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Chapter 8

Chapter 8. The t Test for Independent Means Part 2: Oct. 15, 2013. Effect Size for the t Test for Independent Means. Before conducting a study, if you need to estimate effect size …(to figure power). 1 = estimate of Group 1 mean. 2 = best guess of Group 2 mean. = estimated pop

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Chapter 8

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  1. Chapter 8 The t Test for Independent Means Part 2: Oct. 15, 2013

  2. Effect Size for the t Test for Independent Means • Before conducting a study, if you need to estimate effect size…(to figure power) 1 = estimate of Group 1 mean 2 = best guess of Group 2 mean • = estimated pop SD (may guess) • Use Cohen’s guidelines to interpret… .2=small, .5=medium, .8=large

  3. Effect Size for the t Test for Independent Means • If need to estimate effect size after a completed study, use: M1 = actual mean for Group 1 M2 = actual mean for Grp 2 S pooled = pooled estimate of SD (see Part 1 notes)

  4. Power for the t Test for Independent Means(.05 significance level) Use Table 8-4 to find study’s power, given sample size, # tails, effect size (see previous formula) Note: Assumes Equal group sizes

  5. Power for the t Test for Independent Means • Table 8-4 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

  6. 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?

  7. 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 8-4.

  8. Approximate Sample Size Needed for 80% Power(.05 significance level) Use Table 8-5 if need to plan sample size. Need to know estimated effect size and # tails

  9. 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…)

  10. 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

  11. (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…

  12. 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

  13. 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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