Independent Samples t-testt Test for Independent MeansHypothesesPooled VarianceFinding Estimated Standard Error using SS (lab approach)Estimated Standard Error using S2y (sample variances – book & HW approach)T observedExample – using S2y infoSlide 9SPSS example(cont.)GSS data exampleSlide 13Independent Samples t-testMon, Apr 12tht Test for Independent MeansComparing two samples–e.g., experimental and control group–Scores are independent of each otherFocus on differences betw 2 samples, so comparison distribution is:–Distribution of differences between meansHypothesesHo: or 1 - 2 = 0 (no group difference) or 1 = 2 Ha = 1 - 2 not = 0 (2 tailed) or 1 - 2 > or < 0 (if 1-tailed)If null hypothesis is true, the 2 populations (where we get sample means) have equal meansCompare T obs to T critical (w/Df= N-2)If |Tobs| > |T crit| Reject NullPooled VarianceT observed will use concept of pooled variance to estimate standard error:–Assume the 2 populations have the same variance, but sample variance will differ…– so pool the sample variances to estimate pop variance–Then standard error used in denom of T obsNote – I’ll show you 2 approaches (you decide which to use based on what data is given to you)Finding Estimated Standard Error using SS (lab approach)Pooled variance (S2p) S2p = (SS1 + SS2) / df1 + df2Where, df1 = N1-1 and df2= N2-1 and SS1 and SS2 are given to youThen use this to estimate standard error: (S xbar 1 –xbar2) = sqrt [(S2p/N1) + (S2p/N2)]Estimated Standard Error (using x notation)Estimated Standard Error using S2y (sample variances – book & HW approach)Skip calculating pooled variance and just estimate standard error:Sybar1 – ybar2 = sqrt [((N1-1)S2y1) + ((N2-1)S2y2)] (N1+N2) – 2* Sqrt [(N1 + N2)/ N1N2]Estimated Standard Error(using y notation)Note: See p. 480 in book for betterrepresentation of this formula!!T observedOnce you’ve estimated standard error, this will be used in T obs:T obs = (xbar1 – xbar2) – (1 - 2) S xbar1 – xbar2Always= 0)EstimatedStandardError(doesn’tmatter ifuse x or ynotation!)Example – using S2y infoGroup 1 – watch TV news; Group 2 – radio news; difference in knowledge?Ho: 1 - 2 = 0; Ha: 1 - 2 not = 0–ybar1 = 24, S21 = 4, N1 = 61–ybar2 = 26, S22= 6, N2 = 21–Alpha = .01, 2-tailed test, df tot = N-2 = 80–S ybar1-ybar2 = sqrt[((60)4) +((20)6)](61 + 21) - 2= 2.12 * sqrt [(61 + 21) / 61 *21] == 2.12 * .253 = .536T obs = (24-26) – 0 .536= -3.73t criticals, alpha = .01, df=80, 2 tailed–2.639 and –2.639|T observed | > |T critical| (3.73 > 2.639)Reject null – there is a difference in knowledge based on news source–(check means to see which is best)…radio news was related to higher knowledge.Note: in lab 22 you’ll use other approach (find SS first, then standard error for T denom); this ex. is how HW will look…SPSS exampleAnalyze 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(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 lab for how to interpretGSS data exampleHo: male - female = 0,–Ha: difference not = 0DV = # siblingsMale xbar = 4.00, female xbar = 3.98In output, 1st look at Levene’s test of equality of variances (2 lines) Ho: equal variances:–Equal variances assumed look at sig value–Equal variances not assumed–If ‘sig value” < .05 reject Ho of equal variances and look at ‘equal variance not assumed’ line –If ‘sig’ value > .05 fail to reject Ho of equal variances and use ‘equal variance assumed’ line(cont.)Here, fail to reject Ho, use equal variances assumed–Next, using that line, look for ‘sig 2-tailed’ value this is the main hypothesis test of mean differences–If ‘sig’ < .05 reject Ho of no group differences–Here, > .05, so fail to reject Ho, conclude # sibs doesn’t differ between
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