Question

Answer the within-subjects ANOVA questions using the data below. Use a -0.05. 1 2 3 53 49 47 31 51 34 44 44 39 36 34 39 30 29 46 34 39 37 36 34 47 25 35 30 27 33 28 40 a) Compute the preliminary statistics below. SSGG - ; dfbg - ; dfes SSE - ; dfe - SST ; df = SSBs b) Compute the appropriate test statistic(s) to make a decision about How critical value - 1; test statistic Decision: -Select-- c) Compute the corresponding effect size(s) and indicate magnitude(s). m2 -Select- . d) Make an interpretation based on the results. O At least one week differs on the GRE verbal score. No week is different on GRE verbal score. e) Regardless of the Ho decision in b), conduct Tukey's post hoc test for the following comparisons: 2 vs. 3: difference = significant: --Select- 1 vs. 4: difference ; significant: -Select- f) Regardless of the Ho decision in b), conduct Scheffe's post hoc test for the following comparisons: 1 vs. 3: test statistic - ; significant: ---Select- 1 vs. 4: test statistic - ; significant: -Select-

Answer 1

Testing The Null & Alternative hypothesis, Hoce : l1. = 12. = 113, =lly. ie There is no significance bem the GRE verbal score # HIG! At least two of eli MB els fel4 are different ie At least two of the raters difter significandly all GRE observations Total Score 1 2 34 5 6 153 4947 31 $1 34 44 309 44 39 36 34 89 30 29 251 3 46 34/39 37 36 34 47 273 25 35 130/27 133 28 140 218 Total 168 157 152 29 159 126 160 G=1057 Bi 4

Raw s.s= 532+42 + = 41019 + 282+402 (1051)2 CF = GR N 39450,0357 28 N = 28, n=9, K = 49 T.S.s= Raw sos- 41019 - 39450.0357 IT.S.S. = 1568.9643 ISST-1568.9643 SSB G = S.S. duelo Beth GRE verbal Score S.SBe = E ti? C.F. n (30g)²+(251)²+(273) 34 (2187 7. 39450.0357 IS.Sole 626.3929 SS BS = { Bj 2 ch (168)²+(157]²+ (152)²+(1293²+ (159]²+ (126) 2+ (160)2 39950.0357 ISSAS 393,7143

SSF - SS1-SSBG-SS BS = 1568.9643- 626,3929 - 393,7143 SSE = 548.8571 Degrees of freedom df BG = k-1 = 4-1 2 3 dFB G = 3 dfgs . n-=7-1 = 6 Id FBS =6 dfat = (nt CK- - 3x6 = 18 dfe=18 [dfy N-) = 28-1 = 27 Id fq = 27 ANOVA Tabler Source 8.5 df MS F Beth GRE verbal Score 626.3929 3 208.7976 6.8476 Ben score 1393.7143 6 65,6190 211520 Error 5481857) 18 30.4921 Total 1568.9643 27

b) critical value Fat dtz (3,18), P=0.05 4 antical F = 3,1599 Tes Test statistic F = 6,8476 Decisions Reject Ho, effect size (202) SSBG SS Total m2 = 626,3929 1568. 9643 n - 0.3992 39.92% Beth GRE verbal score 39.92% associated with d) Interpretation or At least one week differs on the GRE verbal score