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## Statistical Hypothesis

From: Methods in Experimental Physics , 1994

## Related terms:

## Inductive Logic

## Testing Statistical Hypotheses

Sheldon M. Ross , in Introductory Statistics (Fourth Edition) , 2017

Null hypothesis : A statistical hypothesis that is to be tested.

Alternative hypothesis : The alternative to the null hypothesis.

p value : The smallest significance level at which the null hypothesis is rejected.

## Statistical Methods for Physical Science

John Kitchin , in Methods in Experimental Physics , 1994

## 6.4.1 Statistical Hypotheses and Decision Making

## Hypothesis Testing and Confidence Intervals

T.R. Konold , X. Fan , in International Encyclopedia of Education (Third Edition) , 2010

## Directional and Nondirectional Alternative Hypotheses

Jan-Willem Romeijn , in Handbook of the History of Logic , 2011

## 5 Bayesian Statistics

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 ).

## Nonparametric Hypotheses Tests

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

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 .

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

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

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

## Hypothesis Testing

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

## Why the Null Hypothesis Is Null

## Hypothesis testing

## 6.6 Chapter summary

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

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

The p value or attained significance level

The Smith–Satterthwaite procedure

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

General method for hypothesis testing

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

## Answers to Chapter Exercises, Part I

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

Ho: μ w = μ w/o ; H 1 : μ w ≠ μ w/o .

## Statistics as Inductive Inference

Jan-Willem Romeijn , in Philosophy of Statistics , 2011

## 7 Bayesian Statistics

## Definition of a Hypothesis

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

- Key Concepts
- Major Sociologists
- News & Issues
- Research, Samples, and Statistics
- Recommended Reading
- Archaeology

## Null Hypothesis

## Alternative Hypothesis

## Formulating a Hypothesis

Updated by Nicki Lisa Cole, Ph.D

## Select your language

## Formulation of Hypothesis

- Addiction Treatment Theories
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- Six Stage Model of Behaviour Change
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- Biological Rhythms
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- Case Studies Psychology
- Computation
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- Correlation
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- Designing Research
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- Dweck's Theory of Mindset
- Ethical considerations in research
- Experimental Method
- Factors Affecting Perception
- Factors Affecting the Accuracy of Memory
- Gibson's Theory of Direct Perception
- Gregory's Constructivist Theory of Perception
- Gunderson et al 2013 study
- Hughes Policeman Doll Study
- Issues and Debates in Developmental Psychology
- Language and Perception
- McGarrigle and Donaldson Naughty Teddy
- Memory Processes
- Memory recall
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- Observed Values and Critical Values
- Presentation of Quantitative Data
- Probability and Significance
- Scientific Data Analysis
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- Adolescence
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- Application of Classical Conditioning
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- Continuity vs Discontinuity
- Death and Dying
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- Gender Development
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- Infant Development
- Kohlberg's Theory of Moral Reasoning
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- Language and the Brain
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- Stability vs Change
- The Law of Effect
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- Stress Definition
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- Zajonc and LeDoux
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- Anger Management and Restorative Justice Programmes
- Atavistic Form
- Biological Evidence
- Biological Theories of Crime
- Custodial Sentencing
- Differential Association Theory
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- Genetic Explanations of Offending Behaviour
- Level of Moral Reasoning and Cognitive Distortions
- Measuring Crime
- Offender Profiling
- Psychodynamic Theories and The Moral Component
- Psychological Evidence
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- Psychology in the Courtroom
- Bem Sex Role Inventory
- Cognitive Explanations of Gender Development
- Gender Dysphoria
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- Gender Schema Theory
- Klinefelter and Turner Syndrome
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- Sexual Orientation
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- Preventive Mental Health Care
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- Current Debates in Psychology
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- Nature Vs Nurture Debate
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- Philosophical Debates in Psychology
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- Introduction to Personality
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- Absence of Gating
- Duck's Phase Model of Relationship Breakdown
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- Factors affecting attraction
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- Aims and Hypotheses
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- Biological Explanations for Schizophrenia
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- Diagnosis and Classification of Schizophrenia
- Dysfunctional Family
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- Interactionist Approach
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- Role of Cannabis
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- Typical and Atypical Antipsychotics
- Ventricular Size
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- Body Senses
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- Gestalt Principles of Perception
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- An introduction to mental health
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- Human Language and Animal Communication
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- Improving Sleep
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- The Social Readjustment Rating Scale
- Workplace Stress

