Student's t test and variations

An overview of the student's t test

1. T test and its variations
Dr. S. A. Rizwan, M.D.
Public Health Specialist
SBCM, Joint Program – Riyadh
Ministry of Health, Kingdom of Saudi Arabia

2. Learning objectives
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Describe the conditions in which this test is used
•Describe the assumptions for this test
•Describe the steps involved in calculating this test
•Interpret the test result
•Describe the types of this test

3. Introduction
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•T test, also called Student’s t test

•Introduced in 1908 by a chemist working
for the Guinness brewery in Dublin,
Ireland

•‘Student’ was his pen name

4. Applications of t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Test the single mean in single sample case
•Test the equality of two means in double sample case
•Independent samples(Independent t test)
•Dependent samples (Paired t test)

•Test the significance of observed correlation coefficient
•Test the significance of observed partial correlation coefficient
•Test the significance of observed regression coefficient

5. Types / variations
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•One sample t test

•Two sample t test

•Independent samples t test
•Equal variance
•Unequal variance (Welch’s t test)

•Paired t test

6. Assumptions of independent t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Independence of groups
•Data collected follows a continuous or ordinal scale
•Simple random sample
•Normal distribution (Reasonably large sample size)
•Homogeneity of variance

7. Assumptions of paired t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Samples are dependent/paired
•Data collected follows a continuous or ordinal scale
•Simple random sample
•Normal distribution (Reasonably large sample size)
•Homogeneity of variance

8. Formula for different
types of t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

9. One sample t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•To test the null hypothesis that the
population mean is equal to a specified
value μ0

•Degrees of freedom: n − 1

10. Independent samples t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Equal sample sizes, equal variance

•Degrees of freedom: 2n − 1

11. Independent samples t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Equal or unequal sample sizes, equal
variance

•Degrees of freedom: n1 + n2 − 1

12. Independent samples t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Equal or unequal sample sizes, unequal
variance

•Welch’s t test

13. Paired t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Used when the samples are dependent

•Degree of freedom: n - 1

14. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Recall the general steps

1.Null hypothesis
2.Alternative hypothesis
3.Level of significance
4.Test statistic
5.Critical value
6.Decision & interpretation

15. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

16. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

17. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

18. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

19. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

20. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

21. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

22. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

23. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

24. Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

25. What about you?
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh

26. Summary
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•With computers, these tests are
performed easily

•But it is important to know when to and
when not to use them

27. Take home messages
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
•Student’s t test is one of the most commonly used tests
•Remember the types of t test available
•Remember the assumptions for applying the test

28. Thank you!

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