# one way ANOVA

| September 27, 2015

one way ANOVA

Paper details:
https://class.waldenu.edu/courses/1/USW1.29904.201610/db/_54296557_1/APA%20Summary%20for%20Oneway%20Repeated%20Measures%20ANOVA.pdf http://studysites.sagepub.com/field4e/study/smartalex/chapter14.pdf Descriptive Statistics N Minimum Maximum Mean Std. Deviation Dr. Field 8 62 78 68.88 5.643 Dr. Smith 8 58 73 64.25 4.713 Dr. Scrote 8 54 75 65.25 6.923 Dr. Death 8 45 65 57.38 7.909 Valid N (listwise) 8 Within-Subjects Factors Measure: MEASURE_1 lecturer Dependent Variable 1 tutor1 2 tutor2 3 tutor3 4 tutor4 Descriptive Statistics Mean Std. Deviation N Dr. Field 68.88 5.643 8 Dr. Smith 64.25 4.713 8 Dr. Scrote 65.25 6.923 8 Dr. Death 57.38 7.909 8 Multivariate Testsa Effect Value F Hypothesis df Error df Sig. Partial Eta Squared lecturer Pillai’s Trace .741 4.760b 3.000 5.000 .063 .741 Wilks’ Lambda .259 4.760b 3.000 5.000 .063 .741 Hotelling’s Trace 2.856 4.760b 3.000 5.000 .063 .741 Roy’s Largest Root 2.856 4.760b 3.000 5.000 .063 .741 a Design: Intercept Within Subjects Design: lecturer b Exact statistic Mauchly’s Test of Sphericitya Measure: MEASURE_1 Within Subjects Effect Mauchly’s W Approx. Chi-Square df Sig. Epsilonb Greenhouse-Geisser Huynh-Feldt Lower-bound lecturer .131 11.628 5 .043 .558 .712 .333 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a Design: Intercept Within Subjects Design: lecturer b May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table. Tests of Within-Subjects Effects Measure: MEASURE_1 Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared lecturer Sphericity Assumed 554.125 3 184.708 3.700 .028 .346 Greenhouse-Geisser 554.125 1.673 331.245 3.700 .063 .346 Huynh-Feldt 554.125 2.137 259.329 3.700 .047 .346 Lower-bound 554.125 1.000 554.125 3.700 .096 .346 Error(lecturer) Sphericity Assumed 1048.375 21 49.923 Greenhouse-Geisser 1048.375 11.710 89.528 Huynh-Feldt 1048.375 14.957 70.091 Lower-bound 1048.375 7.000 149.768 Tests of Within-Subjects Contrasts Measure: MEASURE_1 Source lecturer Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared lecturer Linear 448.900 1 448.900 4.938 .062 .414 Quadratic 21.125 1 21.125 .586 .469 .077 Cubic 84.100 1 84.100 3.689 .096 .345 Error(lecturer) Linear 636.400 7 90.914 Quadratic 252.375 7 36.054 Cubic 159.600 7 22.800 Tests of Between-Subjects Effects Measure: MEASURE_1 Transformed Variable: Average Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Intercept 130816.125 1 130816.125 8858.166 .000 .999 Error 103.375 7 14.768 1. Grand Mean Measure: MEASURE_1 Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound 63.938 .679 62.331 65.544 Estimates Measure: MEASURE_1 lecturer Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound 1 68.875 1.995 64.158 73.592 2 64.250 1.666 60.310 68.190 3 65.250 2.448 59.462 71.038 4 57.375 2.796 50.763 63.987 Pairwise Comparisons Measure: MEASURE_1 (I) lecturer (J) lecturer Mean Difference (I-J) Std. Error Sig.b 95% Confidence Interval for Differenceb Lower Bound Upper Bound 1 2 4.625* 1.085 .022 .682 8.568 3 3.625 2.841 1.000 -6.703 13.953 4 11.500 4.675 .261 -5.498 28.498 2 1 -4.625* 1.085 .022 -8.568 -.682 3 -1.000 2.563 1.000 -10.320 8.320 4 6.875 4.377 .961 -9.039 22.789 3 1 -3.625 2.841 1.000 -13.953 6.703 2 1.000 2.563 1.000 -8.320 10.320 4 7.875 4.249 .637 -7.572 23.322 4 1 -11.500 4.675 .261 -28.498 5.498 2 -6.875 4.377 .961 -22.789 9.039 3 -7.875 4.249 .637 -23.322 7.572 Based on estimated marginal means * The mean difference is significant at the .05 level. b Adjustment for multiple comparisons: Bonferroni. Multivariate Tests Value F Hypothesis df Error df Sig. Partial Eta Squared Pillai’s trace .741 4.760a 3.000 5.000 .063 .741 Wilks’ lambda .259 4.760a 3.000 5.000 .063 .741 Hotelling’s trace 2.856 4.760a 3.000 5.000 .063 .741 Roy’s largest root 2.856 4.760a 3.000 5.000 .063 .741 Each F tests the multivariate effect of lecturer. These tests are based on the linearly independent pairwise comparisons among the estimated marginal means. a Exact statistic

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