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# Dependent T Test

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### Dependent T Test

1. 1. Week 9:Dependent t-test Paired Samples t- test for two dependent samples 1
2. 2. Dependent Samples  When have two dependent or related samples. • Same group measured twice (Time 1 vs. Time 2; Pretest and Posttest). • Samples are matched on some variable.  Each score in one sample is paired with a specific score in the other sample.  Such data are correlated data. 2
3. 3. Examples of Research Questions:  Is there a significant difference students’ mathematics achievement when taught through traditional methods and hands-on problem-solving method? IV = method taught (values = traditional [baseline], hands-on problem-solving) DV = mathematics achievement (score, continuous) 3
4. 4. Examples of Research Questions:  Is there a significant difference in morbidly obese students’ pre-exercise weight and post-exercise weight?  Rather than comparing the means of the pre and post, we compare the pre and post scores for each individual. IV: Time (pre or post) DV: Weight (Value = pounds, continuous) 4
5. 5.  An investigator for NASA examines the effect of cabin temperature on reaction time. A random sample of 10 astronauts and pilots is selected. Each person’s reaction time to an emergency light is measured in a simulator where the cabin temperature is maintained at 70 degrees F and again the next day at 95 degrees F. IV: Temperature (values = 70F or 95F) DV: Reaction Time (Value = seconds, continuous) 5
6. 6.  Is there a significant difference between husband and wife’s annual income? IV: Spouse (values = husband, wife) DV: Annual income (Value = dollars, continuous) 6
7. 7. Steps in hypothesis testing: 7
8. 8. Step 1:State the hypotheses Null hypothesis: H 0:µ D = 0 or Ho: µD ≥ 0 or Ho: µD ≤ 0 Alternative hypothesis: H 1:µ D ≠0 or H 1:µ D >0 or H 1:µ D <0 * Subscript D indicates difference. 8
9. 9. Step 2: Set Criterion for Rejecting HO 1) Compute degrees of freedom df = n – 1 whereby n = number of pairs 2) Set alpha level 3) Locate critical value(s)  Table C. 3 (page 638 of text) – same as in an Independent t - test 9
10. 10. Step 3: Compute test statistic Whereby: D = x2 − x1 D after-before Sum of individual t= D = ∑D n differences S D S = Sample Standard Deviation S D D of difference (D) scores, divided by n 10
11. 11. D t= Example Computation: S D ∑ D = 1+1+1+ 3 + 0 + 2 = 8 Before After D = after - before D= ∑ D = 8 = 1.3 Standard 5 8 6 9 1 1 n 6 deviation of the 4 5 1 differences =S 1.03 3 6 3 S D D n = 6 = .42 7 7 0 Number of 8 10 2 pairs D 1 .3 t= = = 3.09 S D .42 11
12. 12. Step 4: Compare Test Statistic to Criterion  Use t distribution in the appendix to find the critical values (given alpha level, df, and directionality of the test).  In this example, df = n-1= 6-1 = 5 12
13. 13. Step 5: Make decision  Use t distribution in the appendix to find the critical values (given alpha level, df, and directionality of the test).  The graph on the right shows an example of two-tailed test with the c.v. equal to ± 2.776.  For our example, use Table C.3 on page 638 to find out the critical value(s). With alpha = 0.05 and df = 5, the critical values are ± 2.571 (two-tailed test). 13