T-test: Between and within

1. T-test: Between and within Chong Ho (Alex) Yu

2. One-sample test • One-sample z-test and one-sample t-test • Test the sample mean against the population mean • To see whether there is a big gap between the sample and the population • To see whether the sample comes from or belongs to the population. • Seldom used. Why?

3. Before Why, ask how first • Enter the population mean and SD to do the z-test • Enter the mean only to do the t-test. • But if you already know about the population, then you don’t need statistics. • Usually you don’t know!

4. Test results

5. Two independent sample t-test • You need two independent groups e.g. boys and girls. • Test whether there is a performance gap between boys and girls

6. T-test • T-test is a test to get the t-ratio. • The difference between two means based on the standard deviation. • Virtually any comparison test is about looking at the difference adjusted by a common standard • Otherwise, it will be comparing apples and oranges!

7. Before you do the test… • Spot outliers using the boxplot

8. 2 independent sample t-test results • What are these? • Standard error • Upper and Lower CL • P value

9. I come here to bring division! • In experiments we want to have two comparable groups; we want to reduce bias. • We will divide the class into two groups • But the two groups must be equivalent or symmetrical • i.e. the same numbers of two genders; the same numbers of different races; the same numbers of different SES, religion…etc. • Can you do that?

10. 2 dependent sample t-test • Also known as 2 correlated sample t-test • Paired t-test • When you have no control group… • You are your own control. The person that is most similar to you is: YOURSELF!

11. Before you do the test… • Spot ceiling or floor effects

12. Matched pairs

13. Put independent and dependent together

14. Put them together

15. Assignment 14a • Download the data set “between within” from Chapter 14 folder. • Run a 2-sample independent t-test. • Spot and exclude outliers, if there is any. • Use the midterm as the DV • Use sex (gender) as the IV • Report the confidence intervals, the t-ratio and the p value • Is there any performance gap between boys and girls?

16. Assignment 14b • Use the same data set • Run a paired t-test • Use test and midterm as the variables • Spot and exclude students that show floor or ceiling effects, if there is any. • Report the confidence intervals, the t-ratio and the p value • Is there any significant change/growth between the pretest and the midterm?