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# Manova Statistical Assignment (Case Study Sample)

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I WAS GIVEN A DATASET WITH VARIABLES OF INTEREST AND REQUIRED TO STATE A RESEARCH HYPOTHESIS AND AFTERWARD PERFORM MANCOVA ANALYSIS FOR THE GIVEN DATASET. THE ASSIGNMENT'S OBJECTIVE WAS TO FIND HOMOSCEDASTICITY WITH A CLEAR EXPLANATION AND OUTPUTS OF INTEREST. I INCLUDED THE RAVEN TEST AS COVARIATE AND INCLUDED PERTINENT TABLES JUST AS INSTRUCTED BY THE INSTRUCTIONS. source..

Content:

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...

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