Testing Statistical Hypothesis Independent Sample tTest Heibatollah Baghi
Testing Statistical Hypothesis Independent Sample t-Test Heibatollah Baghi, and Mastee Badii 1
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. 2
Example of Independent Groups ttests, 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. 3
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) 4
1. Determine the Appropriate Test • Two samples are independent. • Two populations are normally distributed. • The assumption of homogeneity of variance. (Examine Levene’s Test) Ho: 1 2 = 12 Ha: 1 2 12 If sig. level or p-value is >. 05, the assumption is met. 5
2. Establish Level of Significance • The convention • α =. 05 • α =. 01 • α =. 001 • In this example, assume α = 0. 05 6
3. Determine Whether to Use a One or Two Tailed Test • H 0 : µ 1 = µ 2 • Ha : µ 1 µ 2 – Where – µ 1 = population mean for the experimental group – µ 2 = population mean for the control group 7
4. Calculating Test Statistics 1 2 3 4 5 6 7 8 9 10 Group 1 100 86 112 80 115 83 90 94 85 105 Group 2 105 95 120 85 110 100 115 93 107 120 8
Rearrange the Data 1 100 1 2 86 1 3 112 1 4 80 1 6 Experimental 115 Group 83 7 90 1 8 94 1 9 85 1 10 105 1 11 105 2 12 95 2 13 120 2 14 85 2 5 15 16 Control 110 Group 100 1 1 2 2 17 115 2 18 93 2 19 107 2 20 120 2 9
4. Calculating Test Statistics (continued) Group 1 (Experimental) Group 2 (Control) -------------------------------------------------X 1 ------ X 2 ------- 10
4. Calculating Test Statistics (continued) 11
6. Compare the Computed Test Statistic Against a Tabled Value 12
6. Compare the Computed Test Statistic Against a Tabled Value • If we had chosen a one tail test: – H 0 : µ 1 = µ 2 – Ha : µ 1 < µ 2 1. 73 The null hypothesis can be rejected 13
SPSS Output for Two Sample Independent t-test Example 14
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