load package
library(lattice)
library(nlme)
plot by course and ignore group
xyplot(Score ~ Beauty | Course, data=dta,
ylab="Average course evaluation score",
xlab="Beauty judgment score",
type=c("p", "g", "r"))
ordinary regression
m0 <- lm(Score ~ Beauty, data=dta)
summary(m0)
##
## Call:
## lm(formula = Score ~ Beauty, data = dta)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.80015 -0.36304 0.07254 0.40207 1.10373
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.01002 0.02551 157.205 < 2e-16 ***
## Beauty 0.13300 0.03218 4.133 4.25e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5455 on 461 degrees of freedom
## Multiple R-squared: 0.03574, Adjusted R-squared: 0.03364
## F-statistic: 17.08 on 1 and 461 DF, p-value: 4.247e-05
with(dta, plot(Beauty, Score, bty="n",
xlab="Beauty score",
ylab="Average course evaluation"))
grid()
abline(m0)
create new data
gdta <- # create a new copy of the groupedData object
groupedData(Score ~ Beauty | Course,
data=as.data.frame( dta ),
FUN=mean,
labels=list(x="Beauty score",
y="Couse evaluation score" ))
analysis
#plot
plot(gdta, asp=1)
# t test
t.test(coef(lmList(Score ~ Beauty | Course, data = dta))["Beauty"])
##
## One Sample t-test
##
## data: coef(lmList(Score ~ Beauty | Course, data = dta))["Beauty"]
## t = 0.54197, df = 30, p-value = 0.5918
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -2.188261 3.769231
## sample estimates:
## mean of x
## 0.7904846
#interaction
m1 <- lm(Score ~ Course/Beauty - 1, data = dta)
summary(m1)
##
## Call:
## lm(formula = Score ~ Course/Beauty - 1, data = dta)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.81077 -0.27389 0.01347 0.33138 1.09350
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## Course0 4.03158 0.03035 132.833 < 2e-16 ***
## Course1 3.70492 1.21987 3.037 0.002544 **
## Course2 4.48518 0.48804 9.190 < 2e-16 ***
## Course3 3.88060 0.25348 15.309 < 2e-16 ***
## Course4 3.83589 0.12065 31.793 < 2e-16 ***
## Course5 4.08628 0.30734 13.296 < 2e-16 ***
## Course6 4.21952 0.37751 11.177 < 2e-16 ***
## Course7 3.44907 0.43236 7.977 1.58e-14 ***
## Course8 5.07854 1.02010 4.978 9.54e-07 ***
## Course9 3.92844 0.21504 18.268 < 2e-16 ***
## Course10 4.83934 1.88297 2.570 0.010528 *
## Course11 4.13223 0.40602 10.177 < 2e-16 ***
## Course12 3.30810 0.66667 4.962 1.03e-06 ***
## Course13 4.15742 0.61465 6.764 4.77e-11 ***
## Course14 3.61709 0.44420 8.143 4.93e-15 ***
## Course15 2.42004 0.41873 5.779 1.51e-08 ***
## Course16 -16.97335 22.09391 -0.768 0.442799
## Course17 4.46692 0.29821 14.979 < 2e-16 ***
## Course18 4.20422 0.31468 13.360 < 2e-16 ***
## Course19 3.53618 0.25201 14.032 < 2e-16 ***
## Course20 4.45396 0.49569 8.985 < 2e-16 ***
## Course21 3.66196 0.14246 25.705 < 2e-16 ***
## Course22 3.72860 0.20641 18.064 < 2e-16 ***
## Course23 3.53098 0.50960 6.929 1.70e-11 ***
## Course24 3.78102 0.35515 10.646 < 2e-16 ***
## Course25 20.75287 13.61325 1.524 0.128182
## Course26 4.24619 0.31381 13.531 < 2e-16 ***
## Course27 4.55216 0.67201 6.774 4.48e-11 ***
## Course28 3.60512 1.39744 2.580 0.010241 *
## Course29 3.80386 0.39088 9.732 < 2e-16 ***
## Course30 4.30761 0.32715 13.167 < 2e-16 ***
## Course0:Beauty 0.14625 0.03776 3.873 0.000126 ***
## Course1:Beauty 0.91093 1.33780 0.681 0.496316
## Course2:Beauty 0.24165 0.89779 0.269 0.787948
## Course3:Beauty -0.04582 1.41142 -0.032 0.974118
## Course4:Beauty 0.54012 0.29087 1.857 0.064055 .
## Course5:Beauty 0.22749 0.42058 0.541 0.588877
## Course6:Beauty 0.79477 0.63930 1.243 0.214527
## Course7:Beauty -0.19545 0.44467 -0.440 0.660514
## Course8:Beauty 1.89797 1.41031 1.346 0.179133
## Course9:Beauty -1.96252 0.70060 -2.801 0.005338 **
## Course10:Beauty 0.53484 1.92401 0.278 0.781168
## Course11:Beauty -0.40489 0.50143 -0.807 0.419874
## Course12:Beauty -1.94710 1.67064 -1.165 0.244517
## Course13:Beauty 0.50549 0.92939 0.544 0.586818
## Course14:Beauty -0.13856 0.89166 -0.155 0.876586
## Course15:Beauty -0.37534 0.55780 -0.673 0.501404
## Course16:Beauty -18.21494 19.14113 -0.952 0.341867
## Course17:Beauty 0.33544 0.44705 0.750 0.453490
## Course18:Beauty -0.13033 0.49320 -0.264 0.791719
## Course19:Beauty -0.32019 0.32460 -0.986 0.324512
## Course20:Beauty 0.06920 0.88931 0.078 0.938015
## Course21:Beauty -0.03796 0.18906 -0.201 0.840958
## Course22:Beauty 0.16407 0.24235 0.677 0.498811
## Course23:Beauty -1.33471 0.76494 -1.745 0.081776 .
## Course24:Beauty 0.07561 0.97317 0.078 0.938106
## Course25:Beauty 40.59718 32.65588 1.243 0.214527
## Course26:Beauty 0.22531 0.33634 0.670 0.503322
## Course27:Beauty 0.98153 1.21556 0.807 0.419874
## Course28:Beauty 0.73837 0.96990 0.761 0.446931
## Course29:Beauty 0.47221 0.29240 1.615 0.107110
## Course30:Beauty 0.15439 0.23112 0.668 0.504507
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5254 on 401 degrees of freedom
## Multiple R-squared: 0.9853, Adjusted R-squared: 0.9831
## F-statistic: 434.3 on 62 and 401 DF, p-value: < 2.2e-16
#
summary(m1)$coef[which(summary(m1)$coef[-c(1:31),4] <0.05),]
## Estimate Std. Error t value Pr(>|t|)
## Course0 4.031577 0.03035076 132.83281 0.000000e+00
## Course9 3.928439 0.21504196 18.26824 1.101925e-54