> # This example shows the analysis for the Latin Square experiment
> # using the productivity data example we looked at in class
>
> # Entering the data and defining the variables:
>
> ##########
> ##
> # Reading the data into R:
>
> my.datafile <- tempfile()
> cat(file=my.datafile, "
+ 1 A 1 1 6.3
+ 2 B 1 2 9.8
…
+ 24 C 5 4 9.6
+ 25 D 5 5 11.0
+ ", sep=" ")
>
> options(scipen=999) # suppressing scientific notation
>
> musicprod <- read.table(my.datafile, header=FALSE, col.names=c("OBS", "MUSIC", "DAY", "TIME",
"PRODUCT"))
>
> # Note we could also save the data columns into a file and use a command such as:
> # musicprod <- read.table(file = "z:/stat_516/filename.txt", header=FALSE, col.names = c("OBS",
"MUSIC", "DAY", "TIME", "PRODUCT"))
>
> attach(musicprod)
>
> # The data frame called musicprod is now created,
> # with five variables, OBS, MUSIC, DAY, TIME, and PRODUCT.
> ##
> #########
>
> ############################################################################
>
> # lm() and anova() will do a standard analysis of variance
> # We specify our (qualitative) factors with the factor() function:
>
> # Making MUSIC, DAY, TIME factors:
>
> MUSIC <- factor(MUSIC)
> DAY <- factor(DAY)
> TIME <- factor(TIME)
>
> # The lm statement specifies that PRODUCT is the response
> # and MUSIC, DAY, TIME are the factors
> # MUSIC is the treatment factor here, and TIME and DAY are the row and column factors.
> # The ANOVA table is produced by the anova() function
>
> musicprod.fit <- lm(PRODUCT ~ MUSIC + DAY + TIME);
> anova(musicprod.fit)
Analysis of Variance Table
Response: PRODUCT
Df Sum Sq Mean Sq F value Pr(>F)
MUSIC 4 56.314 14.079 12.2750 0.0003341 ***
DAY 4 41.362 10.341 9.0159 0.0013326 **
TIME 4 42.922 10.731 9.3559 0.0011356 **
Residuals 12 13.763 1.147
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> # From the F-tests and their P-values, there is a significant effect of music type
> # on mean productivity. We also see a significant row (TIME) effect and column (DAY)
> # effect.
>
> ############################################################################
>
> # The sample mean productivity values for each music type, listed from smallest to largest:
>
> sort( tapply(PRODUCT, MUSIC, mean) )
A B E D C
7.96 9.20 10.10 11.28 12.22
>
> # Now, which of these means are significantly different?
>
> # Tukey's procedure tells us which pairs of music types are significantly
> # different:
>
> # Tukey CIs for pairwise treatment mean differences:
