Chapter 10 Notes
Chapter 10 Notes PSYCH 2220 - 0020
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This 0 page Class Notes was uploaded by Emma Dahlin on Sunday November 8, 2015. The Class Notes belongs to PSYCH 2220 - 0020 at Ohio State University taught by Anna Yocom in Summer 2015. Since its upload, it has received 15 views. For similar materials see Data Analysis in Psychology in Psychlogy at Ohio State University.
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Date Created: 11/08/15
CHAPTER 10 NOTES PairedSamples t Test 0 Two sample means and a Withingroups design 0 Same or linked people measured twice under two different conditions 0 Eg Repeated measures matched samples longitudinal data etc The TStatistic for Differences Major difference for paired sample t test 0 Test difference scores MD instead of one mean against population mean 0 Difference scores set of scores that represent the difference between 2 measurements 0 Null hypothesis of no difference between means 0 Ho 11 12 1 1 1 20 HDO Distribution of Differences Between Means Frequency 3 5 n rill 3 2 l U ll 2 3 4 Mean weight differences in pounds Steps for Calculating Paired Sample tTests Step 1 Identify the populations distribution and assumptions Step 2 State the null and research hypotheses Step 3 Determine the characteristics of the comparison distribution Step 4 Determine critical values or cutoffs Step 5 Calculate the test statistic Step 6 Make a decision Example of Paired Sample tTest fIZ In 111 116 113 119 121 Study of how 15 volunteers performed on a set of tasks under two conditions Using a 42inch computer monitor compared to using a 15inch monitor Is there any difference in how long it takes them to complete the tasks STEP 1 Identify populations distribution and assumptions 0 O 0 Population 1 People doing tasks using a 42inch monitor Population 2 People performing tasks using a 15inch monitor The distribution a distribution of mean difference scores Use pairedsample ttest same sample tested under 2 different conditions Assumptions DV time which is scale Participants not randomly selected must be cautious with respect to generalizing Do not know if population is normally distributed STEP 2 State null and research hypothesis 0 Null hypothesis People who use a 42inch screen will complete a set of tasks in the same amount of time on average as people who use a 15inch screen Null No difference between means HO u1u2 Research hypothesis People who use a 42inch screen will complete a set of tasks in a different amount of time on average from people who use a 15inch screen H1 ul 2 u2 STEP 3 Determine characteristics of the comparison distribution EI5 In 122 131 127 123 132 Differenc Diff sq DeVIatIo G MD n 11 O O 15 4 16 14 3 9 4 7 49 11 O O MD11 274 0 MD 11 o N of pairs of scores s Sci M 74 J 4301 O l Nil llt5 1 sM 1923 0 B 0 STEP 4 Determine the critical values or cutoffs o Twotailed test p level005 0 df N1 514 o t critical 2776 and 2776 2 596 276 2716 STEP 5 Calculate the test statistic o t Mg L19 11 O 572 SMD 1923 0 STEP 6 Make a decision 0 572 t observed lt 2776 t critical 0 Reject the null hypothesis 0 t4 572 p lt 005 0 Individuals using a 42 inch screen spend a different amount of time on tasks on average than when they use a 15 inch screen 254 25 2 EJE Eu 2 i quot quotiiEl 2 quotiiE Steps for Calculating Cls Step 1 Draw a normal curve with the sample difference between means MD in center Step 2 Indicate bounds of Cl on either end Step 3 Look up the critical tvalues for lower and upper ends of the CIS in the ttable Step 4 Convert the tvalues to raw differences A 95 CI for Difference Between Means Part 1 31115 415 h Ln 5U 35 L39 hLl l Ellinibquot all 566 MDlower 39tSMD MD MDupper tSMD MD Molower 27761923 11 1634 MDupper 27761923 11 566 0 1634 566 p1634 s 135 566 95 o probability is 95 that an interval computed in this way contains true population change or difference in time to complete a task Effect Size 0 used to supplement hypothesis testing Cohen s d 0 d MEAD sD 4301 0 Size of effect Large 0 Interpretation the average time saved using a 42inch monitor compared to a 15 inch one is 256 standard deviations Order Effects ie practice effects 0 How a participant s behavior changes when the DV is presented as second time o For the computer monitor study 0 The time it took them to complete the