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- First, we will discuss the importance of hypotheses in research.
- We will then cover formulating hypotheses in research, including the steps in the formulation of hypotheses in research methodology.
- We will provide examples of hypotheses in research throughout the explanation.
- Finally, we will delve into the different types of hypotheses in research.

## What is a Hypothesis?

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

## Importance of Hypothesis in Research

The purpose of including hypotheses in psychology research is:

- To provide a summary of the research, how it will be investigated, and what is expected to be found.
- To provide an answer to the research question.

## Steps in the Formulation of Hypothesis in Research Methodology

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

All researchers will likely complete the following.

- Investigating background research in the area of interest.
- Formulating or investigating a theory.
- Identify how the theory will be tested and what the researcher expects to find based on relevant, previously published scientific works.

The above steps are used to formulate testable hypotheses.

## The Formulation of Testable Hypotheses

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.

## Example Hypothesis in Research

## Formulation of Hypothesis - Key Takeaways

- The current community of psychologists believe that the best approach to understanding behaviour is to conduct scientific research . One of the important steps in scientific research is to create a hypothesis.
- The hypothesis is a predictive, testable statement concerning the outcome/results that the researcher expects to find.
- Hypotheses are needed in research to provide a summary of what the research is, how to investigate a theory and what is expected to be found, and to provide an answer to the research question so that the hypothesis can be used for later data analysis.
- There are requirements for the formulation of testable hypotheses. The hypotheses should identify and operationalise the IV and DV. In addition, they should describe the nature of the relationship between the IV and DV.
- There are different types of hypotheses: Null hypothesis, Alternative hypothesis (this is also known as the non-directional, two-tailed hypothesis), and Directional hypothesis (this is also known as the one-tailed hypothesis).

## 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?

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

All researchers will likely complete the following

- Investigating background research in the area of interest
- Formulating or investigating a theory
- Identify how the theory will be tested and what the researcher expects to find based on relevant, previously published scientific works

## --> What is formulation of hypothesis in research?

## --> How to formulate null and alternative hypothesis?

## Final Formulation of Hypothesis Quiz

Directional, alternative hypothesis

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

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

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

- Investigating background research in the area of interest
- Formulating or investigating a theory
- Identify how the theory will be tested and what the researcher expects to find based on relevant, previously published scientific works

Why are hypotheses needed in research?

Hypotheses are needed in research:

- to provide a summary of what the researcher is and how investigating a theory and what is expected to be found
- to provide an answer to the research question
- so that the hypothesis can be used for later data analysis

What type of data analysis may hypotheses be needed for?

What are the requirements of a good hypothesis?

- identify and operationalise the independent and dependent variable
- be testable
- be falsifiable
- predictive statements

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

What is an operationalised variable?

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

What is a hypothesis predicting?

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## 6 Steps to Evaluate the Effectiveness of Statistical Hypothesis Testing

## What Is Research Hypothesis Testing?

## Types of Statistical Hypothesis Testing

## Source: https://www.youtube.com/c/365DataScience

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

## b. Alternate Hypothesis

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 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.

## b. Two-Tailed

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.

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

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

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

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

## Step 6: Present your final results of hypothesis testing

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## How to Write a Null Hypothesis (5 Examples)

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:

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)

## Example 1: Weight of 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

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

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

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

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%)

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## Keyboard Shortcuts

10.1 - setting the hypotheses: examples.

