R will have an approximately normal distribution. The mean and variance, respectively, of this distribution are

Hypothesis Testing

R.H. Riffenburgh , in Statistics in Medicine (Third Edition) , 2012

Why the Null Hypothesis Is Null

It may seem a bit strange at first that our primary statistical hypothesis in testing for a difference says there is no difference, even when, according to our clinical hypothesis, we believe there is one, and might even prefer to see one. The reason lies in the ability to calculate errors in decision making. When the hypothesis says that our sample is no different from known information, we have available a known probability distribution and therefore can calculate the area under the distribution associated with the erroneous decision: a difference is concluded when in truth there is no difference. This area under the probability curve provides us with the risk for a false-positive result. The alternate hypothesis, on the other hand, says just that our known distribution is not the correct distribution, not what the alternate distribution is. Without sufficient information regarding the distribution associated with the alternate hypothesis, we cannot calculate the area under the distribution associated with the erroneous decision: no difference exists when there is one, that is, the risk for a false-negative result.

Hypothesis testing

Kandethody M. Ramachandran , Chris P. Tsokos , in Mathematical Statistics with Applications in R (Third Edition) , 2021

6.6 Chapter summary

In this chapter, we have learned various aspects of hypothesis testing. First, we dealt with hypothesis testing for one sample where we used test procedures for testing hypotheses about true mean, true variance, and true proportion. Then we discussed the comparison of two populations through their true means, true variances, and true proportions. We also introduced the Neyman–Pearson lemma and discussed likelihood ratio tests and chi-square tests for categorical data.

We now list some of the key definitions in this chapter.

Statistical hypotheses

Tests of hypotheses, tests of significance, or rules of decision

The level of significance

The p value or attained significance level

The Smith–Satterthwaite procedure

Power of the test

Most powerful test

Likelihood ratio

In this chapter, we also learned the following important concepts and procedures:

General method for hypothesis testing

Steps to calculate β

Steps to find the p value

Steps in any hypothesis-testing problem

Summary of hypothesis tests for μ

Summary of large sample hypothesis tests for p

Summary of hypothesis tests for the variance σ 2

Summary of hypothesis tests for μ 1 − μ 2 for large samples ( n 1 and n 2 ≥ 30)

Summary of hypothesis tests for p 1 − p 2 for large samples

Testing for the equality of variances

Summary of testing for a matched pairs experiment

Procedure for applying the Neyman–Pearson lemma

Procedure for the likelihood ratio test

Sample Size

Chirayath M. Suchindran , in Encyclopedia of Social Measurement , 2005

Basic Principles

Sampling techniques are used either to estimate statistical quantities with desired precision or to test statistical hypotheses. The first step in the determination of the sample size is to specify the design of the study (simple random samples of the population, stratified samples, cluster sampling, longitudinal measurement, etc.). If the goal is statistical estimation, the endpoint to be estimated and the desired precision would be specified. The desired precision can be stated in terms of standard error or a specified confidence interval. If the goal is to conduct statistical testing, the determination of sample size will involve specifying (1) the statistical test employed in testing the differences in end point, (2) the difference in the end point to be detected, (3) the anticipated level of variability in the end point (either from previous studies or from theoretical models), and (4) the desired error levels (Type I and Type II errors). The value of increased information in the sample is taken into consideration in the context of the cost of obtaining it. Guidelines are often needed for specifications of effect size and associated variability. One strategy is to take into account as much available prior information as possible. Alternatively, a sample size is selected in advance and the information (say, power or effect size) that is likely to be obtained with that sample size is examined. Large-scale surveys often aim to gather many items of information. If a desired degree of precision is prescribed for each item, calculations may lead to a number of different estimates for the sample size. These are usually compromised within the cost constraint. Sample size determinations under several sampling designs or experimental situations are presented in the following sections.

Answers to Chapter Exercises, Part I

ROBERT H. RIFFENBURGH , in Statistics in Medicine (Second Edition) , 2006

It is a clinical hypothesis, stating what the investigator suspects is happening. A statistical hypothesis would be the following: Protease inhibitors do not change the rate of pulmonary admissions. By stating no difference, the theoretical probability distribution can be used in the test. (If there is a difference, the amount of difference is unknown, and thus the associated distribution is unknown.)

Ho: μ w = μ w/o ; H 1 : μ w ≠ μ w/o .

(a) The t distribution is associated with small data sample hypotheses about means. (b) Assumptions include: The data are independent one from another. The data samples are drawn from normal populations. The standard deviations at baseline and at 5 days are equal. (c) The Type I error would be concluding that the baseline mean and the 5-day mean are different when, in fact, they are not. The Type II error would be concluding the two means are the same when, in fact, they are different. (d) The risk for a Type I error is designated α The risk for a Type II error is designated β. The power of the test would be designated 1 – β .

(a) The x 2 distribution is associated with a hypothesis about the variance. (b) Assumptions include: The data are independent one from another. The data sample is drawn from a normal population. (c) The Type I error would be concluding that the platelet standard deviation is different from 60,000 when, in fact, it is 60,000. The Type II error would be concluding the platelet standard deviation is 60,000 when, in fact, it is not. (d) The risk for a Type I error is designated α. The risk for a Type II error is designated β .

(a) The F distribution is associated with a hypothesis about the ratio of two variances. (b) Assumptions include: The data are independent one from another. The data samples are drawn from normal populations. (c) The Type I error would be concluding the variance (or standard deviation) of serum silicon before the implant removal is different from the variance (or standard deviation) after when, in fact, they are the same. The Type II error would be concluding the before and after variances (or standard deviations) are the same when, in fact, they are different. (d) The risk for a Type I error is designated α. The risk for a Type II error is designated β .

The “above versus below” view would interpret this decrease as not significant, end of story. Exercise has no effect on the eNO of healthy subjects. The “level of p” view

would say that, although the 2.15-ppb decrease has an 8% chance of being false, it also has a 92% chance of being correct. The power of the test should be evaluated. Perhaps the effect of exercise on eNO in healthy subjects should be investigated further.

(a) A categorical variable. (b) A rating that might be any type, depending on circumstance. In this case, treating it as a ranked variable is recommended, because it avoids the weaker methods of categorical variables and a five-choice is rather small for use as a continuous variable. (c) A continuous variable.

1, 7, 8, 3, 5, 2, 4, 6.

(1) Does the drug reduce nausea score following gallbladder removal? (2 and 3) Drug/No Drug against Nausea/No Nausea. (4) H 0 : nausea score is independent of drug use; H 1 : nausea score is influenced by drug use. (5) The population of people having laparoscopic gallbladder removals who are treated for nausea with Zofran. The population of people having laparoscopic gallbladder removals who are treated for nausea with a placebo. (6) My samples of treated and untreated patients are randomly selected from patients who present for laparoscopic gallbladder removal. (7) A search of the literature did not indicate any proclivity to nausea by particular subpopulations. (8) These steps seem to be consistent. (9) A chi-square test of the contingency table is appropriate; let us use α = 0.05. (10) (Methodology for step 10 is not given in Part I; Chapter 22 provides information for the student who wishes to pursue this.)

(1) Are our clinic's INR readings different from those of the laboratory? (2) Difference between clinic and laboratory readings. (3) Mean of difference. (4) H 0 : mean difference = 0; H 1 : mean difference ≠ 0. (5) Population: All patients, past and future, subject to the current INR evaluation methods in our Coumadin Clinic. (6) Sample: the 104 consecutive patients taken in this collection. (7) Biases: The readings in this time period might not be representative. We can examine records to search for any cause of nonrepresentativeness. Also, we could test a small sample from a different time and test it for equivalence. (8) Recycle: These steps seem consistent. (9) Statistical test and α : paired t test of mean difference against zero with α = 0.05.

Statistics as Inductive Inference

Jan-Willem Romeijn , in Philosophy of Statistics , 2011

7 Bayesian Statistics

The defining characteristic of Bayesian statistics is that probability assignments do not just range over data, but that they can also take statistical hypotheses as arguments. As will be seen in the following, Bayesian inference is naturally represented in terms of a non-ampliative inductive logic, and it also relates very naturally to Carnapian inductive logic.

Let H be the space of statistical hypotheses h θ , and let Q be the sample space as before. The functions P are probability assignments over the entire space H × Q . Since h θ is a member of the combined algebra, it makes sense to write P ( s t | h θ ) instead of the P h θ ( s t ) written in the context of classical statistics. We can define Bayesian statistics as follows.

