1. 1 Testing Statistical Hypothesis Independent Sample t-Test Heibatollah Baghi, and Mastee Badii

2. 2 Example of Independent Groups t-tests Suppose that we plan to conduct a study to alleviate the distress of preschool children who are about to undergo the finger-stick procedure for a hematocrit (Hct) determination. Note: Hct = % of volume of a blood sample occupied by cells.

3. 3 Example of Independent Groups t- tests, Continued Twenty subjects will be used to examine the effectiveness of the special treatment. 10 subjects randomly assigned to treatment group. 10 assigned to a control group that receives no special preparation.

4. 4 1. Determine the Appropriate Test Testing hypothesis about two independent means (t-test) –Dependent variable = the child’s pulse rate just prior to the finger-stick –Independent variable or grouping variable = treatment conditions (2 levels)

5. 5 1. Determine the Appropriate Test Two samples are independent. Two populations are normally distributed. The assumption of homogeneity of variance. (Examine Levene’s Test) H o :  1 2 =  1 2 H a :  1 2   1 2 If sig. level or p-value is >.05, the assumption is met.

6. 6 2. Establish Level of Significance The convention α =.05 α =.01 α =.001 In this example, assume α = 0.05

7. 7 3. Determine Whether to Use a One or Two Tailed Test H 0 : µ 1 = µ 2 H a : µ 1  µ 2 –Where –µ 1 = population mean for the experimental group –µ 2 = population mean for the control group

8. 8 4. Calculating Test Statistics Group 1Group 2 1100105 2 86 95 3112120 4 80 85 5115110 6 83100 7 90115 8 94 93 9 85107 10105120

9. 9 Rearrange the Data 11001 2 861 31121 4 801 51151 6 831 7 901 8 941 9 851 101051 111052 12 952 131202 14 852 151102 161002 171152 18 932 191072 201202 Experimental Group Control Group

10. 10 4. Calculating Test Statistics (continued) Group 1 (Experimental) Group 2 (Control) -------------------------------------------------------------------------------------------------- X1 X2 ------------ --------------

11. 11 4. Calculating Test Statistics (continued)

12. 12 6. Compare the Computed Test Statistic Against a Tabled Value

13. 13 6. Compare the Computed Test Statistic Against a Tabled Value If we had chosen a one tail test: –H 0 : µ 1 = µ 2 –H a : µ 1 < µ 2 1.73 The null hypothesis can be rejected

14. 14 SPSS Output for Two Sample Independent t-test Example