Mixed Analysis of Variance in SPSS

This article explains the Mixed Analysis of Variance in SPSS. It includes Tests of Normality, Test of Homogeneity of Variance, One-way Repeated Measures Analysis of Variance, Multivariate Tests, Mauchly's Test of Sphericity, and Tests of Within-Subjects Effects.

SPSS

Mixed Analysis of Variance in SPSS
Tests of Normality
Main Sport participated in Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
HR Trial 1 level 1 Runner .176 8 .200* .964 8 .848
Rower .183 8 .200* .978 8 .951
HR trial 1 level 2 Runner .236 8 .200* .922 8 .446
Rower .117 8 .200* .954 8 .753
HR trial 1 level 3 Runner .206 8 .200* .837 8 .070
Rower .193 8 .200* .884 8 .204
HR trial 1 level 4 Runner .211 8 .200* .959 8 .804
Rower .250 8 .150 .857 8 .112
HR trial 2 level 1 Runner .204 8 .200* .922 8 .445
Rower .214 8 .200* .913 8 .375
HR trial 2 level 2 Runner .321 8 .015 .856 8 .110
Rower .149 8 .200* .983 8 .975
HR trial 2 level 3 Runner .203 8 .200* .938 8 .596
Rower .164 8 .200* .967 8 .873
HR trial 2 level 4 Runner .168 8 .200* .969 8 .890
Rower .215 8 .200* .944 8 .649
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
From the interpretation above table it can be said that various ‘HR trial’ variables being
tested with the variable of ‘Main Sport participated in’ there exists no relationship between the
two variables. However, in HR trial 1 level 3 Runner being one of the pair of variable showed a
positive relationship between the other determinant i.e., ‘Main Sport participated in’.
Test of Homogeneity of Variance
Levene Statistic df1 df2 Sig.
HR Trial 1 level 1
Based on Mean 2.002 1 14 .179
Based on Median 1.494 1 14 .242
Based on Median and with
adjusted df 1.494 1 10.648 .248
Based on trimmed mean 2.067 1 14 .173
HR trial 1 level 2 Based on Mean .736 1 14 .405
Based on Median .247 1 14 .627

Based on Median and with
adjusted df .247 1 10.595 .630
Based on trimmed mean .647 1 14 .435
HR trial 1 level 3
Based on Mean .001 1 14 .975
Based on Median .022 1 14 .885
Based on Median and with
adjusted df .022 1 13.899 .885
Based on trimmed mean .002 1 14 .962
HR trial 1 level 4
Based on Mean .005 1 14 .947
Based on Median .001 1 14 .973
Based on Median and with
adjusted df .001 1 13.974 .973
Based on trimmed mean .008 1 14 .929
HR trial 2 level 1
Based on Mean 3.657 1 14 .077
Based on Median 2.615 1 14 .128
Based on Median and with
adjusted df 2.615 1 9.244 .139
Based on trimmed mean 3.360 1 14 .088
HR trial 2 level 2
Based on Mean 1.606 1 14 .226
Based on Median .552 1 14 .470
Based on Median and with
adjusted df .552 1 9.182 .476
Based on trimmed mean 1.233 1 14 .286
HR trial 2 level 3
Based on Mean .525 1 14 .480
Based on Median .204 1 14 .658
Based on Median and with
adjusted df .204 1 12.108 .659
Based on trimmed mean .459 1 14 .509
HR trial 2 level 4
Based on Mean .082 1 14 .779
Based on Median .179 1 14 .679
Based on Median and with
adjusted df .179 1 13.691 .679
Based on trimmed mean .079 1 14 .783
From the interpretation of the normal distribution table Test of Homogeneity of
Variance, it can be analyzed that a null hypothesis can be selected. This states about negative
relationship between the two variables.

One-way Repeated Measures Analysis of Variance in SPSS
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
HR Trial 1 level 1 .195 16 .104 .941 16 .359
HR trial 1 level 2 .173 16 .200* .941 16 .363
HR trial 1 level 3 .158 16 .200* .925 16 .205
HR trial 1 level 4 .181 16 .167 .951 16 .499
HR trial 2 level 1 .174 16 .200* .885 16 .046
HR trial 2 level 2 .238 16 .016 .894 16 .065
HR trial 2 level 3 .158 16 .200* .966 16 .764
HR trial 2 level 4 .122 16 .200* .974 16 .901
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
From the analysis of the above table, the significant value was obtained above .05 which
signifies the selection of null hypothesis. However, HR trial 2 level 1 denotes the selection of
alternate hypothesis reflection a P value of .046.
Multivariate Testsa
Effect Value F Hypothesis df Error df Sig.
trials
Pillai's Trace .965 35.303b 7.000 9.000 .000
Wilks' Lambda .035 35.303b 7.000 9.000 .000
Hotelling's Trace 27.458 35.303b 7.000 9.000 .000
Roy's Largest Root 27.458 35.303b 7.000 9.000 .000
a. Design: Intercept
Within Subjects Design: trials
b. Exact statistic
The above table in which multivariate tests was being performed denotes that alternative
hypothesis can be selected reflecting to the P value of .000.
Mauchly's Test of Sphericitya
Measure: MEASURE_1
Mauchly's W df Sig. Epsilonb

Within Subjects
Effect
Approx. Chi-
Square
Greenhouse-
Geisser
Huynh-
Feldt
Lower-
bound
trials .001 81.939 27 .000 .432 .553 .143
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: trials
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.
From the Mauchly's Test of Sphericity it can be said that there exists a positive
relationship between the set of variables.
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source Type III Sum of
Squares
df Mean Square F Sig.
trials
Sphericity Assumed 15918.094 7 2274.013 86.892 .000
Greenhouse-Geisser 15918.094 3.022 5267.475 86.892 .000
Huynh-Feldt 15918.094 3.870 4113.529 86.892 .000
Lower-bound 15918.094 1.000 15918.094 86.892 .000
Error(trials)
Sphericity Assumed 2747.906 105 26.171
Greenhouse-Geisser 2747.906 45.329 60.621
Huynh-Feldt 2747.906 58.045 47.341
Lower-bound 2747.906 15.000 183.194
From the evaluation of the given table, the significant value was being obtained at .000
this identified selection of alternate hypothesis.

Appendix

Histograms

Normal Q-Q Plots

Detrended Normal Q-Q Plots

HR trial 2 level 1
Histograms

Normal Q-Q Plots

Detrended Normal Q-Q Plots

HR trial 2 level 2
Histograms

Normal Q-Q Plots

Detrended Normal Q-Q Plots

HR trial 2 level 3
Histograms

Normal Q-Q Plots

Detrended Normal Q-Q Plots

Normal Q-Q Plots

Detrended Normal Q-Q Plots

HR Trial 1 level 1

HR trial 1 level 2

HR trial 1 level 3

HR trial 1 level 4

HR trial 2 level 1

HR trial 2 level 2

HR trial 2 level 3

HR trial 2 level 4