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**The t Test for Independent Means**

Chapter 8 The t Test for Independent Means Part 2: Oct. 7, 2014

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**Effect Size for the t Test for Independent Means**

If need to estimate effect size after a completed study, use: Use Cohen’s guidelines to interpret: around .2 or -.2 small, around .5 or -.5, med, around .8 or -.8, large S pooled = pooled estimate of SD (see Part 1 notes)

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**Power for the t Test for Independent Means (.05 significance level)**

Use Table 8-5 to find study’s power, given sample size, # tails, effect size (see previous formula) Note: Assumes Equal group sizes

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**Power for the t Test for Independent Means**

Table 8-5 assumed equal group sizes Power when sample sizes are not equal Harmonic mean – gives equivalent sample size for how much power you’d have w/2 equal samples Can then use Power Table w/this as mean

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Harmonic Mean Example Example from pt 1 notes (TV/radio news), we had N1 = 61, N2 = 21 What is the harmonic mean here? What is its interpretation? Note – we actually had 82 participants, but how much power did we have?

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Harmonic Mean (cont.) **Main point – try to get equal group sizes, otherwise you’re penalized in terms of power Once you find harmonic mean, can use that as group size in Table 8-5

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**Approximate Sample Size Needed for 80% Power (.05 significance level)**

Use Table 8-6 if need to plan sample size. Need to know estimated effect size and # tails

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**Assumptions of Ind T-test**

1) Each of the population distributions (from which we get the 2 sample means) follows a normal curve 2) The two populations have the same variance This becomes important when interpreting Ind Samples t using SPSS SPSS provides 2 sets of results for ind samples t-test: 1st assumes equal variances in 2 groups 2nd assumes unequal variances You have to check output to see which of these is true SPSS provides “Levene’s test” to indicate whether the 2 groups have equal variance or not. use the results for either equal or unequal variances (depending on results of Levene’s test…)

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**SPSS example Analyze Compare Means Independent Samples t**

Pop up window…for “Test Variable” choose the variable whose means you want to compare. For “Grouping Variable” choose the group variable After clicking into “Grouping Variable”, click on button “Define Groups” to tell SPSS how you’ve labeled the 2 groups

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(cont.) Pop up window, “Use Specified Values” and type in the code for Group 1, then Group 2, hit “continue” For example, can label these groups anything you’d like when entering data. Are they coded 0 and 1? 1 and 2?…etc. Specify it here. Finally, hit OK See output example in class for how to interpret…

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**SPSS Output for Ind T-test**

“Group Statistics” section at top reports means for the 2 groups “Independent Samples Test” section reports both Levene’s test and the actual t-test: First, check Levene’s test to determine whether the Null Hypothesis (the 2 groups have equal variances) is rejected or not. So, to meet the t-test assumption, we want to fail to reject this null… If not, we can still interpret t, but need to use adjusted stats

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**Under the “Levene’s test” section, if “Sig” is <**

Under the “Levene’s test” section, if “Sig” is < .05 (or your alpha level), REJECT Null assumption of equal variances & interpret remaining output labeled “Equal variances NOT assumed” But if “Sig” is > .05, we fail to reject Null assumption of equal variances & interpret the line labeled “Equal variances assumed” Next, interpret “t-test for equality of means”. Now the null states that the 2 group means are equal. Notice “t” is your t observed, its df, and sig value. If “sig” < .05 reject Null stating group means are equal; conclude the 2 group means differ significantly Go back to info on which group mean is higher/lower to interpret. If sig > .05, fail the reject Null, conclude group means are equal

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