Single Factor ANOVA is a method we use when we want to compare a quantitative variable among more than two categories. It evaluates whether the means of different treatment groups, or populations, are equivalent. When we only have two populations then we can perform a two-sample t procedure, but when we have more populations we need to examine the data with Single Factor ANOVA. In the R script DA6_Single_Factor_ANOVA. R, follow along with the analysis that compares average number of roommates between majors for the ST314 online students. You will need to upload the student information dataset ST314SISW19.csv.
PART 1 START
# R code and explanation for data analysis 6.
# Read in the Student Information Data. Call it st314data.
st314data= read. csv(file. choose(), header = TRUE)
# gives variable names.
names(st314data) # gives variable names.
levels(st314data$Major) # gives group names for majors
# This analysis compares number of Roommates among majors of ST314 students.
# Follow along with my code.
# For your own analysis choose either "Roommates","GamingHours" or "SocialTime to compare between majors.
# Create a side-by-side boxplot to compare number of Roommates among the different majors.
# Expand the plot if you can't see the group names.
# add a title with main = "title" and a vertical axis title using ylab = "title".
# color can be added with the rainbow commmand or blues9, or by assigning a specific color like "yellow"
boxplot(Roommates~Major, data = st314data, main = "Comparison between Major and Number of GamingHours
for ST314 FallStudents", ylab = "Number of gaming hours", col = rainbow(5))
# Find the mean, sd and group sizes using the aggregate command.
# aggregate splits the quantitative variable by the categorical variable groups then performs the command specified.
aggregate(Roommates~Major, data =st314data, mean)
aggregate(Roommates~Major, data =st314data, sd)
aggregate(Roommates~Major, data =st314data, length)
# Perform a single factor ANOVA F test to compare the means using the aov() command.
# call the output something. I like to call it "mod". Then take the summary() of this object to get the ANOVA table.
mod = aov(Roommates~Major, data =st314data)
summary(mod)
# If the single factor ANOVA test indicates a difference in means,
# perform a multiple comparisons procedure to see which means differ significantly.
# Use the TukeysHSD() command with your object from the aov() command. For this example this is called "mod".
TukeyHSD(mod, conf. level = 0.90)
#Check out this "cool" Multiple COmparisons Plot.
plot(TukeyHSD(mod, conf. level = 0.90), col = "blue")
YOUR TURN
#Choose "Roommates", "GamingHours" or "Terms" and compare it among majors.
#You can do this by simply changing Roommates (and only Roommates) in each line of code above.
State the conditions for the Single Factor ANOVA F Test. Is it reasonable to seem that these conditions are satisfied? If not, still proceed. e. Perform the Single Factor ANOVA F test in R. 1. (2 point) Paste the ANOVA table. 2. (2 points) From the ANOVA table, what is the average between group variability and the average within group variability, respectively the MSTr and MSE? f. Use the F statistic and p-value from the ANOVA table to state whether there is a significant difference between at least two of the group means. 1. (2 points) State whether to reject the null. State the test statistic and p-value. 2. (2 points) Include a statement in terms of the strength of evidence in terms of the alternative. Include context. g. Using the Tukey's Multiple Comparison procedure output. Are there any individual comparisons that are significant at the 0.10 significance level?
1. (2 point) Paste R output for the multiple comparisons procedure.
2. (2 point) List all comparisons that are significant (or state those that are not).
3. (3 points) Interpret the 90% F-W confidence interval for the difference with the smallest p-value (even if it is not significant).