Manova Statistical Assignment (Case Study Sample)

MANOVA Statistics Assignment Student Name Institution Affiliated Statistics Assignment Question 1: State the research hypotheses. The dependent variables in the analysis are: Reading comprehension, copy word, composition, and write word. The independent variable in the analysis are: Ability to perform different reading/writing abilities The hypothesis for the MANOVA analysis HO: There are significant differences between individuals in the three groups of abilities with respect to their reading comprehension, ability to copy words, composition, and writing words. H1: There are no significant differences between individuals in the three groups of abilities with respect to their reading comprehension, ability to copy words, composition, and writing words. The hypothesis for the MANCOVA analysis HO: There are significant differences between individuals in the three groups of abilities with respect to their reading comprehension, ability to copy words, composition, and writing words with raven test as a covariate. H1: There are no significant differences between individuals in the three groups of abilities with respect to their reading comprehension, ability to copy words, composition, and writing words with raven test as a covariate. 2) Perform MANOVA for this data set.Does this meet the assumption of Homoscedasticity? Explain. Box's Test of Equality of Covariance Matricesa Box's M 17.634 F .864 df1 20 df2 295448.499 Sig. .635 Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups. a. Design: Intercept + ablity The assumption of homoscedasticity of the dependent variables is valid. This is because the p-value of the homoscedasticity test is greater than 0.05 which is therefore not significant (Cook, 2013). Accordingly, an Anova test an be conducted to investigate the association between the dependent and independent variables (Huberty & Petoskey, 2000). Between-Subjects Factors Value Label N ablity 1.00 low ability 98 2.00 average 96 3.00 high ability 96 Multivariate Testsa Effect Value F Hypothesis df Error df Sig. Intercept Pillai's Trace .968 2178.846b 4.000 284.000 .000 Wilks' Lambda .032 2178.846b 4.000 284.000 .000 Hotelling's Trace 30.688 2178.846b 4.000 284.000 .000 Roy's Largest Root 30.688 2178.846b 4.000 284.000 .000 ablity Pillai's Trace .201 7.955 8.000 570.000 .000 Wilks' Lambda .800 8.396b 8.000 568.000 .000 Hotelling's Trace .250 8.836 8.000 566.000 .000 Roy's Largest Root .247 17.595c 4.000 285.000 .000 a. Design: Intercept + ablity b. Exact statistic c. The statistic is an upper bound on F that yields a lower bound on the significance level. Tests of Between-Subjects Effects Source Dependent Variable Type III Sum of Squares df Mean Square F Sig. Corrected Model reading comprehension 1.372a 2 .686 18.993 .000 copy word .215b 2 .107 5.784 .003 composition 5.732c 2 2.866 5.756 .004 write word 4739.751d 2 2369.876 16.372 .000 Intercept reading comprehension 133.955 1 133.955 3708.093 .000 copy word 48.241 1 48.241 2596.875 .000 composition 673.540 1 673.540 1352.800 .000 write word 650019.637 1 650019.637 4490.480 .000 ablity reading comprehension 1.372 2 .686 18.993 .000 copy word .215 2 .107 5.784 .003 composition 5.732 2 2.866 5.756 .004 write word 4739.751 2 2369.876 16.372 .000 Error reading comprehension 10.368 287 .036 copy word 5.331 287 .019 composition 142.893 287 .498 write word 41544.694 287 144.755 Total reading comprehension 145.496 290 copy word 53.735 290 composition 821.167 290 write word 695477.000 290 Corrected Total reading comprehension 11.740 289 copy word 5.546 289 composition 148.625 289 write word 46284.445 289 a. R Squared = .117 (Adjusted R Squared = .111) b. R Squared = .039 (Adjusted R Squared = .032) c. R Squared = .039 (Adjusted R Squared = .032) d. R Squared = .102 (Adjusted R Squared = .096) As seen in the MANOVA test above, the null hypothesis is not rejected since the p-vale for the level of ability variable is less than 0.05 on all the four dependent variables and therefore significant (Mayers, 2013). Similarly, the significance of the Wilks F-Test is less than 0.05 which is significant and further suggests that there is a significant difference in performance of the test between the three levels of the dependent variable. Therefore, we conclude that there is a significant difference between individuals in the three groups of abilities with respect t...