Anova, Ancova, Manova, Mancova assignment
Data summary
## rank discipline yrs.since.phd yrs.service sex
## AsstProf : 67 A:181 Min. : 1.00 Min. : 0.00 Female: 39
## AssocProf: 64 B:216 1st Qu.:12.00 1st Qu.: 7.00 Male :358
## Prof :266 Median :21.00 Median :16.00
## Mean :22.31 Mean :17.61
## 3rd Qu.:32.00 3rd Qu.:27.00
## Max. :56.00 Max. :60.00
## salary
## Min. : 57800
## 1st Qu.: 91000
## Median :107300
## Mean :113706
## 3rd Qu.:134185
## Max. :2315453-way Anova with and w/o interactions
w/o interactions
## Df Sum Sq Mean Sq F value Pr(>F)
## sex 1 6.980e+09 6.980e+09 13.62 0.000256 ***
## discipline 1 8.792e+09 8.792e+09 17.15 4.23e-05 ***
## rank 2 1.466e+11 7.329e+10 142.98 < 2e-16 ***
## Residuals 392 2.009e+11 5.126e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Rank, discipline and sex are statistically significant.
with interactions
## Df Sum Sq Mean Sq F value Pr(>F)
## sex 1 6.980e+09 6.980e+09 13.460 0.000278 ***
## discipline 1 8.792e+09 8.792e+09 16.955 4.69e-05 ***
## rank 2 1.466e+11 7.329e+10 141.336 < 2e-16 ***
## sex:discipline 1 4.001e+08 4.001e+08 0.772 0.380295
## sex:rank 2 2.909e+08 1.455e+08 0.281 0.755553
## discipline:rank 2 4.748e+08 2.374e+08 0.458 0.632997
## sex:discipline:rank 2 1.324e+08 6.620e+07 0.128 0.880195
## Residuals 385 1.996e+11 5.186e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Each interaction has a high p-value, which means there is not much variation that can be explained by the interaction between sex, discipline and rank. So, there are no significant interactions.
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = salary ~ sex + discipline + rank, data = data)
##
## $sex
## diff lwr upr p adj
## Male-Female 14088.01 6582.02 21594 0.0002559
##
## $discipline
## diff lwr upr p adj
## B-A 9448.914 4963.365 13934.46 4.23e-05
##
## $rank
## diff lwr upr p adj
## AssocProf-AsstProf 13443.16 4132.913 22753.40 0.0021636
## Prof-AsstProf 45910.92 38629.823 53192.01 0.0000000
## Prof-AssocProf 32467.76 25051.605 39883.92 0.0000000From the post-hoc test results, we see that there are statistically significant differences (p < 0.05) between sex group Male-Female, between discipline group B-A and between rank groups AsspcProf-AsstProf, Prof-AsstProf, Prof-AssocProf. So, basically between each group.
Can years since doctorate (yrs.since.phd), length of service (yrs.service) be significant as covariates?
## Df Sum Sq Mean Sq F value Pr(>F)
## sex 1 6.980e+09 6.980e+09 13.740 0.00024 ***
## discipline 1 8.792e+09 8.792e+09 17.308 3.91e-05 ***
## rank 2 1.466e+11 7.329e+10 144.278 < 2e-16 ***
## yrs.since.phd 1 1.185e+08 1.185e+08 0.233 0.62935
## yrs.service 1 2.710e+09 2.710e+09 5.335 0.02143 *
## Residuals 390 1.981e+11 5.080e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Years since doctorate is not significant as covariate but length of service is (0.02143 < 0.05).
Is there any significant difference in years since PhD (yrs.since.phd) and seniority (yrs.service) of different rank professors?
## Df Pillai approx F num Df den Df Pr(>F)
## rank 2 0.49855 65.414 4 788 < 2.2e-16 ***
## Residuals 394
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Response yrs.since.phd :
## Df Sum Sq Mean Sq F value Pr(>F)
## rank 2 32390 16194.8 191.18 < 2.2e-16 ***
## Residuals 394 33376 84.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response yrs.service :
## Df Sum Sq Mean Sq F value Pr(>F)
## rank 2 24812 12406 115.9 < 2.2e-16 ***
## Residuals 394 42175 107
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1There is significant difference in both years since PhD (2.2e-16 < 0.05) and seniority (2.2e-16 < 0.05) of different rank professors.