series of tasks was recorded under each condition 0 Confound Counterbalancing Minimizes order effects by varying order of presentation of different levels of the N from one participant to next 0 In the computer monitor example what could we change New Example 0 Teaching technique to shorten test taking time 0 Will students have a difference in their testtaking time before amp after the teaching technique 0 Sample 4 students measure test taking time 0 Introduce teaching technique measure test taking time again same 4 students Step 1 Identify the populations distribution and assumptions 0 Population 1 People taking test before technique 0 Population 2 People taking test after technique 0 The distribution a distribution of mean difference scores 0 Test Pairedsample ttest Assumptions 0 DVtime which is scale 0 Participants not randomly selected must be cautious with respect to generalizing 0 Do not know whether population is normally distributed Step 2 State the null and research hypotheses o Null hypothesis Ho 11 12 0 Research hypothesis H1 11 7412 Step 3 Determine the characteristics of the comparison distribution 0 Mean difference 3 o 1 o 45 o 42 o 3 o O o O 2 o 44 o 42 0 2 0 1 0 1 o 3 o 44 o 41 o 3 o O o O o 4 0 46 0 42 0 4 0 1 o 1 o MD3 0 X2 S ZlXMl2 SO816 N 1 0 SM i 08164 0408 N Step 4 Determine the critical values or cutoffs dfN1413 o twotailed test p level 005 o t critical 3182 0 So reject if tobt gt tcrit Step 5 calculate test statistic t MD up 3OO408 735 SSMD Step 6 Make a decision 0 735 t observed gt 3182 t critical REJECT THE NULL HYPOTHESIS t3 735 p lt005 Calculating Con dence Intervals 0 Draw a picture of the distribution 0 Indicate the bounds 95 CI 0 25 in each tail mean at 3 0 Look up the t critical 0 3182 0 Convert the t value into raw mean difference 0 MDupper3182 0408 3 430 o Molower 3182 0408 3 170 o 170 430 o This group does not include 0 which would mean no difference SPSS for Repeated Measures Paired Samples Statistics 5tdl 5tdl Error Mean N Deviation Mean Pair 1 timel 445 4 05 APE time2 41500 4 50000 25000 Paired Samples Correlations I I N ICorrelation I Sig I IPairiL timel etimeE a 522 wa Paired Samples Te st Paired Differences 05 Con dence Interval of ad Ettll Error 5 D39 EfME Sig 2 Mean Deviation Mean Lower I Upper 1 dl f tailedli Pair 1 time1 time2 30GUUEI 11550 ADS EE 1TUUTT I 429923 T345 3 EDGE Effect Size Cohen s d d 30816368 Students were faster on average by 368 sd after intervention Review 0 A psychologist designed a new treatment for depression He predicted depressive symptoms would decrease following treatment 0 Calculate and interpret the t statistic p 05 rreeatmen POSt39 Subje t treatment ct d depression epreSSI score on score 1 16 14 LOOONOWU39lbUUN O 17 19 18 13 19 14 2O 18 16 13 3O 25 25 27 38 2O 2O 20 MY NOTES ON CHAPTER 1O We use a pairedsample t test when we have a Withingroups design the same group is studied before and after 0 EX same people are weighed before and after the holiday season 0 Comparing two samples and every participant is in both samples Major difference with pairedsample t tests is that we have to create difference scores for every participant 0 Now working with a distribution of mean differences In a pairedsample ttest each participant has two scores one in each condition 0 Ideally a positive difference score indicates an increase and a negative difference score indicates a decrease 0 Comparison distribution is based on null hypothesis that posits no mean difference mean differenceO 0 To get difference scores you look at what happens when going from control condition to the experimental condition We can calculate a CI for a pairedsamples ttest lf 0 is NOT in the Cl then it is not plausible that there is no difference bt the sample and population mean difference 0 We reject null when the Cl doesn t include 0 Effect size lets us know if about the size of the observed effect and lets us know if a statistically signi cant nding is likely to be practically important Order effects refers to how a participant s behavior changes when the dependent variable is presented for a second time sometimes called practice effects Counterbalancing minimizes order effects by varying the order of presentation of different levels of the independent variable from one participant to the next
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