DEFINITION 3 Bayesian Statistical Inference. Assume the prior probability P ( h θ ) assigned to hypotheses h θ ∈ H , with θ ∈ Θ, the space of parameter values. Further assume P ( s t | h θ ) , the probability assigned to the data s t conditional on the hypotheses, called the likelihoods. Bayes’ theorem determines that

Bayesian statistics outputs the posterior probability assignment, P ( h θ | s t ) . See [ Barnett, 1999 ] and [ Press, 2003 ] for a more detailed discussion. The further results form a Bayesian inference, such as estimations and measures for the accuracy of the estimations, can all be derived from the posterior distribution over the statistical hypotheses.

The result of a Bayesian statistical inference is not always a posterior probability. Often the interest is only in comparing the ratio of the posteriors of two hypotheses. By Bayes’ theorem we have

and if we assume equal priors P( h θ ) = P( h θ′ ), we can use the ratio of the likelihoods of the hypotheses, the so-called Bayes factor, to compare the hypotheses.

Let me give an example of a Bayesian procedure. Consider the hypotheses of Equation (3) , concerning the fraction of green pears in Emma's orchard. Instead of choosing among them on the basis of the data, assign a so-called Beta-distribution over the range of hypotheses,

with θ ∈ Θ = [0,1]. For λ = 2, this function is uniform over the domain. Now say that we obtain a certain sequence of pears, s 000101 . By the likelihood of the hypotheses as given in Equation (4) , we can derive

More generally, the likelihood function for the data s t with numbers t k of earlier instances q i k is θ t 1 ( 1 − θ ) t 0 , so that

is the posterior distribution over the hypotheses. This posterior is derived by the axioms of probability theory alone, specifically by Bayes’ theorem.

As said, capturing this statistical procedure in a non-ampliative inference is relatively straightforward. The premises are the prior over the hypotheses, P ( h θ ) for θ ∈ Θ, and the likelihood functions, P ( s t | h θ ) over the algebras Q , which are determined for each hypothesis h θ separately. These premises are such that only a single probability assignment over the space H × Q remains. In other words, the premises have a unique probability model. Moreover, all the conclusions are straightforward consequences of this probability assignment. They can be derived from the assignment by applying theorems of probability theory, primarily Bayes’ theorem.

Before turning to the relation of Bayesian inference with Carnapian logic, let me compare it to the classical procedures sketched in the foregoing. In all cases, we consider a set of statistical hypotheses, and in all cases our choice among these is informed by the probability of the data according to the hypotheses. The difference is that in the two classical procedures, this choice is absolute: acceptance, rejection, and the appointment of a best estimate. In the Bayesian procedure, by contrast, all this is expressed in a posterior probability assignment over the set of hypotheses.

Note that this posterior over hypotheses can be used to generate the kind of choices between hypotheses that classical statistics provides. Consider Fisherian parameter estimation. We can use the posterior to derive an expectation for the parameter θ , as follows:

Clearly, E[ θ ] is a function that brings us from the hypotheses h θ and the data st to a preferred value for the parameter. The function depends on the prior probability over the hypotheses, but it is in a sense analogous to the maximum likelihood estimator. In analogy to the confidence interval, we can also define a so-called credal interval from the posterior probability distribution:

This set of values for θ is such that the posterior probability of the corresponding h θ jointly add up to 1 − ɛ of the total posterior probability.

Most of the controversy over the Bayesian method concerns the determination and interpretation of the probability assignment over hypotheses. As for interpretation, classical statistics objects to the whole idea of assigning probabilities to hypotheses. The data have a well-defined probability, because they consist of repeatable events, and so we can interpret the probabilities as frequencies, or as some other kind of objective probability. But the probability assigned to a hypothesis cannot be understood in this way, and instead expresses an epistemic state of uncertainty. One of the distinctive features of classical statistics is that it rejects such epistemic probability assignments, and that it restricts itself to a straightforward interpretation of probability as relative frequency.

Even if we buy into this interpretation of probability as epistemic uncertainty, how do we determine a prior probability? At the outset we do not have any idea of which hypothesis is right, or even which hypothesis is a good candidate. So how are we supposed to assign a prior probability to the hypotheses? The literature proposes several objective criteria for filling in the priors, for instance by maximum entropy or by other versions of the principle of indifference, but something of the subjectivity of the starting point remains. The strength of the classical statistical procedures is that they do not need any such subjective prior probability.

Definition of a Hypothesis

What it is and how it's used in sociology.

A hypothesis is a prediction of what will be found at the outcome of a research project and is typically focused on the relationship between two different variables studied in the research. It is usually based on both theoretical expectations about how things work and already existing scientific evidence.

Within social science, a hypothesis can take two forms. It can predict that there is no relationship between two variables, in which case it is a null hypothesis . Or, it can predict the existence of a relationship between variables, which is known as an alternative hypothesis.

In either case, the variable that is thought to either affect or not affect the outcome is known as the independent variable, and the variable that is thought to either be affected or not is the dependent variable.

Researchers seek to determine whether or not their hypothesis, or hypotheses if they have more than one, will prove true. Sometimes they do, and sometimes they do not. Either way, the research is considered successful if one can conclude whether or not a hypothesis is true.

Null Hypothesis

A researcher has a null hypothesis when she or he believes, based on theory and existing scientific evidence, that there will not be a relationship between two variables. For example, when examining what factors influence a person's highest level of education within the U.S., a researcher might expect that place of birth, number of siblings, and religion would not have an impact on the level of education. This would mean the researcher has stated three null hypotheses.

Alternative Hypothesis

Taking the same example, a researcher might expect that the economic class and educational attainment of one's parents, and the race of the person in question are likely to have an effect on one's educational attainment. Existing evidence and social theories that recognize the connections between wealth and cultural resources , and how race affects access to rights and resources in the U.S. , would suggest that both economic class and educational attainment of the one's parents would have a positive effect on educational attainment. In this case, economic class and educational attainment of one's parents are independent variables, and one's educational attainment is the dependent variable—it is hypothesized to be dependent on the other two.

Conversely, an informed researcher would expect that being a race other than white in the U.S. is likely to have a negative impact on a person's educational attainment. This would be characterized as a negative relationship, wherein being a person of color has a negative effect on one's educational attainment. In reality, this hypothesis proves true, with the exception of Asian Americans , who go to college at a higher rate than whites do. However, Blacks and Hispanics and Latinos are far less likely than whites and Asian Americans to go to college.

Formulating a Hypothesis

Formulating a hypothesis can take place at the very beginning of a research project , or after a bit of research has already been done. Sometimes a researcher knows right from the start which variables she is interested in studying, and she may already have a hunch about their relationships. Other times, a researcher may have an interest in a particular topic, trend, or phenomenon, but he may not know enough about it to identify variables or formulate a hypothesis.

Whenever a hypothesis is formulated, the most important thing is to be precise about what one's variables are, what the nature of the relationship between them might be, and how one can go about conducting a study of them.

Updated by Nicki Lisa Cole, Ph.D

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Formulation of Hypothesis

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Children who spend more time playing outside are more likely to be imaginative. What do you think this statement is an example of in terms of scientific research? If you guessed a hypothesis, then you'd be correct. The formulation of hypotheses is a fundamental step in psychology research.

What is a Hypothesis?

The current community of psychologists believe that the best approach to understanding behaviour is to conduct scientific research. To be classed as scientific research, it must be observable, valid, reliable and follow a standardised procedure.

One of the important steps in scientific research is to formulate a hypothesis before starting the study procedure.

The hypothesis is a predictive, testable statement predicting the outcome and the results the researcher expects to find.

The hypothesis provides a summary of what direction, if any, is taken to investigate a theory.

In scientific research, there is a criterion that hypotheses need to be met to be regarded as acceptable.

If a hypothesis is disregarded, the research may be rejected by the community of psychology researchers.

Importance of Hypothesis in Research

The purpose of including hypotheses in psychology research is:

When carrying out research, researchers first investigate the research area they are interested in. From this, researchers are required to identify a gap in the literature.

Filling the gap essentially means finding what previous work has not been explained yet, investigated to a sufficient degree, or simply expanding or further investigating a theory if doubt exists.

The researcher then forms a research question that the researcher will attempt to answer in their study.

