One-Way Analysis of Variance Revealed

Class Outcomes

In this example I am using some data from an evaluation of my research classes, where I did a pre-test and a post-test of my classes. What I want to do here is to compare the three classes, Tuesday, Saturday, online. Tuesday was a regular face-to-face class, Saturday was a hybrid class, where students watched pre-recorded lecture and came to class to do discussion and online had the same pre-recorded lectures as Saturday, but did their discussion via synchronous video enabled chats. the NULL hypothesis would be that the means of the percent improvement PERCENTIMP variable would be equal between the three groups.

We import the data

SW <-read.delim("/Volumes/Mirror Mirror /Google Drive/Research_UMKC/SE4SW.FE/T_Tests/prepost.txt")
names(SW)

## [1] "Class"      "PRE"        "POST"       "IMPROVE"    "PERCENTIMP"
## [6] "PrePF"      "PostPF"     "PrePF.1"    "PostPF.1"

first do the anova

we do this by creating a R object, which we are calling ‘model’

model <- aov(PERCENTIMP ~ Class, data = SW)

here is the play by play

the aov is our R function, it tells R we want to do an Analysis of Variance,

inside the ( ) we have PERCENTIMP ~ Class which tells R we want to test the differences in PERCENTIMP by categories of Class finally where we see data = SW that is us telling R where to find PERCENTIMP and Class

Now our ANOVA

we view our ANOVA by summarizing the object i.e., model we just created.

summary(model)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Class        2   1439   719.7   1.168  0.322
## Residuals   39  24036   616.3

using the numSummary function from the RcmdrMisc package

using numSummary gives us an easy way to get summary stats of our groups when doing ANOVA.

require(RcmdrMisc)
numSummary(SW$PERCENTIMP, groups = SW$Class, statistics = c('mean','sd'))

##              mean       sd data:n
## online    9.74375 30.22536     16
## Saturday 11.86600 24.88175     10
## Tuesday  22.49812 17.81388     16

Analyzing our ANOVA

here we wee that our analysis of variance test gives us a F of 2.5 and our probability is P = 0.095. Which is under .1, ## where the differences lie

Then we take a look at the between groups differences. Using the Tukey Honest Significant Differences test

require(graphics)
TukeyHSD(model,'Class', ordered = FALSE) 

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = PERCENTIMP ~ Class, data = SW)
## 
## $Class
##                      diff        lwr      upr     p adj
## Saturday-online   2.12225 -22.258847 26.50335 0.9755278
## Tuesday-online   12.75437  -8.629261 34.13801 0.3243128
## Tuesday-Saturday 10.63213 -13.748972 35.01322 0.5427289

IT is often helpful for some folks to visualize their Tukey scores using the plot see below. You could also make an object and name it like we did above with the aov. We ‘read’ the plot by looking at the 0 line in the middle and if they all overlap,

plot(TukeyHSD(model,'Class', ordered = FALSE) )

The ANOVA Test in R is pretty simple to do, either using R Commander or via scripting.
## we were only interested in Class and PERCENTIMP variables above. But what if we wanted to know if there was a pass and fail difference in the two groups.

But wait that would be two-way ANOVA

Follow the link to the two-way anova here….