Week 12 Notes - Psychology 211
Week 12 Notes - Psychology 211 Psychology 211
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This 5 page Class Notes was uploaded by Kennedy Patterson on Monday April 6, 2015. The Class Notes belongs to Psychology 211 at University of Alabama - Tuscaloosa taught by Andre Souza in Spring2015. Since its upload, it has received 151 views. For similar materials see Psychology 211-003 Elem Statistical Methods in Psychlogy at University of Alabama - Tuscaloosa.
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Date Created: 04/06/15
Psychology 211 330154315 Independent Samples ttest Comparing Two Means One of the most common uses of the ttest involves testing the difference between 2 independent samples 0 Boys vs girls 0 Bilinguals vs monolinguals 0 Young vs old 0 Condition A vs condition B The main question is whether the two groups differ significantly from each other to justify the conclusions that the two groups were drawn from different populations Because this is a parametric test we need to know more about the sampling distribution of the differences between two means Same population if G Sample A G Different population if A amp B are the same A amp B are different Sample B G P l IJ f Combine all sample means 0 Sampling Distribution of i Means Normally Distributed IJ Standard Deviation of the Distribution Standard Error g 1A 2 GA distribution of differences B I GB fB IJB IJA Psychology 211 330154315 Independent Samples ttest Sampling Distribution of the difference between means Imagine two different populations A and B with means JB JA respectively Each distribution has its own variance 02A and 023 Now you randomly draw a sample of size n from distribution A and a sample of size n from distribution B 0 Then you record the mean for eachsample IA and I3 and the difference between these means IA I3 0 Then you repeat this procedure 10000 times 0 What would the distribution look like Example with numbers Population A J 20 and 02 4 Population B J 30 and 02 9 A 2 IJA 20 0A2 4 H3 IJA 10 B IJA 30 0A 9 Sampling Distribution of the difference between means The mean of the sampling distribution of the differences between two independent means is JA JB What about its standard error What would the standard error of the sampling distribution of means for Population A be m 51 A f r39n What would the standard error of the sampling distribution of means for Population B be 1 55 g 39n The SE of the sampling distribution of the difference between means the variance sum law states that the variance of the sum or the difference of two independent variables is equal to the sum of their variances imagine you want to know the sum of squares of the difference between 2 populations A and B first you express each score X in each population in terms of its departure from its own mean XA UA and X3 UB Psychology 211 330154315 Independent Samples ttest Then you calculate the difference between these residuals square them and sum them up Sum of Squares 9 1quotquot X5 5 The SE of the sampling distribution of the difference between means ZXA UA XB uB2 is the Sum of Squares of the difference between population A and population B 0 Then XA lJA XB lJBXA lJA XB lJB XA W2 XB lJB2 2XA HAXXB lJB Apply summation ZXA W2 ZXB lJB2 2ZXA HAXXB lJB The term ZXA LIAXB LIB is the covariance of population A and B Because the populations are independent uncorrelated the covariance is zero The SE of the sampling distribution of the difference between means We already know that if we divide ZXA LIA2 by NA we get the variance of population A o If we divide ZXB pB2 by NB we get the variance of population B Therefore 2 Xlxa 02 220 s 592 a v Iquot g N N5 03922 39Af V For two independent samples the variance of the difference between them is the sum of the two individual variances The SE of the sampling distribution of the difference between means is 55 55 SS f b C Ct H a 39 0 no Example Processing fluency how easy we process information influences our decision making We tend to dislike things that are harder to process We also tend to believe things that are easier to process To test that I presented 30 people with trivia sentences that were either easy or difficult to read A dim Ian 115 hips wound Ila edge Psychology 211 330154315 Independent Samples ttest I asked them to rate using a scale ranging from 1 to 7 whether they believe the sentence they read 1 means I do not believe it and 7 means I believe it The 30 participants were randomly assigned to one of two groups one that only saw the difficult font and the other that only saw the easy font Each participant read 70 sentences and rated each one For each participant an average score was calculated and this average score served as the dependent variable Here is all the information needed to perform an independent samples t test o Difficult 39 Mean 334 Easy Difficult s 071 n 15 0 Easy 2 2 uA 5 24 uA 3 34 2433 3524 5 1 23 s o 71 39 n 15 n 15 n 15 t va t 524 334 524 334 5 13 39 5 sf 5123 71 037 39 15 0 P o 39 390 39 i i Psychology 211 330154315 Independent Samples ttest Equations to Remember 5 amp SE measure of difference z standardized score that represents a z score score X z X 1 X r zscore of 3 X is 3 standard deviations s of the mean z test one sample z standardized score that z f I 9 f I represents a score X SE 0 H ztest of 3 I is 3 SE from p F I t testone sample a t test two samplesrelated t QM o QM t represents difference of mean WW t test twosamplesindependent t A1 39 15 O Variance Sum Law 9 sum variances no 5A 5E matter what nA nB ttest of 518 Dmean is 518 SE from O
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