R day 8

t -tests

one-way ANOVAs

Mutiple categorical predictors

within groups and between groups

compare SSbetween and SSwithin using our F statistic

anova(m)
summary(aov(m))

the highest-level interactions

> m <- lm(breaks ~ wool+tension+wool:tension, contrasts=list(wool="contr.helmert", tension="contr.helmert"), data=warpbreaks)
> anova(m)
Analysis of Variance Table

Response: breaks
             Df Sum Sq Mean Sq F value    Pr(>F)   
wool          1  450.7  450.67  3.7653 0.0582130 . 
tension       2 2034.3 1017.13  8.4980 0.0006926 ***
wool:tension  2 1002.8  501.39  4.1891 0.0210442 * 
Residuals    48 5745.1  119.69                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


with(warpbreaks, interaction.plot(wool, tension, breaks))
with is a generic function that evaluates expr in a local environment constructed from data.

interaction.plot()


the durationsOnt data set from the languageR package


> head(CO2)
Grouped Data: uptake ~ conc | Plant
<environment: R_EmptyEnv>
  Plant   Type  Treatment conc uptake
1   Qn1 Quebec nonchilled   95   16.0
2   Qn1 Quebec nonchilled  175   30.4
3   Qn1 Quebec nonchilled  250   34.8
4   Qn1 Quebec nonchilled  350   37.2
5   Qn1 Quebec nonchilled  500   35.3
6   Qn1 Quebec nonchilled  675   39.2

> with(CO2, interaction.plot(Treatment, Type, uptake))


library(languageR)

englishy <- english[english$AgeSubject=="young",]
被験者「young」だけの抽出。


plot(RTlexdec ~ WrittenFrequency, englishy)
「young」の被験者データについて、反応時間と頻度の対応関係をプロット。

右下がりの傾向＝＞頻度の高い単語は反応が速い。

> m <- lm(RTlexdec ~ WrittenFrequency, englishy)
>
> m

Call:
lm(formula = RTlexdec ~ WrittenFrequency, data = englishy)

Coefficients:
     (Intercept)  WrittenFrequency 
         6.62556          -0.03711

> summary(m)

Call:
lm(formula = RTlexdec ~ WrittenFrequency, data = englishy)

Residuals:
     Min       1Q   Median       3Q      Max
-0.34664 -0.05523 -0.00546  0.05167  0.34877

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)   
(Intercept)       6.6255559  0.0049432 1340.34   <2e-16 ***
WrittenFrequency -0.0371069  0.0009242  -40.15   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08142 on 2282 degrees of freedom
Multiple R-squared: 0.414,    Adjusted R-squared: 0.4137
F-statistic:  1612 on 1 and 2282 DF,  p-value: < 2.2e-16

more than one continuous predictor

n <- lm(RTlexdec ~ WrittenFrequency + FrequencyInitialDiphoneSyllable, englishy)
> n <- lm(RTlexdec ~ WrittenFrequency + FrequencyInitialDiphoneSyllable, englishy)
>
> n

Call:
lm(formula = RTlexdec ~ WrittenFrequency + FrequencyInitialDiphoneSyllable,
    data = englishy)

Coefficients:
                    (Intercept)                 WrittenFrequency 
                       6.614295                        -0.037193 
FrequencyInitialDiphoneSyllable 
                       0.001084 

> summary(n)

Call:
lm(formula = RTlexdec ~ WrittenFrequency + FrequencyInitialDiphoneSyllable,
    data = englishy)

Residuals:
     Min       1Q   Median       3Q      Max
-0.34483 -0.05525 -0.00584  0.05185  0.34635

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)   
(Intercept)                      6.614295   0.012171 543.435   <2e-16 ***
WrittenFrequency                -0.037193   0.000928 -40.077   <2e-16 ***
FrequencyInitialDiphoneSyllable  0.001084   0.001070   1.012    0.311   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08141 on 2281 degrees of freedom
Multiple R-squared: 0.4143,    Adjusted R-squared: 0.4137
F-statistic: 806.6 on 2 and 2281 DF,  p-value: < 2.2e-16

Regression diagnostics

plot(n)

> q <- lm(RTlexdec ~ WrittenFrequency + I(WrittenFrequency^2), englishy)
>
> plot(q)