Student's t test and variations
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This document discusses the t test and its variations. It describes the t test as a statistical significance test introduced in 1908. The t test can be used to test single or double sample means and the significance of observed values. There are different types of t tests, including one sample t tests, independent samples t tests, and paired t tests. The document reviews the assumptions, formulas, and steps to perform the different t tests, noting they can now be easily conducted with computers.
Student's t test and variations
- 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! Email your queries to sarizwan1986@outlook.com