Remember, the hypothesis is a predictive statement of what is expected to happen when testing the research question.

The hypothesis can be used for later data analysis. This includes inferential tests such as hypothesis testing and identifying if statistical findings are significant.

Formulation of testable hypotheses, four people with question marks above their heads, StudySmarter

Steps in the Formulation of Hypothesis in Research Methodology

Researchers must follow certain steps to formulate testable hypotheses when conducting research.

Overall, the researcher has to consider the direction of the research, i.e. will it be looking for a difference caused by independent variables? Or will it be more concerned with the correlation between variables?

All researchers will likely complete the following.

The above steps are used to formulate testable hypotheses.

The Formulation of Testable Hypotheses

The hypothesis is important in research as it indicates what and how a variable will be investigated.

The hypothesis essentially summarises what and how something will be investigated. This is important as it ensures that the researcher has carefully planned how the research will be done, as the researchers have to follow a set procedure to conduct research.

This is known as the scientific method.

Formulating Hypotheses in Research

When formulating hypotheses, things that researchers should consider are:

Types of Hypotheses in Research

Researchers can propose different types of hypotheses when carrying out research.

The following research scenario will be discussed to show examples of each type of hypothesis that the researchers could use. "A research team was investigating whether memory performance is affected by depression."

The identified independent variable is the severity of depression scores, and the dependent variable is the scores from a memory performance task.

The null hypothesis predicts that the results will show no or little effect. The null hypothesis is a predictive statement that researchers use when it is thought that the IV will not influence the DV.

In this case, the null hypothesis would be there will be no difference in memory scores on the MMSE test of those who are diagnosed with depression and those who are not.

An alternative hypothesis is a predictive statement used when it is thought that the IV will influence the DV. The alternative hypothesis is also called a non-directional, two-tailed hypothesis, as it predicts the results can go either way, e.g. increase or decrease.

The example in this scenario is there will be an observed difference in scores from a memory performance task between people with high- or low-depressive scores.

The directional alternative hypothesis states how the IV will influence the DV, identifying a specific direction, such as if there will be an increase or decrease in the observed results.

The example in this scenario is people with low depressive scores will perform better in the memory performance task than people who score higher in depressive symptoms.

Example Hypothesis in Research

To summarise, let's look at an example of a straightforward hypothesis that indicates the relationship between two variables : the independent and the dependent.

If you stay up late, you will feel tired the following day; the more caffeine you drink, the harder you find it to fall asleep, or the more sunlight plants get, the taller they will grow.

Formulation of Hypothesis - Key Takeaways

Frequently Asked Questions about Formulation of Hypothesis

--> what are the 3 types of hypotheses.

The three types of hypotheses are:

--> What is an example of a hypothesis in psychology?

An example of a null hypothesis in psychology is, there will be no observed difference in scores from a memory performance task between people with high- or low-depressive scores.

--> What are the steps in formulating a hypothesis?

All researchers will likely complete the following

--> What is formulation of hypothesis in research?

The formulation of a hypothesis in research is when the researcher formulates a predictive statement of what is expected to happen when testing the research question based on background research.

--> How to formulate null and alternative hypothesis?

When formulating a null hypothesis the researcher would state a prediction that they expect to see no difference in the dependent variable when the independent variable changes or is manipulated. Whereas, when using an alternative hypothesis then it would be predicted that there will be a change in the dependent variable. The researcher can state in which direction they expect the results to go.

Final Formulation of Hypothesis Quiz

What type of hypothesis matches the following definition. A predictive statement that researchers use when it is thought that the IV will not influence the DV.

Show answer

Null hypothesis

Show question

What type of hypothesis matches the following definition. A hypothesis that states that the IV will influence the DV. But, the hypothesis does not state how the IV will influence the DV.

Alternative hypothesis

What type of hypothesis matches the following definition. A hypothesis that states that the IV will influence the DV, and states how it will influence the DV.

Directional, alternative hypothesis

Which type of hypothesis is also known as a two-tailed hypothesis?

What type of hypothesis is the following example. There will be no observed difference in scores from a memory performance task between people with high- or low-depressive scores.

What type of hypothesis is the following example. There will be an observed difference in scores from a memory performance task between people with high- or low-depressive scores.

What type of hypothesis is the following example. People with low depressive scores will perform better in the memory performance task than people who score higher in depressive symptoms.

What is a hypothesis?

The hypothesis is a predictive, testable statement concerning the outcome/ results the researcher expects to find.

What method states that a hypothesis needs to be formulated to produce good research?

The scientific method states that researchers need to formulate a good hypothesis before starting the research.

What steps do researchers need to take when formulating a testable hypothesis?

Why are hypotheses needed in research?

Hypotheses are needed in research:

What type of data analysis may hypotheses be needed for?

Hypotheses are needed when doing inferential tests such as hypothesis testing. In addition, identifying if research findings are statistically significant.

What are the requirements of a good hypothesis?

A good hypothesis should:

Is the following example a falsifiable hypothesis, "leprechauns always find the pot of gold at the end of the rainbow".

Is memory an operationalised variable that could be used in a good hypothesis?

What is an operationalised variable?

An operationalised variable is when the researcher describes how a variable (independent or dependent variable) will be measured. The operationalisation of variables also needs to be defined. For example, memory may be operationalised by stating performance in memory tasks such as the Mini-Mental Status Examination.

What happens if a hypothesis is regarded as not meeting the standards of scientific research?

If a hypothesis is disregarded, the research may be rejected by the community of psychology researchers.

What is a hypothesis predicting?

The hypothesis predicts the nature of the relationship between the independent and dependent variables. For instance, if the dependent variable changes due to changes/ manipulation of the independent variable.

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6 Steps to Evaluate the Effectiveness of Statistical Hypothesis Testing

You know what is tragic? Having the potential to complete the research study but not doing the correct hypothesis testing. Quite often, researchers think the most challenging aspect of research is standardization of experiments, data analysis or writing the thesis! But in all honesty, creating an effective research hypothesis is the most crucial step in designing and executing a research study. An effective research hypothesis will provide researchers the correct basic structure for building the research question and objectives.

In this article, we will discuss how to formulate and identify an effective research hypothesis testing to benefit researchers in designing their research work.

Table of Contents

What Is Research Hypothesis Testing?

Hypothesis testing is a systematic procedure derived from the research question and decides if the results of a research study support a certain theory which can be applicable to the population. Moreover, it is a statistical test used to determine whether the hypothesis assumed by the sample data stands true to the entire population.

The purpose of testing the hypothesis is to make an inference about the population of interest on the basis of random sample taken from that population. Furthermore, it is the assumption which is tested to determine the relationship between two data sets.

Types of Statistical Hypothesis Testing

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1. there are two types of hypothesis in statistics, a. null hypothesis.

This is the assumption that the event will not occur or there is no relation between the compared variables. A null hypothesis has no relation with the study’s outcome unless it is rejected. Null hypothesis uses H0 as its symbol.

b. Alternate Hypothesis

The alternate hypothesis is the logical opposite of the null hypothesis. Furthermore, the acceptance of the alternative hypothesis follows the rejection of the null hypothesis. It uses H1 or Ha as its symbol

Hypothesis Testing Example: A sanitizer manufacturer company claims that its product kills 98% of germs on average. To put this company’s claim to test, create null and alternate hypothesis H0 (Null Hypothesis): Average = 98% H1/Ha (Alternate Hypothesis): The average is less than 98%

2. Depending on the population distribution, you can categorize the statistical hypothesis into two types.

A. simple hypothesis.

A simple hypothesis specifies an exact value for the parameter.

b. Composite Hypothesis

A composite hypothesis specifies a range of values.

Hypothesis Testing Example: A company claims to have achieved 1000 units as their average sales for this quarter. (Simple Hypothesis) The company claims to achieve the sales in the range of 900 to 100o units. (Composite Hypothesis).

3. Based on the type of statistical testing, the hypothesis in statistics is of two types.

A. one-tailed.

One-Tailed test or directional test considers a critical region of data which would result in rejection of the null hypothesis if the test sample falls in that data region. Therefore, accepting the alternate hypothesis. Furthermore, the critical distribution area in this test is one-sided which means the test sample is either greater or lesser than a specific value.

b. Two-Tailed

Two-Tailed test or nondirectional test is designed to show if the sample mean is significantly greater than and significantly less than the mean population. Here, the critical distribution area is two-sided. If the sample falls within the range, the alternate hypothesis is accepted and the null hypothesis is rejected.

