Aron chpt 8 ed

Basic Principle of the t Test: Estimating the Population Variance from the Sample Scores ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved

The t Distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hypothesis Testing When the Population Variance Is Unknown ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

EXAMPLE– Aron, Coups, Aron (pg 264) ,[object Object]

Step 1: Restate the question about the research hypothesis and a null hypothesis about the populations. ,[object Object]

Step 1: Restate the question about the research hypothesis and a null hypothesis about the populations. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2: Determine the characteristics of the comparison distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2: Determine the characteristics of the comparison distribution (cont.) ,[object Object],[object Object],[object Object],X M (X-M) (X-M) 2 14 - 9 " = 5 25 8 - 9 " = " -1 1 6 - 9 " = " -3 9 5 - 9 " = " -4 16 13 - 9 " = 4 16 10 - 9 " = 1 1 10 - 9 " = 1 1 6 - 9 " = " -3 9 72 78 8 Sample M = 9 df = 8-1 (7)

Step 2: Determine the characteristics of the comparison distribution (cont.) ,[object Object],[object Object],[object Object],S 2 = 11.14 N = 8 (# scores in sample)

Step 2: Determine the characteristics of the comparison distribution (cont.) ,[object Object],[object Object],[object Object]

Step 3: Determine the significance cutoff ,[object Object],[object Object],[object Object],[object Object],H a = “Participants given the experimental procedure will score differently than the general population”

Step 4: Determine your sample’s score on the comparison distribution. M = 9 Pop. M = 6 S M = 1.18

Step 5: Decide whether to reject the null hypothesis. ,[object Object],[object Object],[object Object],[object Object],[object Object]

The t Test for Dependent Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Steps for a t Test for Dependent Means ,[object Object],[object Object],[object Object],[object Object],[object Object]

EXAMPLE– Aron, Coups, Aron (pg 265) ,[object Object],[object Object]

Step 1: Restate the question about the research hypothesis and a null hypothesis about the populations. ,[object Object],[object Object],[object Object],[object Object]

Step 2: Determine the characteristics of the comparison distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2: Determine the characteristics of the comparison distribution (cont.) ,[object Object],[object Object],Participant Before After Difference (After-Before) 1 10.4 10.8 0.4 2 12.6 12.1 -0.5 3 11.2 12.1 0.9 4 10.9 11.4 0.5 5 14.3 13.9 -0.4 6 13.2 13.5 0.3 7 9.7 10.9 1.2 8 11.5 11.5 0 9 10.8 10.4 -0.4 10 13.1 12.5 -0.6 117.7 119.1 1.4

Step 2: (cont.) ,[object Object],[object Object],(df = N-1) Participant Before After Difference (After-Before) Deviation (Difference - M) Squared Deviation 1 10.4 10.8 0.4 0.26 0.068 2 12.6 12.1 -0.5 -0.64 0.410 3 11.2 12.1 0.9 0.76 0.578 4 10.9 11.4 0.5 0.36 0.130 5 14.3 13.9 -0.4 -0.54 0.292 6 13.2 13.5 0.3 0.16 0.026 7 9.7 10.9 1.2 1.06 1.124 8 11.5 11.5 0 -0.14 0.020 9 10.8 10.4 -0.4 -0.54 0.292 10 13.1 12.5 -0.6 -0.74 0.548 117.7 119.1 1.4 3.484 M = 0.14

Step 2: (cont.) ,[object Object],[object Object],[object Object],[object Object]

Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. ,[object Object],[object Object],[object Object],“ Participants given the experimental procedure will have an increase in scores following the procedure”

Step 4: Determine the sample’s score on the comparison distribution. ,[object Object]

Review of the Z test, t Test for a Single Sample, and t Test for Dependent Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved

Assumptions of the t Test for a Single Sample and t Test for Dependent Means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Copyright © 2011 by Pearson Education, Inc. All rights reserved

Aron chpt 8 ed

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