Hypothesis Testing

Presented by

Dr. Bikash Barman

Assistant Professor

Department of Geography

Malda Women’s College

Type-I Error & Type-II Error

Types of Hypothesis Testing:�1. Parametric Test: T-test, Z-Test and ANOVA�2. Non-Parametric Test: Chi square test, Mann-Whitney U test, Kruskal-Walis test

Steps for Hypothesis Testing

1. Formulate null and alternative hypothesis
2. Specify the level of significance ( alpha level)
3. Choose the appropriate test statistics
4. Calculate the value of test statistics
5. Make decision with calculated value and tabulated value

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When t-test and When z-test?

Types of T-Test

Steps for t-test

Degrees of Freedom

Formula for One Sample T-Test

Two Sample t-test

Decision

*If calculated t value is greater than the tabulated t value then the null hypothesis (H₀)can be reject and alternative hypothesis (H₁) can be accepted which means that there is a significant difference between the experimental group mean and control group mean.

Calculated t> Tabulated t= Reject H₀

Paired Sample t-test: Question

Z-Test

One Sample Z-test

Critical Values for Z-Test

TWO SAMPLE Z-TEST

Chi-Square Test

*Test of significance based on frequencies not the parameters like mean and standard deviation

*First used by Karl Pearson in 1900

*Useful measure of comparing experimentally obtained result with those expected theoretically and based on the hypothesis

*It is denoted by χ²

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Uses of Chi-Square Test

1. Chi-square test as a test of independence (Whether two or more attributes or variables are associated or not)
2. Chi-square test as a test of goodness of fit (Whether or not an observed frequency distribution differs from a expected frequency distribution)

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Steps for calculation of Chi-Square Test

1. Setting up the hypothesis (H₀ and H₁)

2. Prepare a cross tabulation observation on two variables

3. Calculate the observed and expected values

f_e= (Row Total × Column Total)/N

4. Calculate Chi-Square value

5. Calculate the Degree of freedom= (Columns-1) (Rows-1)

6. Find out the tabulated value from the Critical values of Chi-Square on alpha level 0.05 (Significance level)

7. Made the decision (If calculated chi value is greater than tabulated value than null hypothesis can be rejected and alternative hypothesis can be accepted)

Example of �Test of Independence

Survey �on �Marital Status among the Muslim Women of Maldah District

Hypothesis Setting:

H₀= There is no relationship between educational attainment and marital status

H₁= There is a significant relationship between educational attainment and marital status

Step-1: Table of Observed Values

Step-2: Table of Expected Value

f_e= (Row Total × Column Total)/N

Step-3: Calculation of Chi value

Step-4: Calculate the degree of freedom:�DF= (R-1)(C-1)� Where, R= Total number of Rows�C= Total number of columns��DF= (4-1) ×(5-1)�= 3 × 4�= 12��

Step-5: Find out the Critical values of chi square on significance level 0.05 = 21.026

Step-6: Decision Rule

Calculated value= 23.57

Tabulated value= 21.03

Reject H₀ if the calculated value is greater than tabulated value and accept the H₁

Step-7: Conclusion

There is a significant relationship between educational attainment and marital status among the Muslim Women of Maldah district.

Example of �Test of Goodness of Fit

Q. A dice was thrown 60 times with the following results:�

Are the data consistent with the hypothesis that the dice is unbiased?

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Ans: Step-1: Setting up Hypothesis

H0= The dice is unbiased

H1= The dice is biased

Then the probability of each face is 1/6

And the expected frequency is 1/6×60= 10 for each

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Calculated Chi-Square= 3.4

Step-2: Calculation of Chi-Square

Degrees of Freedom= (N-1)�= (6-1)= 5

Thank You