Statistical Hypothesis Testing Example: Suppose H0: mean = 100 and H1: mean is not equal to 100 According to the H1, the mean can be greater than or less than 100. (Two-Tailed test) Similarly, if H0: mean >= 100, then H1: mean < 100 Here the mean is less than 100. (One-Tailed test)

Steps in Statistical Hypothesis Testing

Step 1: develop initial research hypothesis.

Research hypothesis is developed from research question. It is the prediction that you want to investigate. Moreover, an initial research hypothesis is important for restating the null and alternate hypothesis, to test the research question mathematically.

Step 2: State the null and alternate hypothesis based on your research hypothesis

Usually, the alternate hypothesis is your initial hypothesis that predicts relationship between variables. However, the null hypothesis is a prediction of no relationship between the variables you are interested in.

Step 3: Perform sampling and collection of data for statistical testing

It is important to perform sampling and collect data in way that assists the formulated research hypothesis. You will have to perform a statistical testing to validate your data and make statistical inferences about the population of your interest.

Step 4: Perform statistical testing based on the type of data you collected

There are various statistical tests available. Based on the comparison of within group variance and between group variance, you can carry out the statistical tests for the research study. If the between group variance is large enough and there is little or no overlap between groups, then the statistical test will show low p-value. (Difference between the groups is not a chance event).

Alternatively, if the within group variance is high compared to between group variance, then the statistical test shows a high p-value. (Difference between the groups is a chance event).

Step 5: Based on the statistical outcome, reject or fail to reject your null hypothesis

In most cases, you will use p-value generated from your statistical test to guide your decision. You will consider a predetermined level of significance of 0.05 for rejecting your null hypothesis , i.e. there is less than 5% chance of getting the results wherein the null hypothesis is true.

Step 6: Present your final results of hypothesis testing

You will present the results of your hypothesis in the results and discussion section of the research paper . In results section, you provide a brief summary of the data and a summary of the results of your statistical test. Meanwhile, in discussion, you can mention whether your results support your initial hypothesis.

Note that we never reject or fail to reject the alternate hypothesis. This is because the testing of hypothesis is not designed to prove or disprove anything. However, it is designed to test if a result is spuriously occurred, or by chance. Thus, statistical hypothesis testing becomes a crucial statistical tool to mathematically define the outcome of a research question.

Have you ever used hypothesis testing as a means of statistically analyzing your research data? How was your experience? Do write to us or comment below.

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How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

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10.1 - setting the hypotheses: examples.

A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.

Example 10.2: Hypotheses with One Sample of One Categorical Variable Section

About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.

State Null and Alternative Hypotheses

Example 10.3: Hypotheses with One Sample of One Measurement Variable Section

A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.

Example 10.4: Hypotheses with Two Samples of One Categorical Variable Section

Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.

Example 10.5: Hypotheses with Two Samples of One Measurement Variable Section

Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.

Example 10.6: Hypotheses about the relationship between Two Categorical Variables Section

This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.

Example 10.7: Hypotheses about the relationship between Two Measurement Variables Section

Example 10.8: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples Section

Calculation of a person's approximate tip for their meal

How to Write a Hypothesis in 6 Steps

A hypothesis is a statement that explains the predictions and reasoning of your research—an “educated guess” about how your scientific experiments will end. As a fundamental part of the scientific method, a good hypothesis is carefully written, but even the simplest ones can be difficult to put into words.

Want to know how to write a hypothesis for your academic paper ? Below we explain the different types of hypotheses, what a good hypothesis requires, the steps to write your own, and plenty of examples.

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What is a hypothesis?

One of our 10 essential words for university success , a hypothesis is one of the earliest stages of the scientific method. It’s essentially an educated guess—based on observations—of what the results of your experiment or research will be.

If you’ve noticed that watering your plants every day makes them grow faster, your hypothesis might be “plants grow better with regular watering.” From there, you can begin experiments to test your hypothesis; in this example, you might set aside two plants, water one but not the other, and then record the results to see the differences.

The language of hypotheses always discusses variables , or the elements that you’re testing. Variables can be objects, events, concepts, etc.—whatever is observable.

There are two types of variables: independent and dependent. Independent variables are the ones that you change for your experiment, whereas dependent variables are the ones that you can only observe. In the above example, our independent variable is how often we water the plants and the dependent variable is how well they grow.

Hypotheses determine the direction and organization of your subsequent research methods, and that makes them a big part of writing a research paper . Ultimately the reader wants to know whether your hypothesis was proven true or false, so it must be written clearly in the introduction and/or abstract of your paper.

7 examples of hypotheses (with examples)

Depending on the nature of your research and what you expect to find, your hypothesis will fall into one or more of the seven main categories. Keep in mind that these categories are not exclusive, so the same hypothesis might qualify as several different types.

1 Simple hypothesis

A simple hypothesis suggests only the relationship between two variables: one independent and one dependent.

2 Complex hypothesis

A complex hypothesis suggests the relationship between more than two variables, for example, two independents and one dependent, or vice versa.

3 Null hypothesis

A null hypothesis, abbreviated as H 0 , suggests that there is no relationship between variables.

4 Alternative hypothesis

An alternative hypothesis, abbreviated as H 1 or H A , is used in conjunction with a null hypothesis. It states the opposite of the null hypothesis, so that one and only one must be true.

5 Logical hypothesis

A logical hypothesis suggests a relationship between variables without actual evidence. Claims are instead based on reasoning or deduction, but lack actual data.

6 Empirical hypothesis

An empirical hypothesis, also known as a “working hypothesis,” is one that is currently being tested. Unlike logical hypotheses, empirical hypotheses rely on concrete data.

7 Statistical hypothesis

A statistical hypothesis is when you test only a sample of a population and then apply statistical evidence to the results to draw a conclusion about the entire population. Instead of testing everything , you test only a portion and generalize the rest based on preexisting data.

What makes a good hypothesis?

No matter what you’re testing, a good hypothesis is written according to the same guidelines. In particular, keep these five characteristics in mind:

Cause and effect

Hypotheses always include a cause-and-effect relationship where one variable causes another to change (or not change if you’re using a null hypothesis). This can best be reflected as an if-then statement: If one variable occurs, then another variable changes.

Testable prediction

Most hypotheses are designed to be tested (with the exception of logical hypotheses). Before committing to a hypothesis, make sure you’re actually able to conduct experiments on it. Choose a testable hypothesis with an independent variable that you have absolute control over.

Independent and dependent variables

Define your variables in your hypothesis so your readers understand the big picture. You don’t have to specifically say which ones are independent and dependent variables, but you definitely want to mention them all.

Candid language

Writing can easily get convoluted, so make sure your hypothesis remains as simple and clear as possible. Readers use your hypothesis as a contextual pillar to unify your entire paper, so there should be no confusion or ambiguity. If you’re unsure about your phrasing, try reading your hypothesis to a friend to see if they understand.

Adherence to ethics

It’s not always about what you can test, but what you should test. Avoid hypotheses that require questionable or taboo experiments to keep ethics (and therefore, credibility) intact.

How to write a hypothesis in 6 steps

1 ask a question.

Curiosity has inspired some of history’s greatest scientific achievements, so a good place to start is to ask yourself questions about the world around you. Why are things the way they are? What causes the factors you see around you? If you can, choose a research topic that you’re interested in so your curiosity comes naturally.

2 Conduct preliminary research

Next, collect some background information on your topic. How much background information you need depends on what you’re attempting. It could require reading several books, or it could be as simple as performing a web search for a quick answer. You don’t necessarily have to prove or disprove your hypothesis at this stage; rather, collect only what you need to prove or disprove it yourself.

3 Define your variables

Once you have an idea of what your hypothesis will be, select which variables are independent and which are dependent. Remember that independent variables can only be factors that you have absolute control over, so consider the limits of your experiment before finalizing your hypothesis.

4 Phrase it as an if-then statement

When writing a hypothesis, it helps to phrase it using an if-then format, such as, “ If I water a plant every day, then it will grow better.” This format can get tricky when dealing with multiple variables, but in general, it’s a reliable method for expressing the cause-and-effect relationship you’re testing.

