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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
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
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
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
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
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
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
Formula for different types of t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
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
Independent samples t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
• Equal sample sizes, equal variance
• Degrees of freedom: 2n − 1
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
Independent samples t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
• Equal or unequal sample sizes, unequal variance
• Welch’s t test
Paired t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
• Used when the samples are dependent
• Degree of freedom: n - 1
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
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
Steps in performing t test
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
What about you?
Demystifying statistics! – Lecture 7 SBCM, Joint Program – Riyadh
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
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
Thank you! Email your queries to [email protected]