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

- Research Question : Are artists more likely to be left-handed than people found in the general population?
- Response Variable : Classification of the student as either right-handed or left-handed

## State Null and Alternative Hypotheses

- Null Hypothesis : Students in the College of Arts and Architecture are no more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Art and Architecture = 10% or p = .10).
- Alternative Hypothesis : Students in the College of Arts and Architecture are more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Arts and Architecture > 10% or p > .10). This is a one-sided alternative hypothesis.

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

- Research Question : Does the data suggest that the population mean dosage of this brand is different than 50 mg?
- Response Variable : dosage of the active ingredient found by a chemical assay.
- 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 Section

- Research Question : Does the data suggest that females are more likely than males to eat vegetarian meals on a regular basis?
- Response Variable : Classification of whether or not a person eats vegetarian meals on a regular basis
- Explanatory (Grouping) Variable: Sex
- Null Hypothesis : There is no sex effect regarding those who eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis = population percent of males who eat vegetarian meals on a regular basis or p females = p males ).
- Alternative Hypothesis : Females are more likely than males to eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis > population percent of males who eat vegetarian meals on a regular basis or p females > p males ). This is a one-sided alternative hypothesis.

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

- Research Question : Does the data suggest that, on the average, people are able to lose more weight on a low carbohydrate diet than on a low fat diet?
- Response Variable : Weight loss (pounds)
- Explanatory (Grouping) Variable : Type of diet
- Null Hypothesis : There is no difference in the mean amount of weight loss when comparing a low carbohydrate diet with a low fat diet (population mean weight loss on a low carbohydrate diet = population mean weight loss on a low fat diet).
- Alternative Hypothesis : The mean weight loss should be greater for those on a low carbohydrate diet when compared with those on a low fat diet (population mean weight loss on a low carbohydrate diet > population mean weight loss on a low fat diet). This is a one-sided alternative hypothesis.

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

- Research Question : Do the odds of having a stroke increase if you inhale second hand smoke ? A case-control study of non-smoking stroke patients and controls of the same age and occupation are asked if someone in their household smokes.
- Variables : There are two different categorical variables (Stroke patient vs control and whether the subject lives in the same household as a smoker). Living with a smoker (or not) is the natural explanatory variable and having a stroke (or not) is the natural response variable in this situation.
- Null Hypothesis : There is no relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is = 1).
- Alternative Hypothesis : There is a relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is > 1). This is a one-tailed alternative.

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

- Research Question : A financial analyst believes there might be a positive association between the change in a stock's price and the amount of the stock purchased by non-management employees the previous day (stock trading by management being under "insider-trading" regulatory restrictions).
- Variables : Daily price change information (the response variable) and previous day stock purchases by non-management employees (explanatory variable). These are two different measurement variables.
- Null Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) = 0.
- Alternative Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) > 0. This is a one-sided alternative hypothesis.

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

- Research Question : Is there a linear relationship between the amount of the bill (\$) at a restaurant and the tip (\$) that was left. Is the strength of this association different for family restaurants than for fine dining restaurants?
- Variables : There are two different measurement variables. The size of the tip would depend on the size of the bill so the amount of the bill would be the explanatory variable and the size of the tip would be the response variable.
- Null Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the same at family restaurants as it is at fine dining restaurants.
- Alternative Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the difference at family restaurants then it is at fine dining restaurants. This is a two-sided alternative hypothesis.

## How to Write a Hypothesis in 6 Steps

Write with confidence Grammarly helps you polish your academic writing Write with Grammarly

## What is a hypothesis?

## 7 examples of hypotheses (with examples)

## 1 Simple hypothesis

- If you stay up late, then you feel tired the next day.
- Turning off your phone makes it charge faster.