5 Collect data to support your hypothesis

A hypothesis is merely a means to an end. The priority of any scientific research is the conclusion. Once you have your hypothesis laid out and your variables chosen, you can then begin your experiments. Ideally, you’ll collect data to support your hypothesis, but don’t worry if your research ends up proving it wrong—that’s all part of the scientific method.

6 Write with confidence

Last, you’ll want to record your findings in a research paper for others to see. This requires a bit of writing know-how, quite a different skill set than conducting experiments.

That’s where Grammarly can be a major help; our writing suggestions point out not only grammar and spelling mistakes , but also new word choices and better phrasing. While you write, Grammarly automatically recommends optimal language and highlights areas where readers might get confused, ensuring that your hypothesis—and your final paper—are clear and polished.

Investigation and Management of Disease in Wild Animals pp 73–86 Cite as

Formulating and Testing Hypotheses

Gary A. Wobeser 2

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The term hypothesis has been mentioned several times in the preceding chapters. The definition that will be used here is that a hypothesis is a proposition set forth as explanation for the occurrence of a specified phenomenon. The basis of scientific investigation is the collection of information that is used either to formulate or to test hypotheses. One assesses the important variables and tries to build a model or hypothesis that explains the observed phenomenon. In general, a hypothesis is formulated by rephrasing the objective of a study as a statement, e.g., if the objective of an investigation is to determine if a pesticide is safe, the resulting hypothesis might be “ the pesticide is not safe ”, or alternatively that “ the pesticide is safe ”. A hypothesis is a statistical hypothesis only if it is stated in terms related to the distribution of populations. The general hypothesis above might be refined to: “ this pesticide, when used as directed, has no effect on the average number of robins in an area ”, which is a testable hypothesis. The hypothesis to be tested is called the null hypothesis (H 0 ). The alternative hypothesis (H 1 ) for the above example would be “ this pesticide, when used as directed, has an effect on the average number of robins in an area”. In testing a hypothesis, H 0 is considered to be true, unless the sample data indicate otherwise, (i.e., that the pesticide is innocent, unless proven guilty). Testing cannot prove H 0 to be true but the results can cause it to be rejected. In accepting or rejecting H 0 , two types of error may be made. If H 0 is rejected when, in fact, it is true a type 1 error has been committed. If Ho is not true and the test fails to reject it, a type 2 error has been made.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

“ Research in the field, through study of disease as it manifests itself in nature, is an important and independent approach to solution of medical problems. Modern medical progress has been so thoroughly associated with research in the biological laboratory, and it has been so largely a development of the experimental method, that this other and older method has come in recent years to be overshadowed ” (Gordon, 1950)

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Wobeser, G.A. (1994). Formulating and Testing Hypotheses. In: Investigation and Management of Disease in Wild Animals. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5609-8_6

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AP®︎/College Statistics

Unit 10: lesson 3.

Idea behind hypothesis testing

Examples of null and alternative hypotheses

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Hypothesis Testing Steps & Real Life Examples

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Table of Contents

What is a Hypothesis testing?

As per the definition from Oxford languages, a hypothesis is a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation. As per the Dictionary page on Hypothesis , Hypothesis means a proposition or set of propositions, set forth as an explanation for the occurrence of some specified group of phenomena, either asserted merely as a provisional conjecture to guide investigation (working hypothesis) or accepted as highly probable in the light of established facts.

The hypothesis can be defined as the claim that can either be related to the truth about something that exists in the world, or, truth about something that’s needs to be established a fresh . In simple words, another word for the hypothesis is the “claim” . Until the claim is proven to be true, it is called the hypothesis. Once the claim is proved, it becomes the new truth about the thing. For example , let’s say that a claim is made that students studying for more than 6 hours a day gets more than 90% of marks in their examination. Now, this is just a claim or a hypothesis and not the truth in the real world. However, in order for the claim to become the truth for widespread adoption, it needs to be proved using pieces of evidence, e.g., data. In order to reject this claim or otherwise, one needs to do some empirical analysis by gathering data samples and evaluating the claim. The process of gathering data and evaluating the claims or hypotheses with the goal to reject or otherwise (failing to reject) is termed hypothesis testing . Note the wordings – “failing to reject”. It means that we don’t have enough evidence to reject the claim. Thus, until the time that new evidence comes up, the claim can be considered the truth. There are different techniques to test the hypothesis in order to reach the conclusion of whether the hypothesis can be used to represent the truth of the world. One must note that the hypothesis testing never constitutes a proof that the hypothesis is absolute truth based on the observations. It only provides added support to consider the hypothesis as truth until the time that new evidences can against the hypotheses can be gathered. We can never be 100% sure about truth related to those hypotheses based on the hypothesis testing.

Simply speaking, hypothesis testing is a framework that can be used to assert whether the claim or the hypothesis made about a real-world/real-life event can be seen as the truth or otherwise based on the given data (evidences). For example :

Now that the hypothesis is stated, let’s go ahead and state and formulate the hypothesis as the null and alternate hypothesis in order to perform hypothesis testing.

Hypothesis Testing Examples

Before we get ahead and start understanding more details about hypothesis and hypothesis testing steps, lets take a look at some real-world examples of how to think about hypothesis and hypothesis testing when dealing with real-world problems :

State the Hypothesis to begin Hypothesis Testing

The first step to hypothesis testing is defining or stating a hypothesis. Before the hypothesis can be tested, we need to formulate the hypothesis in terms of mathematical expressions. There are two important aspects to pay attention to, prior to the formulation of the hypothesis. The following represents different types of hypothesis that could be put to hypothesis testing:

Based on the above considerations, the following hypothesis can be stated for doing hypothesis testing.

Formulate Null & Alternate Hypothesis as Next Step

Once the hypothesis is defined or stated, the next step is to formulate the null and alternate hypothesis in order to begin hypothesis testing as described above.

What is a null hypothesis?

In the case where the given statement is a well-established fact or default state of being in the real world, one can call it a null hypothesis (in the simpler word, nothing new). Well-established facts don’t need any hypothesis testing and hence can be called the null hypothesis. In cases, when there are any new claims made which is not well established in the real world, the null hypothesis can be thought of as the default state or opposite state of that claim. For example , in the previous section, the claim or hypothesis is made that the students studying for more than 6 hours a day gets more than 90% of marks in their examination. The null hypothesis, in this case, will be that the claim is not true or real. The null hypothesis can be stated as the fact that it is not a truth that the students reading more than 6 hours a day would get more than 90% of the marks. Another example of hypothesis is when somebody is alleged that they have performed a crime. The default state of the world is that the person has not committed the crime and he/she is guilty. This will be null hypothesis.

What is an alternate hypothesis?

In case the given statement is a claim (unexpected event in the real world) and not yet proven, one can call/formulate it as an alternate hypothesis and accordingly define a null hypothesis which is the opposite state of the hypothesis. In simple words, the hypothesis or claim that needs to be tested against reality in the real world can be termed the alternate hypothesis. In order to reach a conclusion that the claim (alternate hypothesis) can be considered the new truth (based on the available evidence), it would be important to reject the null hypothesis. It should be noted that null and alternate hypotheses are mutually exclusive and at the same time asymmetric. In the example given in the previous section, the claim that the students studying for more than 6 hours get more than 90% of marks can be termed as the alternate hypothesis.

Once the hypothesis is formulated as null and alternate hypothesis, there are two possible outcomes that can happen from hypothesis testing as a function of null and alternate hypothesis. These outcomes are the following:

Examples of formulating the null and alternate hypothesis

The following are some examples of the null and alternate hypothesis.

Hypothesis Testing Steps

Here is the diagram which represents the workflow of Hypothesis Testing.

Figure 1. Hypothesis Testing Steps

Based on the above, the following are some of the steps to be taken when doing hypothesis testing:

P-Value: Key to Statistical Hypothesis Testing

Once you formulate the hypotheses, there is the need to test those hypotheses. Meaning, say that the null hypothesis is stated as the statement that housing price does not depend upon the average income of people staying in the locality, it would be required to be tested by taking samples of housing prices and, based on the test results, this Null hypothesis could either be rejected or failed to be rejected . In hypothesis testing, the following two are the outcomes:

Take the above example of the sugar packet weighing 500 gm. The Null hypothesis is set as the statement that the sugar packet weighs 500 gm. After taking a sample of 20 sugar packets and testing/taking its weight, it was found that the average weight of the sugar packets came to 495 gm. The test statistics (t-statistics) were calculated for this sample and the P-value was determined. Let’s say the P-value was found to be 15%. Assuming that the level of significance is selected to be 5%, the test statistic is not statistically significant (P-value > 5%) and thus, the null hypothesis fails to get rejected. Thus, one could safely conclude that the sugar packet does weigh 500 gm. However, if the average weight of canned sauce would have found to be 465 gm, this is way beyond/away from the mean value of 500 gm and one could have ended up rejecting the Null Hypothesis based on the P-value .

