These notes build on the prior chapters’ R Code and Instructions, where we discuss some operational aspects of R and detail the use of many functions and how to install packages. Here, we skip details that have already been discussed in the prior R Code and Instructions.
Load the AMCP package.
library(AMCP)
data(chapter_11_table_1)
chapter_11_table_1## YCondition1 YCondition2
## 1 8 10
## 2 3 6
## 3 12 13
## 4 5 9
## 5 7 8
## 6 13 14str(chapter_11_table_1)## 'data.frame': 6 obs. of 2 variables:
## $ YCondition1: int 8 3 12 5 7 13
## $ YCondition2: int 10 6 13 9 8 14Paired samples \(t\)-test. Note that the square of the resulting t-value below is equal to the F-value shown just after Table 11.3.
t.test(x=chapter_11_table_1$YCondition1, paired=TRUE, y=chapter_11_table_1$YCondition2)##
## Paired t-test
##
## data: chapter_11_table_1$YCondition1 and chapter_11_table_1$YCondition2
## t = -3.873, df = 5, p-value = 0.01172
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3.3274428 -0.6725572
## sample estimates:
## mean of the differences
## -2data(chapter_11_table_5)
chapter_11_table_5## Months30 Months36 Months42 Months48
## 1 108 96 110 122
## 2 103 117 127 133
## 3 96 107 106 107
## 4 84 85 92 99
## 5 118 125 125 116
## 6 110 107 96 91
## 7 129 128 123 128
## 8 90 84 101 113
## 9 84 104 100 88
## 10 96 100 103 105
## 11 105 114 105 112
## 12 113 117 132 130str(chapter_11_table_5)## 'data.frame': 12 obs. of 4 variables:
## $ Months30: int 108 103 96 84 118 110 129 90 84 96 ...
## $ Months36: int 96 117 107 85 125 107 128 84 104 100 ...
## $ Months42: int 110 127 106 92 125 96 123 101 100 103 ...
## $ Months48: int 122 133 107 99 116 91 128 113 88 105 ...Marginal means
# Means by column across rows.
apply(chapter_11_table_5, MARGIN=1, FUN=mean)## [1] 109 120 104 90 121 101 127 97 94 101 109 123# Means by row across columns.
apply(chapter_11_table_5, MARGIN=2, FUN=mean)## Months30 Months36 Months42 Months48
## 103 107 110 112First, we need to change the structure of the data. We use PP here to denote “person-period”, which means that the data will be in the “univariate” (or “long”) form from the “multivariate” form it is currently in. We find the easiest way to do this is using the tidyr and dplyr packages.
library(tidyr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Add an ID variable (by row number)
C11_T5_PP <- chapter_11_table_5
C11_T5_PP$ID <- as.factor(1:nrow(C11_T5_PP))
# Note that the "sep=-3" partitions between the 3rd and 2nd value from the end.
# The "-ID" here means to leave ID as it is (i.e., without "gathering" it)
C11_T5_PP = C11_T5_PP %>%
gather(key=Unit.Month, value=Values, -ID) %>%
separate(col=Unit.Month, into=c("Unit", "Month"), sep=-3) %>%
arrange(ID, Month)
# Display the data
C11_T5_PP## ID Unit Month Values
## 1 1 Months 30 108
## 2 1 Months 36 96
## 3 1 Months 42 110
## 4 1 Months 48 122
## 5 2 Months 30 103
## 6 2 Months 36 117
## 7 2 Months 42 127
## 8 2 Months 48 133
## 9 3 Months 30 96
## 10 3 Months 36 107
## 11 3 Months 42 106
## 12 3 Months 48 107
## 13 4 Months 30 84
## 14 4 Months 36 85
## 15 4 Months 42 92
## 16 4 Months 48 99
## 17 5 Months 30 118
## 18 5 Months 36 125
## 19 5 Months 42 125
## 20 5 Months 48 116
## 21 6 Months 30 110
## 22 6 Months 36 107
## 23 6 Months 42 96
## 24 6 Months 48 91
## 25 7 Months 30 129
## 26 7 Months 36 128
## 27 7 Months 42 123
## 28 7 Months 48 128
## 29 8 Months 30 90
## 30 8 Months 36 84
## 31 8 Months 42 101
## 32 8 Months 48 113
## 33 9 Months 30 84
## 34 9 Months 36 104
## 35 9 Months 42 100
## 36 9 Months 48 88
## 37 10 Months 30 96
## 38 10 Months 36 100
## 39 10 Months 42 103
## 40 10 Months 48 105
## 41 11 Months 30 105
## 42 11 Months 36 114
## 43 11 Months 42 105
## 44 11 Months 48 112
## 45 12 Months 30 113
## 46 12 Months 36 117
## 47 12 Months 42 132
## 48 12 Months 48 130#Note that we do not need "Unit" variable, so we drop it.
C11_T5_PP$Unit <- NULL
# Examining the structure of the data.
str(C11_T5_PP)## 'data.frame': 48 obs. of 3 variables:
## $ ID : Factor w/ 12 levels "1","2","3","4",..: 1 1 1 1 2 2 2 2 3 3 ...
## $ Month : chr "30" "36" "42" "48" ...
## $ Values: int 108 96 110 122 103 117 127 133 96 107 ...# Examining the structure of the data we saw that "Month" is being treated as a character variable,
# yet we want it to be a factor:
C11_T5_PP$Month <- as.factor(C11_T5_PP$Month)
C11_T5_PP$ID <- as.factor(C11_T5_PP$ID)
str(C11_T5_PP)## 'data.frame': 48 obs. of 3 variables:
## $ ID : Factor w/ 12 levels "1","2","3","4",..: 1 1 1 1 2 2 2 2 3 3 ...
## $ Month : Factor w/ 4 levels "30","36","42",..: 1 2 3 4 1 2 3 4 1 2 ...
## $ Values: int 108 96 110 122 103 117 127 133 96 107 ...Importantly, ID and Month must both be treated as factors. If not, the incorrect model will be fitted. This gives a basic (uncorrected for sphericity) repeated measures ANOVA. The car package provides methods, using the Anova() function for obtaining corrected output.
Repeated.Measures.ANOVA <- aov(Values ~ Month + Error(ID/Month), data=C11_T5_PP)
summary(Repeated.Measures.ANOVA)##
## Error: ID
## Df Sum Sq Mean Sq F value Pr(>F)
## Residuals 11 6624 602.2
##
## Error: ID:Month
## Df Sum Sq Mean Sq F value Pr(>F)
## Month 3 552 184.00 3.027 0.0432 *
## Residuals 33 2006 60.79
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1