## 2 Complex hypothesis

- People who both (1) eat a lot of fatty foods and (2) have a family history of health problems are more likely to develop heart diseases.
- Older people who live in rural areas are happier than younger people who live in rural areas.

## 3 Null hypothesis

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

- There is no difference in plant growth when using either bottled water or tap water.
- Professional psychics do not win the lottery more than other people.

## 4 Alternative hypothesis

- Plants grow better with bottled water than tap water.
- Professional psychics win the lottery more than other people.

## 5 Logical hypothesis

- An alien raised on Venus would have trouble breathing in Earth’s atmosphere.
- Dinosaurs with sharp, pointed teeth were probably carnivores.

## 6 Empirical hypothesis

- Customers at restaurants will tip the same even if the wait staff’s base salary is raised.
- Washing your hands every hour can reduce the frequency of illness.

## 7 Statistical hypothesis

- In humans, the birth-gender ratio of males to females is 1.05 to 1.00.
- Approximately 2% of the world population has natural red hair.

## What makes a good hypothesis?

## Cause and effect

## Testable prediction

## Independent and dependent variables

## Candid language

## Adherence to ethics

## How to write a hypothesis in 6 steps

## 2 Conduct preliminary research

## 3 Define your variables

## 4 Phrase it as an if-then statement

## 5 Collect data to support your hypothesis

## 6 Write with confidence

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

## Formulating and Testing Hypotheses

“ 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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## Author information

Western College of Veterinary Medicine, University of Saskatchewan, Saskatoon, Canada

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## AP®︎/College Statistics

## Examples of null and alternative hypotheses

- P-values and significance tests
- Comparing P-values to different significance levels
- Estimating a P-value from a simulation
- Using P-values to make conclusions

## Want to join the conversation?

## Video transcript

## Hypothesis Testing Steps & Real Life Examples

## What is a Hypothesis testing?

- It is claimed that a 500 gm sugar packet for a particular brand, say XYZA, contains sugar of less than 500 gm, say around 480gm. Can this claim be taken as truth? How do we know that this claim is true? This is a hypothesis until proved.
- A group of doctors claims that quitting smoking increases lifespan. Can this claim be taken as new truth? The hypothesis is that quitting smoking results in an increase in lifespan.
- It is claimed that brisk walking for half an hour every day reverses diabetes. In order to accept this in your lifestyle, you may need evidence that supports this claim or hypothesis.
- It is claimed that doing Pranayama yoga for 30 minutes a day can help in easing stress by 50%. This can be termed as hypothesis and would require testing / validation for it to be established as a truth and recommended for widespread adoption.
- One common real-life example of hypothesis testing is election polling. In order to predict the outcome of an election, pollsters take a sample of the population and ask them who they plan to vote for. They then use hypothesis testing to assess whether their sample is representative of the population as a whole. If the results of the hypothesis test are significant, it means that the sample is representative and that the poll can be used to predict the outcome of the election. However, if the results are not significant, it means that the sample is not representative and that the poll should not be used to make predictions.
- Machine learning models make predictions based on the input data. Can the predictions made on a particular set of data be taken as the real characteristic of the model? Or, the model performance on a given data set was a chance occurrence. The hypothesis can be that the model predictions do represent the real characteristics of the model.
- As part of a linear regression machine learning model , it is claimed that there is a relationship between the response variables and predictor variables? Can this hypothesis or claim be taken as truth? Let’s say, the hypothesis is that the housing price depends upon the average income of people already staying in the locality. How true is this hypothesis or claim? The relationship between response variable and each of the predictor variables can be evaluated using T-test and T-statistics .
- For linear regression model , one of the hypothesis is that there is no relationship between the response variable and any of the predictor variables. Thus, if b1, b2, b3 are three parameters, all of them is equal to 0. b1 = b2 = b3 = 0. This is where one performs F-test and use F-statistics to test this hypothesis.