Hypothesis testing quiz

The claim that needs to be established is set as ____________, the outcome of hypothesis testing is _________.

Please select 2 correct answers

P-value is defined as the probability of obtaining the result as extreme given the null hypothesis is true

There is a claim that doing pranayama yoga results in reversing diabetes. which of the following is true about null hypothesis.

In this post, you learned about hypothesis testing and related nuances such as the null and alternate hypothesis formulation techniques, ways to go about doing hypothesis testing etc. In data science, one of the reasons why one needs to understand the concepts of hypothesis testing is the need to verify the relationship between the dependent (response) and independent (predictor) variables. One would, thus, need to understand the related concepts such as hypothesis formulation into null and alternate hypothesis, level of significance, test statistics calculation, P-value, etc. Given that the relationship between dependent and independent variables is a sort of hypothesis or claim , the null hypothesis could be set as the scenario where there is no relationship between dependent and independent variables.

Ajitesh Kumar

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[…] Kumar · Leave a comment This article describes Type I and Type II errors made during hypothesis testing, based on a couple of examples such as House on Fire, and Covid-19. You may want to note that it is […]

[…] of the most neglected skills found with the data scientists. Here is my related post titled – Hypothesis testing explained with examples. Data scientists are required to model data, assess the suitability of data for analysis, develop […]

[…] hypotheses with corresponding null hypotheses. Check out this post on hypothesis testing – Hypothesis testing explained with examples. For example, let’s say one hypothesis for increasing sales of gaming laptops in the chosen […]

[…] Hypothesis testing: Hypothesis testing is a statistical procedure used to determine whether an assertion or hypothesis about a population is true. It uses data taken from a sample of that population to draw conclusions. A null hypothesis that states there is no difference between the observed data and what we would expect if the null hypothesis were true, must first be formulated. Then, an alternative hypothesis is proposed and tested. After performing the test, we can accept or reject the null hypothesis depending on whether it is statistically significant […]

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Hypothesis Testing

What is Hypothesis Testing?

Hypothesis testing ascertains whether a particular assumption is true for the whole population. It is a statistical tool. It determines the validity of inference by evaluating sample data from the overall population.

The concept of hypothesis works on the probability of an event’s occurrence. It confirms whether the primary hypothesis results are correct or not. It is widely applied in research—biology, criminal trials, marketing, and manufacturing.

Hypothesis testing in statistics explained, hypothesis testing types, hypothesis testing steps, hypothesis testing formula, hypothesis testing calculation with examples, relevance and use, limitations, frequently asked questions (faqs), recommended articles, key takeaways.

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Hypothesis testing uses sample data to validate the research. Researchers speculate on relationships between various factors. They then collect data to test those relationships. Based on the data, researchers draw conclusions. In statistics Statistics Statistics is the science behind identifying, collecting, organizing and summarizing, analyzing, interpreting, and finally, presenting such data, either qualitative or quantitative, which helps make better and effective decisions with relevance. read more , it is very important to eliminate randomness. The data should not have been caused by chance or a random factor. Hypothesis testing eliminates such uncertainties.

For every research experiment, there are mainly two explanations: the null hypothesis Null Hypothesis Null hypothesis presumes that the sampled data and the population data have no difference or in simple words, it presumes that the claim made by the person on the data or population is the absolute truth and is always right. So, even if a sample is taken from the population, the result received from the study of the sample will come the same as the assumption. read more and the alternative hypothesis. It is often difficult to prove a theory; therefore, investigators test to reject the null hypothesis. So, when the null hypothesis is rejected, the remaining alternate theory is believed to be true.

For example, if we believe that the returns from the NASDAQ stock index Stock Index The stock index, which is also known as the stock market index, is a tool used to determine the performance of shares/securities in the market and to calculate the return on the stock of their investment investors use it to have knowledge about the performance of investments and access the total value they possess. read more are not zero. Then the null hypothesis would state: ‘the recovery from the NASDAQ is zero.’ Tests are conducted for different levels of statistical significance Statistical Significance Statistical significance is the probability of an observation not being caused by a sampling error. read more .

Hypothesis tests are prone to two errors—type 1 and type 2. If the null hypothesis is rejected by the sample outcome despite being true—it is considered a type 1 error. Similarly, if the sample data fails to reject the null hypothesis, despite the null hypothesis being false, it is considered a type 2 error.

Based on population distribution, hypothesis testing is further categorized into sub-types:

Two-tailed : The two-tailed hypothesis test works when the critical distribution of the population is two-sided. Here the test sample is either higher or lower than a number of given values.

Hypothesis tests involve the following steps:

Researchers opt for different statistical tests like t-tests T-tests A T-test is a method to identify whether the means of two groups differ from one another significantly. It is an inferential statistics approach that facilitates the hypothesis testing. read more or z-tests Z-tests Z-test formula is applied hypothesis testing for data with a large sample size. It denotes the value acquired by dividing the population standard deviation from the difference between the sample mean, and the population mean. read more . The z-test formula is as follows:

Z = ( x̅ – μ 0 ) / (σ /√n)

Based on the Z-test result, the research derives the hypothesis conclusion. It can either be a null or its alternative. They are measured using the following formula:

H 0 : μ=μ 0

H a : μ≠μ 0

H 0 = null hypothesis

H a = alternate hypothesis

If the mean value Mean Value Mean refers to the mathematical average calculated for two or more values. There are primarily two ways: arithmetic mean, where all the numbers are added and divided by their weight, and in geometric mean, we multiply the numbers together, take the Nth root and subtract it with one. read more is equal to the population mean, then the null hypothesis is proven true. Otherwise, the alternate hypothesis is taken into consideration.

A battery manufacturing company claims that the average life of its two-wheeler batteries is 2.1 years. The quality inspector surveyed ten customers to know the lasting period of their batteries. The following data was collected:

If the standard deviation is 0.17 and the significance level is 0.05, conduct a hypothesis testing to prove the company’s claim.

μ 0 = 2.1 years

Level of Significance = 0.05

Assuming that the company’s claim of average battery life being 2.1 years is true,

We need to prove that:

H 0 : μ=μ 0 , or

Sample mean (x̅) = (1.9 + 2.3 + 2.1 + 2.2 + 1.9 + 2.4 + 2.1 + 2.3 + 2.2 + 2.0) / 10 = 2.14 years.

Applying the Z-test formula:

Z = (2.14 – 2.1) / (0.17 / √10) = 0.744

We already know that the level of significance is 0.05, and the z-score is 1.645. Let us now compare the Z-test with it.

0.744 ˂ 1.645; therefore, the null hypothesis is true.

Thus, the company’s claim that the average life of its batteries is 2.1 years is proven true.

Hypothesis testing validates a theory with the help of systematic statistical inference. However, in practice, it is not easy. Therefore, researchers try to reject the null hypothesis in order to validate the alternate explanation.

Hypothesis testing is widely applied in psychology, biology, medicine, finance, production, marketing, advertising, and criminal trials.

Hypothesis testing is all about assumptions and interpretations. It, therefore, requires superior analytical abilities. As a result, it is inaccessible for most.

Also, this method heavily relies on mere probability. There can be errors in data. It works better for large sample sizes. For smaller sample sets, this approach may not be the most suitable.

P-value refers to the probability of the null hypothesis getting rejected. P-value calculation determines whether the assumed result will hold true or not. A higher value determines the acceptance of the assumed result, while a lower value signifies rejection of this assumed result and acceptance of the alternate result.

A null hypothesis is a statement that proves that the sample mean is the same as the population mean. An alternative hypothesis is the opposite of the null hypothesis, i.e., it states that there is a difference between the sample mean and the population mean.

It is a useful statistical tool that interprets data-based conclusions—such that it stands true for the whole population. It is implemented in scientific research, medical research, psychology, manufacturing, marketing, advertising, and criminal trials.

