Hypothesis Testing Using z- and t-tests In hypothesis testing, one ...

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B. Weaver (24-Aug-2010) z- and t-tests ... 14Table 4: Data for paired t-test example.Popularity RatingsCandidate Before After Difference1 42 43 12 41 45 43 50 56 64 52 54 25 58 65 76 32 29 -37 39 46 78 42 48 69 48 47 -110 47 53 6I entered these BEFORE and AFTER scores into SPSS, and performed a paired t-test as follows:T-TESTPAIRS= after WITH before (PAIRED)/CRITERIA=CIN(.95)/MISSING=ANALYSIS.This yielded the following output.Paired Samples StatisticsPair1AFTERBEFOREStd. ErrorMean N Std. Deviation Mean48.60 10 9.489 3.00145.10 10 7.415 2.345Paired Samples CorrelationsPair 1AFTER & BEFOREN Correlation Sig.10 .940 .000Paired Samples TestPair 1AFTER - BEFOREPaired Differences95% ConfidenceInterval of theStd. Error DifferenceMean Std. Deviation Mean Lower Upper t df Sig. (2-tailed)3.50 3.567 1.128 .95 6.05 3.103 9 .013The first output table gives descriptive information on the BEORE and AFTER popularityratings, and shows that the mean is higher after politicians have endorsed increased spending.
B. Weaver (24-Aug-2010) z- and t-tests ... 15The second output table gives the Pearson correlation (r) between the BEFORE and AFTERscores. (The correlation coefficient is measure of the direction and strength of the linearrelationship between two variables. I will say more about it in a later section called Testing thesignificance of Pearson r.)The final output table shows descriptive statistics for the AFTER – BEFORE difference scores,and the t-value with it’s degrees of freedom and p-value.The null hypothesis for this test states that the mean difference in the population is zero. In otherwords, endorsing increased social spending has no effect on popularity ratings in the populationfrom which we have sampled. If that is true, the probability of seeing a difference of 3.5 pointsor more is 0.013 (the p-value). Therefore, the politician would likely reject the null hypothesis,and would endorse increased social spending.The same example done using a one-sample t-testEarlier, I said that the paired t-test is really just a single-sample t-test done on difference scores.Let’s demonstrate for ourselves that this is really so. Here are the BEFORE, AFTER, and DIFFscores from my SPSS file. (I computed the DIFF scores using “compute diff = after – before.”)BEFORE AFTER DIFF42 43 141 45 450 56 652 54 258 65 732 29 -339 46 742 48 648 47 -147 53 6Number of cases read: 10 Number of cases listed: 10I then ran a single-sample t-test on the difference scores using the following syntax:T-TEST/TESTVAL=0/MISSING=ANALYSIS/VARIABLES=diff/CRITERIA=CIN (.95) .The output is shown below.One-Sample StatisticsDIFFStd. ErrorN Mean Std. Deviation Mean10 3.50 3.567 1.128
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Hypothesis Testing Using z- and t-tests In hypothesis testing, one ...

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