## Hypothesis Testing Examples

- Customers are churning because they ain’t getting response to their complaints or issues
- Customers are churning because there are other competitive services in the market which are providing these services at lower cost.
- Customers are churning because there are other competitive services which are providing more services at the same cost.

## State the Hypothesis to begin Hypothesis Testing

- Claim made against the well-established fact : The case in which a fact is well-established, or accepted as truth or “knowledge” and a new claim is made about this well-established fact. For example , when you buy a packet of 500 gm of sugar, you assume that the packet does contain at the minimum 500 gm of sugar and not any less, based on the label of 500 gm on the packet. In this case, the fact is given or assumed to be the truth. A new claim can be made that the 500 gm sugar contains sugar weighing less than 500 gm. This claim needs to be tested before it is accepted as truth. Such cases could be considered for hypothesis testing if this is claimed that the assumption or the default state of being is not true.
- Claim to establish the new truth : The case in which there is some claim made about the reality that exists in the world (fact). For example , the fact that the housing price depends upon the average income of people already staying in the locality can be considered as a claim and not assumed to be true. Another example could be the claim that running 5 miles a day would result in a reduction of 10 kg of weight within a month. There could be varied such claims which when required to be proved as true have to go through hypothesis testing.

- The packet of 500 gm of sugar contains sugar of weight less than 500 gm. (Claim made against the established fact)
- The housing price depends upon the average income of the people staying in the locality. (Claim to establish new truth)
- Running 5 miles a day results in a reduction of 10 kg of weight within a month. (Claim to establish new truth)

## Formulate Null & Alternate Hypothesis as Next Step

## What is a null hypothesis?

## What is an alternate hypothesis?

- Reject the null hypothesis : There is enough evidence based on which one can reject the null hypothesis. Let’s understand this with the help of an example provided earlier in this section. The null hypothesis is that there is no relationship between the students studying more than 6 hours a day and getting more than 90% marks. In a sample of 30 students studying more than 6 hours a day, it was found that they scored 91% marks. Given that the null hypothesis is true, this kind of hypothesis testing result will be highly unlikely. This kind of result can’t happen by chance. That would mean that the claim can be taken as the new truth in the real world. One can go and take further samples of 30 students to perform some more testing to validate the hypothesis. If similar results show up with other tests, it can be said with very high confidence that there is enough evidence to reject the null hypothesis that there is no relationship between the students studying more than 6 hours a day and getting more than 90% marks. In such cases, one can go to accept the claim as new truth that the students studying more than 6 hours a day get more than 90% marks. The hypothesis can be considered the new truth until the time that new tests provide evidence against this claim.
- Fail to reject the null hypothesis : There is not enough evidence-based on which one can reject the null hypothesis (well-established fact or reality). Thus, one would fail to reject the null hypothesis. In a sample of 30 students studying more than 6 hours a day, the students were found to score 75%. Given that the null hypothesis is true, this kind of result is fairly likely or expected. With the given sample, one can’t reject the null hypothesis that there is no relationship between the students studying more than 6 hours a day and getting more than 90% marks.