This has been a guide to Hypothesis Testing and its meaning. We explain hypothesis testing steps, types, calculation, significance level, p-value, and z-test using examples. You can learn more about excel modeling from the articles below –

Hypothesis Testing Formula

Hypothesis Testing Formula (Table of Contents)

What is the Hypothesis Testing Formula?

Before we deep dive into hypothesis testing, we need to understand what is hypothesis at first place. In a very simple language, a hypothesis is basically an educated and informed guess about anything around you, which can be tested by experiment or simply by observation. For example, A new variant of mobile will be accepted by people or not, new medicine might work or not, etc. So hypothesis test is a statistical tool for testing that hypothesis which we will make and if that statement is meaning full or not. Basically, we select a sample from the data set and test a hypothesis statement by determining the likelihood that a sample statistics. So If your results from that test are not significant, it means that the hypothesis is not valid.

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Formula For Hypothesis Testing:

Hypothesis testing is given by the z test. The formula for Z – Test is given as:

But this is not so simple as it seems. To correctly perform the hypothesis test, you need to follow certain steps:

Step 1: First and foremost thing to perform a hypothesis test is that we have to define the null hypothesis and alternative hypothesis. Example of the null and alternate hypothesis is given by:

Step 2: Next thing we have to do is that we need to find out the level of significance. Generally, its value is 0.05 or 0.01

Step 3: Find the z test value also called test statistic as stated in the above formula.

Step 4: Also, find the z score from z table given the level of significance and mean .

Step 5: Compare these two values and if test statistic greater than z score, reject the null hypothesis. In case test statistic is less than z score, you cannot reject the null hypothesis.

Examples of Hypothesis Testing Formula (With Excel Template)

Let’s take an example to understand the calculation of Hypothesis Testing formula in a better manner.

Hypothesis Testing Formula – Example #1

Suppose you have been given the following parameters and you have to find the Z value and state if you accept the null hypothesis or not:

Null hypothesis H0: Population Mean = 30

Alternate hypothesis Ha: Population Mean ≠ 30

Z – Test is calculated using the formula given below

Z = (X – U) / (SD / √n)

Level of significance = 0.05

This is a Two tail test, so the probability lies on both side of the distribution. So 0.025 each side and we will look at this value on the z table.

Source: https://www.z-table.com/

Since the level of significance is 0.025 each side, we need to find 0.025 in the z table. Once we find that value from the table, we need to extract z value.

If you see here, on the left side the values of z are given and in the top row, decimal places are given. So from that, we can say that 0.025 will give z value of -1.96

So Z – Score = -1.96

Since the Z Test > Z Score, we can reject the null hypothesis.

Hypothesis Testing Formula – Example #2

Let’s say you are a principal of a school you are claiming that the students in your school are above average intelligence. An analyst wants to double check your claim and use hypothesis testing. He measures the IQ of all the students in the school and then takes a sample of 20 students. Following is the data points:

Null Hypothesis : Since population mean = 100,

Level of Significance = 0.05

Since the level of significance is 0.05, we need to find 1 – 0.05 = 0.95 in the z table. Once we find that value from the table, we need to extract z value.

Z – Table:

If you see here, on the left side the values of z are given and in the top row, decimal places are given. So from that, we can say that 0.95 lies between 1.64 to 1.65, mid-point in 1.645.

So Z Score = 1.645

Since the Z Test > Z Score, we can reject the null hypothesis and can say that students intelligence is above average.

Explanation

One thing everyone should keep in mind that No hypothesis test is 100% correct and there is always a chance of making an error. There is 2 type of errors which can arise in hypothesis testing: type I and type II.

Type 1: When the null hypothesis is true but it is rejected in the model. The probability of this is given by the level of significance. So if the level of significance is 0.05, there is a 5% chance that you will reject the null which is true.

Type 2: When the null hypothesis is not true but it is not rejected in the model. The probability of this is given the power of the test. This probability of occurrence of this type of error can be reduced by having sample which is large enough to give us confidence about the model.

Relevance and Uses of Hypothesis Testing Formula

As discussed above, the hypothesis test helps the analyst in testing the statistical sample and at the end will either accept or reject the null hypothesis. So the test helps in understanding the hypothesis formed is true or not and if not then the new hypothesis can be formed and tested again. There are steps for any hypothesis test. The first step is to state the hypothesis, both the null and alternate hypothesis. The next step is to determine all the relevant parameters like mean, standard deviation , level of significance, etc. which helps in determining the z test value . The third step determines the z score from the z table and for this step, we need to see is it two tail or single tail test and accordingly extract z score. The fourth and final step is to compare the results and then based on that either accept or reject the null hypothesis.

Hypothesis Testing Formula Calculator

You can use the following Hypothesis Testing Calculator

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Chi-Square (Χ²) Tests | Types, Formula & Examples

Published on May 23, 2022 by Shaun Turney . Revised on November 10, 2022.

A Pearson’s chi-square test is a statistical test for categorical data. It is used to determine whether your data are significantly different from what you expected. There are two types of Pearson’s chi-square tests:

What is a chi-square test, the chi-square formula, when to use a chi-square test, types of chi-square tests, how to perform a chi-square test, how to report a chi-square test, practice questions, frequently asked questions about chi-square tests.

Pearson’s chi-square (Χ 2 ) tests, often referred to simply as chi-square tests, are among the most common nonparametric tests . Nonparametric tests are used for data that don’t follow the assumptions of parametric tests , especially the assumption of a normal distribution .

If you want to test a hypothesis about the distribution of a categorical variable you’ll need to use a chi-square test or another nonparametric test. Categorical variables can be nominal or ordinal and represent groupings such as species or nationalities. Because they can only have a few specific values, they can’t have a normal distribution.

Test hypotheses about frequency distributions

There are two types of Pearson’s chi-square tests, but they both test whether the observed frequency distribution of a categorical variable is significantly different from its expected frequency distribution. A frequency distribution describes how observations are distributed between different groups.

Frequency distributions are often displayed using frequency distribution tables . A frequency distribution table shows the number of observations in each group. When there are two categorical variables, you can use a specific type of frequency distribution table called a contingency table to show the number of observations in each combination of groups.

Both of Pearson’s chi-square tests use the same formula to calculate the test statistic , chi-square (Χ 2 ):

$\begin{equation*} X^2=\sum{\frac{(O-E)^2}{E}} \end{equation*}$

The larger the difference between the observations and the expectations ( O − E in the equation), the bigger the chi-square will be. To decide whether the difference is big enough to be statistically significant , you compare the chi-square value to a critical value.

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A Pearson’s chi-square test may be an appropriate option for your data if all of the following are true:

The two types of Pearson’s chi-square tests are:

Chi-square goodness of fit test

Chi-square test of independence.

Mathematically, these are actually the same test. However, we often think of them as different tests because they’re used for different purposes.

You can use a chi-square goodness of fit test when you have one categorical variable. It allows you to test whether the frequency distribution of the categorical variable is significantly different from your expectations. Often, but not always, the expectation is that the categories will have equal proportions.

Expectation of different proportions

You can use a chi-square test of independence when you have two categorical variables. It allows you to test whether the two variables are related to each other. If two variables are independent (unrelated), the probability of belonging to a certain group of one variable isn’t affected by the other variable .

Other types of chi-square tests

Some consider the chi-square test of homogeneity to be another variety of Pearson’s chi-square test. It tests whether two populations come from the same distribution by determining whether the two populations have the same proportions as each other. You can consider it simply a different way of thinking about the chi-square test of independence.

McNemar’s test is a test that uses the chi-square test statistic. It isn’t a variety of Pearson’s chi-square test, but it’s closely related. You can conduct this test when you have a related pair of categorical variables that each have two groups. It allows you to determine whether the proportions of the variables are equal.

There are several other types of chi-square tests that are not Pearson’s chi-square tests, including the test of a single variance and the likelihood ratio chi-square test .

The exact procedure for performing a Pearson’s chi-square test depends on which test you’re using, but it generally follows these steps:

If you decide to include a Pearson’s chi-square test in your research paper , dissertation or thesis , you should report it in your results section . You can follow these rules if you want to report statistics in APA Style :

The two main chi-square tests are the chi-square goodness of fit test and the chi-square test of independence .

Both chi-square tests and t tests can test for differences between two groups. However, a t test is used when you have a dependent quantitative variable and an independent categorical variable (with two groups). A chi-square test of independence is used when you have two categorical variables.

