student's t test and variations

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 sarizwan1986@outlook.com