## 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:

- State the hypothesis : First and foremost, the hypothesis needs to be stated. The hypothesis could either be the statement that is assumed to be true or the claim which is made to be true.
- Formulate the hypothesis : This step requires one to identify the Null and Alternate hypotheses or in simple words, formulate the hypothesis. Take an example of the canned sauce weighing 500 gm as the Null Hypothesis.
- Set the criteria for a decision : Identify test statistics that could be used to assess the Null Hypothesis. The test statistics with the above example would be the average weight of the sugar packet, and t-statistics would be used to determine the P-value. For different kinds of problems, different kinds of statistics including Z-statistics, T-statistics, F-statistics, etc can be used.
- Identify the level of significance (alpha) : Before starting the hypothesis testing, one would be required to set the significance level (also called as alpha ) which represents the value for which a P-value less than or equal to alpha is considered statistically significant. Typical values of alpha are 0.1, 0.05, and 0.01. In case the P-value is evaluated as statistically significant, the null hypothesis is rejected. In case, the P-value is more than the alpha value, the null hypothesis is failed to be rejected.
- Compute the test statistics : Next step is to calculate the test statistics (z-test, t-test, f-test, etc) to determine the P-value. If the sample size is more than 30, it is recommended to use z-statistics. Otherwise, t-statistics could be used. In the current example where 20 packets of canned sauce is selected for hypothesis testing, t-statistics will be calculated for the mean value of 505 gm (sample mean). The t-statistics would then be calculated as the difference of 505 gm (sample mean) and the population means (500 gm) divided by the sample standard deviation divided by the square root of sample size (20).
- Calculate the P-value of the test statistics : Once the test statistics have been calculated, find the P-value using either of t-table or a z-table. P-value is the probability of obtaining a test statistic (t-score or z-score) equal to or more extreme than the result obtained from the sample data, given that the null hypothesis H0 is true.
- Compare P-value with the level of significance : The significance level is set as the allowable range within which if the value appears, one will be failed to reject the Null Hypothesis. This region is also called as Non-rejection region . The value of alpha is compared with the p-value. If the p-value is less than the significance level, the test is statistically significant and hence, the null hypothesis will be rejected.

## P-Value: Key to Statistical Hypothesis Testing

## Hypothesis testing quiz

Please select 2 correct answers

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

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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.

## Table of contents

- Hypothesis testing is a statistical interpretation that examines a sample to determine whether the results stand true for the population.
- The test allows two explanations for the data—the null hypothesis or the alternative hypothesis. If the sample mean matches the population mean, the null hypothesis is proven true.
- Alternatively, if the sample mean is not equal to the population mean, the alternate hypothesis is accepted.
- This method requires superior analytical abilities and, therefore, is inaccessible for most. Also, this method heavily relies on probability.

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

- Simple : In a simple hypothesis, the population parameter is stated as a specific value, making the analysis easier.
- Composite : In a composite hypothesis, the population parameter ranges between a lower and upper value.
- One-tailed : When the majority of the population is concentrated on one side, it is called a one-tailed test . In a one-tailed test, the sample test is either higher or lower than the population parameter.

Hypothesis tests involve the following steps:

- Researchers first mention whether the idea is a null theory or an alternative hypothesis. If the variables are not correlated, then it is assumed null. Alternatively, if the variables show correlation, then it is the alternative hypothesis.
- Then they collect relevant data for sampling—it closely represents the whole population on which the test is to be performed.
- Next, researchers choose a statistical test that suits the collected data.
- Based on the test results and level of significance, they either accept or reject the null hypothesis.
- Finally, the statistical findings are compiled and summarized into a research report.

- Here, x̅ is the sample mean,
- μ 0 is the population mean,
- σ is the standard deviation,
- n is the sample size.

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

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.

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

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.

- Calculate P-Value in Excel
- Formula for F-Test
- Formula of P-Value
- Bell Curve Bell Curve Bell Curve graph portrays a normal distribution which is a type of continuous probability. It gets its name from the shape of the graph which resembles to a bell. read more

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## Hypothesis Testing Formula

Hypothesis Testing Formula (Table of Contents)

## What is the Hypothesis Testing Formula?

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Formula For Hypothesis Testing:

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

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 .

## Examples of Hypothesis Testing Formula (With Excel Template)

## Hypothesis Testing Formula – Example #1

Null hypothesis H0: Population Mean = 30

Alternate hypothesis Ha: Population Mean ≠ 30

Z – Test is calculated using the formula given below

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

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

## Hypothesis Testing Formula – Example #2

Null Hypothesis : Since population mean = 100,

## Explanation

## Relevance and Uses of Hypothesis Testing Formula

## 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.

- The chi-square goodness of fit test is used to test whether the frequency distribution of a categorical variable is different from your expectations.
- The chi-square test of independence is used to test whether two categorical variables are related to each other.

