HYPOTHESIS TESTING


In the 1920s, Ronald Fisher developed the theory behind the p value and Jerzy Neyman and Egon Pearson developed the theory of hypothesis testing.

Definition by Various Authors

"A hypothesis is a conjectural statement of the relation between two or more variables". (Kerlinger, 1956)

"Hypotheses are single tentative guesses, good hunches assumed for use in devising theory or planning experiments intended to be given a direct experimental test when possible". (Eric Rogers, 1966)

- NULL HYPOTHESIS is the hypothesis which is tested for possible rejection under the assumption that it is true. It is denoted by Ho.

-  ALTERNATIVE HYPOTHESIS is any hypothesis which is complementary to the null hypothesis. It is very important to explicitly state the alternative hypothesis is respect of any Null Hypothesis Ho, 

because the acceptance or rejection of Ho is meaningful only if it is being tested against a rival hypothesis.

- We make type 1 error by rejecting a true null hypothesis. It is also called  level of significance, Alpha.

- We make type 2 error by accepting a false null hypothesis. It is also called beta, and power function of test (1-β)


There are two types of hypothesis test 

 1. Parametric test 

 2. Non-Parametric test

# Parametric test include :-T- Test, F-Test, Z- Test Are Called Parametric Test.

# Non -Parametric test :- 1) Sign test. 2) Median test. 3) Mann Whitney u test. 4) Run test. 5) Ks test. 6) Chi square test

1) Z- test is also known as Standard Normal Variable Test Or Standard Normal Deviate Test. Published by R.A Fisher

Conditions for apply Z-test 

1) large sample size (more than 30)

2) normal distributed data 

3) population variance is known 

4) Z-Transformation or Z-score test 

5) observation are independent 

6) Z= mean - μ/σ/√n. or μ/σ/ S.E (Standard Error).

2 T- Test is also known as Student T Distribution, Exact Test Or Small Sample Test.

T-TEST is any statistical hypothesis test in which the test statistics follows a student

Conditions apply for T-test 

1 T- test is given by W S Gooset 1908.

2 small sample size (less than 30)

3 normally distributed data 

4 population variance is unknown

5 measure mean of 2 samples of 1 population 

6 Can be one tail or two tail test 

7 observations are independent 

3. F-Test 

Variance of 1st Data set/

Variance of 2nd Data set

CONDITIONS APPLY FOR F-TEST

-in memory of R.A Fisher 

-Small sample size (less than 30)

-normally distributed data 

-population variance is known

-measure variance of 2 samples of 1 population 

-can be one tail or two tail test 

-observation are independent 

4. ANOVA  :-

-Published by Sir Ronald A Fisher 1920

-Normally distributed data 

-Extension of T-Test

-Measure mean of more than 2 samples 

-Measures mean of more than 2 population 

-Observations are independent 

-Sample variance = population variance

5. Chi Square Test: (non-parametric) Is known as Goodness of fit 

It was first of all used by Karl Pearson in the year 1900.

 1) Goodness of fit of distributions

2) test of independence of attributes

3) test of homogenity.

4) Can be used only on raw counts (no measurements)

5) Sample size must be more than 20

Chi-square test is the test of significance.

*It is denoted by the Gr. sign- X

Following is the formula.

x² = (Observed - Expected)² 

                Expected

Parametric vs. Nonparametric Tests

Parametric Tests tests used to analyze data from which parameters such as the mean, median, and mode can be calculated e.g. reaction time, height jumped, grade on a test, etc.

Nonparametric Tests tests used to analyze data that cannot be described by the mean, median, or mode e.g. letter grades, state of residence, gender.