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Unformatted text preview: Review of Paired Ttests A paired ttest is used when we have observations for the same group of people at two time points. Each person gets a difference score. Observation Observation Time 1 Time 1 Time 2 Time 2 Difference Difference 1 1 x x 11 11 x x 21 21 X X d1 d1 =X =X 11 11XX 21 21 2 2 x x 12 12 x x 22 22 i i x x 1i 1i x x 2i 2i n n x x 1n 1n x x 2n 2n X X d2 d2 =X =X 12 12XX 22 22 X X di di =X =X 1i 1iXX 2i 2i X X dn dn =X =X 1n 1nXX 2n 2n The null hypothesis is: H : There is no difference between the means. H : 1 = 2// D = 0 (D i = X 1 i X 2 i ) The alternative hypothesis is: H 1 : There is a difference between the means. H 1 : 1 2// D 0 ( D i = X 1 i X 2 i ) We use the paired ttest to see if the means are different between scores at two different points in time. Note: Research Questions Research Questions Hypothesis Hypothesis No Difference No Difference Any Difference Any Difference Pop 1 Pop 1 Pop 2 Pop 2 Pop 1 &lt; Pop 2 Pop 1 &lt; Pop 2 Pop 1 Pop 1 Pop 2 Pop 2 Pop 1 &gt; Pop 2 Pop 1 &gt; Pop 2 H H D = 0 = 0 D D H H 1 D D &lt; 0 &lt; 0 D &gt; 0 &gt; 0 Be careful with identifying hypotheses for directional tests. You believe that 2 has the higher mean. You believe that 1 has the higher mean. Once again, the paired ttest has certain assumptions. 1. Sample of paired observations is randomly drawn. 2. Both sets are normally distributed with same variance. 3. The established pairs of observations are correlated. Formulae for paired ttest 1 2 1 2 d d X X X X X X t s s = = SE of Mean Difference d d X X s s n = 1 df v n = = 2 SD of Difference 1 d d X X S n = Because we only have one group of people, the degrees of freedom is n1. Example 1 You work in Human Resources. You want to see if there is a difference in test scores following a new training program. You collect the following test score data: Name Before (1) After (2) Sam 85 94 Tamika 94 87 Brian 78 79 Mike 87 88 Using a twotailed test with alpha = 0.05, was the training effective? 1. State the null and alternative hypotheses....
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This note was uploaded on 01/27/2011 for the course EDPSY 400 at Pennsylvania State University, University Park.
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 MURPHY,PRICILLAK

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