## Table of contents

## Test hypotheses about frequency distributions

- Χ 2 is the chi-square test statistic
- Σ is the summation operator (it means “take the sum of”)
- O is the observed frequency
- E is the expected frequency

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- 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 separating the observations into intervals.
- The sample was randomly selected from the population .
- There are a minimum of five observations expected in each group or combination of groups.

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

## Chi-square goodness of fit test

Chi-square test of independence.

- Null hypothesis ( H 0 ): The bird species visit the bird feeder in equal proportions.
- Alternative hypothesis ( H A ): The bird species visit the bird feeder in different proportions.

Expectation of different proportions

- Null hypothesis ( H 0 ): The bird species visit the bird feeder in the same proportions as the average over the past five years.
- Alternative hypothesis ( H A ): The bird species visit the bird feeder in different proportions from the average over the past five years.

- Null hypothesis ( H 0 ): The proportion of people who are left-handed is the same for Americans and Canadians.
- Alternative hypothesis ( H A ): The proportion of people who are left-handed differs between nationalities.

## Other types of chi-square tests

- Null hypothesis ( H 0 ): The proportion of people who like chocolate is the same as the proportion of people who like vanilla.
- Alternative hypothesis ( H A ): The proportion of people who like chocolate is different from the proportion of people who like vanilla.

- Create a table of the observed and expected frequencies. This can sometimes be the most difficult step because you will need to carefully consider which expected values are most appropriate for your null hypothesis.
- Calculate the chi-square value from your observed and expected frequencies using the chi-square formula.
- Find the critical chi-square value in a chi-square critical value table or using statistical software.
- Compare the chi-square value to the critical value to determine which is larger.
- Decide whether to reject the null hypothesis. You should reject the null hypothesis if the chi-square value is greater than the critical value. If you reject the null hypothesis, you can conclude that your data are significantly different from what you expected.

- You don’t need to provide a reference or formula since the chi-square test is a commonly used statistic.
- Refer to chi-square using its Greek symbol, Χ 2 . Although the symbol looks very similar to an “X” from the Latin alphabet, it’s actually a different symbol. Greek symbols should not be italicized.
- Include a space on either side of the equal sign.
- If your chi-square is less than zero, you should include a leading zero (a zero before the decimal point) since the chi-square can be greater than zero.
- Provide two significant digits after the decimal point.
- Report the chi-square alongside its degrees of freedom , sample size, and p value , following this format: Χ 2 (degrees of freedom, N = sample size) = chi-square value, p = p value).

## Cite this Scribbr article

Turney, S. (2022, November 10). Chi-Square (Χ²) Tests | Types, Formula & Examples. Scribbr. Retrieved March 11, 2023, from https://www.scribbr.com/statistics/chi-square-tests/

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## Shaun Turney

## Research Hypothesis: Definition, Types, & Examples

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

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## Types of research hypotheses

## Null Hypothesis

## Nondirectional Hypothesis

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

## Directional Hypothesis

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

## Falsifiability

## 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

- 1. To write the alternative and null hypotheses for an investigation, you need to identify the key variables in the study.The independent variable is manipulated by the researcher and the dependent variable is the outcome which is measured.
- 2. Operationalized the variables being investigated.Operationalisation of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression you might count the number of punches given by participants
- 3. Decide on a direction for your prediction. If there is evidence in the literature to support a specific effect on the independent variable on the dependent variable, write a directional (one-tailed) hypothesis.If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
- 4. Write your hypothesis. A good hypothesis is short (i.e. concise) and comprises clear and simple language.

## What are examples of a hypothesis?

- The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
- The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

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## IMAGES

## VIDEO

## COMMENTS

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.

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.

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 »

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: 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.

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 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

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.

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.

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...

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

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:

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 ".

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.

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 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 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:

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 ...

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 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 ...