Both correlations and chi-square tests can test for relationships between two variables. However, a correlation is used when you have two quantitative variables and a chi-square test of independence is used when you have two categorical variables.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

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Research Hypothesis: Definition, Types, & Examples

Saul Mcleod, PhD

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BSc (Hons) Psychology, MRes, PhD, University of Manchester

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Olivia Guy-Evans

Associate Editor for Simply Psychology

BSc (Hons), Psychology, MSc, Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

A hypothesis (plural hypotheses) is a precise, testable statement of what the researcher(s) predict will be the outcome of the study. It is stated at the start of the study.

This usually involves proposing a possible relationship between two variables: the independent variable (what the researcher changes) and the dependent variable (what the research measures).

In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment ).

A fundamental requirement of a hypothesis is that is can be tested against reality, and can then be supported or rejected.

To test a hypothesis the researcher first assumes that there is no difference between populations from which they are taken. This is known as the null hypothesis. The research hypothesis is often called the alternative hypothesis.

In This Article

Types of research hypotheses

Alternative hypothesis.

The alternative hypothesis states that there is a relationship between the two variables being studied (one variable has an effect on the other).

An experimental hypothesis predicts what change(s) will take place in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Null Hypothesis

The null hypothesis states that there is no relationship between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to the manipulation of the independent variable.

It states results are due to chance and are not significant in terms of supporting the idea being investigated.

Nondirectional Hypothesis

A non-directional (two-tailed) hypothesis predicts that the independent variable will have an effect on the dependent variable, but the direction of the effect is not specified. It just states that there will be a difference.

E.g., there will be a difference in how many numbers are correctly recalled by children and adults.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e. greater, smaller, less, more)

E.g., adults will correctly recall more words than children.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory to be considered scientific it must be able to be tested and conceivably proven false.

However many confirming instances there are for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory, rather than attempt to continually support theoretical hypotheses.

Can a hypothesis be proven?

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to write a hypothesis

What are examples of a hypothesis?

Let’s consider a hypothesis that many teachers might subscribe to: that students work better on Monday morning than they do on a Friday afternoon (IV=Day, DV=Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and on a Friday afternoon and then measuring their immediate recall on the material covered in each session we would end up with the following:

The null hypothesis is, therefore, the opposite of the alternative hypothesis in that it states that there will be no change in behavior.

At this point, you might be asking why we seem so interested in the null hypothesis. Surely the alternative (or experimental) hypothesis is more important?

Well, yes it is. However, we can never 100% prove the alternative hypothesis. What we do instead is see if we can disprove, or reject, the null hypothesis.

If we reject the null hypothesis, this doesn’t really mean that our alternative hypothesis is correct – but it does provide support for the alternative / experimental hypothesis.

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😍 How to formulate a hypothesis in research. How to Formulate Hypothesis?. 2019-01-06
Formulating Hypothesis In Research
Which Statement Is True Regarding The Diagram Of Circle P
Definition Of Ha Hypothesis
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State The Null Hypothesis And The Alternative Hypothesis

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Formulating Hypothesis
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Introduction to Hypothesis Testing Part 2
Khan Academy's explanation of Type I and Type II errors in statistical hypothesis testing
Formulating a hypothesis
Hypothesis independent samples

COMMENTS

How to Write a Strong Hypothesis
Developing a hypothesis (with example) Step 1. Ask a question Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question Do students who attend more lectures get better exam results? Step 2.
Null & Alternative Hypotheses
The alternative hypothesis ( Ha) answers "Yes, there is an effect in the population." The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
5.2
μ 0 is the hypothesized population mean A paired means test is comparable to conducting a one group mean test on the differences. p 0 is the hypothesized population proportion Note: μ 1 = μ 2 is equivalent to μ 1 − μ 2 = 0 Note: p 1 = p 2 is equivalent to p 1 − p 2 = 0 « Previous »
Hypothesis Testing
Step 1: State your null and alternate hypothesis Step 2: Collect data Step 3: Perform a statistical test Step 4: Decide whether to reject or fail to reject your null hypothesis Step 5: Present your findings Frequently asked questions about hypothesis testing Step 1: State your null and alternate hypothesis
Statistical Hypothesis
Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter. Null hypothesis: A statistical hypothesis that is to be tested. Alternative hypothesis: The alternative to the null hypothesis. Test statistic: A function of the sample data.
What a Hypothesis Is and How to Formulate One
Formulating a hypothesis can take place at the very beginning of a research project, or after a bit of research has already been done. Sometimes a researcher knows right from the start which variables she is interested in studying, and she may already have a hunch about their relationships.
Formulation of Hypotheses: Definition, Types & Example
Formulation of Hypothesis Raw data Scientific Data Analysis Statistical Tests Thematic Analysis Wilcoxon Signed-Rank Test Developmental Psychology Adolescence Adulthood and Aging Application of Classical Conditioning Biological Factors in Development Childhood Development Cognitive Development in Adolescence Cognitive Development in Adulthood
6 Steps to Evaluate a Statistical Hypothesis Testing
Step 3: Perform sampling and collection of data for statistical testing. It is important to perform sampling and collect data in way that assists the formulated research hypothesis. You will have to perform a statistical testing to validate your data and make statistical inferences about the population of your interest.
How to Write a Null Hypothesis (5 Examples)
Here is how to write the null and alternative hypotheses for this scenario: H0: μ = 300 (the true mean weight is equal to 300 pounds) HA: μ ≠ 300 (the true mean weight is not equal to 300 pounds) Example 2: Height of Males It's assumed that the mean height of males in a certain city is 68 inches.
How to Formulate a Hypothesis for an Experiment
Steps for Formulating a Hypothesis for an Experiment Step 1: State the question your experiment is looking to answer. Step 2: Identify your independent and dependant variables. Step 3: Write...
10.1
Null Hypothesis: On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg). Alternative Hypothesis: On the average, the dosage sold under this brand is not 50 mg (population mean dosage ≠ 50 mg). This is a two-sided alternative hypothesis. Example 10.4: Hypotheses with Two Samples of One Categorical Variable
How to Write a Hypothesis in 6 Steps
A statistical hypothesis is when you test only a sample of a population and then apply statistical evidence to the results to draw a conclusion about the entire population. Instead of testing everything, you test only a portion and generalize the rest based on preexisting data. Examples:
Formulating and Testing Hypotheses
In general, a hypothesis is formulated by rephrasing the objective of a study as a statement, e.g., if the objective of an investigation is to determine if a pesticide is safe, the resulting hypothesis might be " the pesticide is not safe ", or alternatively that " the pesticide is safe ".
Examples of null and alternative hypotheses
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
Hypothesis Testing Steps & Real Life Examples
The hypothesis can be defined as the claim that can either be related to the truth about something that exists in the world, or, truth about something that's needs to be established a fresh. In simple words, another word for the hypothesis is the "claim". Until the claim is proven to be true, it is called the hypothesis.
Hypothesis Testing
Hypothesis Testing Formula Researchers opt for different statistical tests like t-tests or z-tests. The z-test formula is as follows: Z = ( x̅ - μ0 ) / (σ /√n) Here, x̅ is the sample mean, μ0 is the population mean, σ is the standard deviation, n is the sample size. Based on the Z-test result, the research derives the hypothesis conclusion.
Hypothesis Testing Formula
Hypothesis testing is given by the z test. The formula for Z - Test is given as: Z = (X - U) / (SD / √n) Where: X - Sample Mean U - Population Mean SD - Standard Deviation n - Sample size But this is not so simple as it seems. To correctly perform the hypothesis test, you need to follow certain steps:
Chi-Square (Χ²) Tests
When to use a chi-square test. A Pearson's chi-square test may be an appropriate option for your data if all of the following are true:. You want to test a hypothesis about one or more categorical variables.If one or more of your variables is quantitative, you should use a different statistical test.Alternatively, you could convert the quantitative variable into a categorical variable by ...
Research Hypothesis: Definition, Types, & Examples
A hypothesis (plural hypotheses) is a precise, testable statement of what the researcher (s) predict will be the outcome of the study. It is stated at the start of the study. This usually involves proposing a possible relationship between two variables: the independent variable (what the researcher changes) and the dependent variable (what the ...
Formulating the Research Hypothesis and Null Hypothesis
Formulating a Hypothesis. You have a question and now you need to turn it into a hypothesis. A hypothesis is an educated prediction that provides an explanation for an observed event. An observed ...