Seasonal affective disorder (SAD) is a type of depression during seasons with le

Question

Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of SAD patients to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

Light Intensity Low Medium High Time of
Day Morning 5 5 7 6 6 8 4 4 6 7 7 9 5 9 5 6 8 8 Night 5 5 9 8 8 7 6 7 6 7 5 8 4 9 7 3 8 6

Explanation / Answer

We shall do the analysis in the open source statistical package R , the complete R snippet is as follows

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\Intensity.csv",header=TRUE)
str(data.df)

# perform anova analysis
a<- aov(lm(Value~ Time*Intensity,data=data.df))

#summarise the results
summary(a)

colr<-c("tomato","turquoise","violetred2" ,"cornflowerblue" ,"gainsboro" ,
"whitesmoke","yellow3","slateblue1","sienna3" , "wheat1",
"salmon3" , "plum2","coral1","palegreen1" ,"orangered" ,"magenta4" )
# plots

boxplot(Value~ Time*Intensity, data=data.df,ylab="Values",
main="Boxplots of the Data",col=colr,horizontal=TRUE)

attach(data.df)
interaction.plot(Time,Intensity,Value, type="b", col=c(2:6),
leg.bty="o", leg.bg="beige", lwd=2, pch=c(18,24,22),  
xlab="Time",
ylab="Value",
main="Interaction Plot")

# Plot Means with Error Bars
library(gplots)

plotmeans(Value~ Time,xlab="Time Types",
ylab="Value", main="Mean Plot with 95% CI")

library(gplots)

plotmeans(Value~ Intensity,xlab="Time Types",
ylab="Value", main="Mean Plot with 95% CI")

The results are , The ANOVA table is as shown below

summary(a)
Df Sum Sq Mean Sq F value Pr(>F)
Time 1 0.69 0.694 0.286 0.5967 ## not signficant as the p value is not less than 0.05
Intensity 2 20.72 10.361 4.268 0.0234 * ## signficant as the p value is less than 0.05
Time:Intensity 2 0.72 0.361 0.149 0.8624 ## not signficant as the p value is not less than 0.05
Residuals 30 72.83 2.428   
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The required table is highlighted above

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