R Notes for Topic 22: Comparing Two Means
R notes for Activity 22-1: Close Friends
22-1 i. Computing the test statistic
You can use R to compute the test statistic. Recall that this
test statistic has the form
(x1bar - x2bar)/sqrt(s1*s1/n1 + s2*s2/n2)
You can fill in the values.
22-1 o. Computing a confidence interval
Okay, you need to compute
(xfbar-xfbar) +/- tkstar*sqrt(sf*sf/nf + sm*sm/nm)
I'll leave you to fill in the details.
22-1 p. Computing the p-value
As the book suggests, you can use the applet. You can also use
R's pt function to compute the
p-value. Since it's a two-sided test, we should
double the computed value.
t = (1.861-2.089)/sqrt(1.777*1.777/654 + 1.760*1.760/813)
2*pt(t, df=653)
R notes for Activity 22-2: Hypothetical Commuting Times
This is one of those fun times in which our data set combines a number
of essentially independent columns into a single data frame. Since R
pads the empty cells in the data frame with NA values,
our analyses may be slightly more complicated.
Let's start by loading the data. There's little enough data that we
can look at all of it.
CommuteTimes = read.csv("/home/rebelsky/Stats115/Data/HypoCommute.csv")
CommuteTimes
The columns are named A1 (for Alex's Route 1),
A2 (for Alex's Route 2), B1 (for Barb's Route 1), and
so on and so forth.
22-2 c. Computing Alex's route statistics
You should be able to read the sample size from the table. To get
the sample mean and standard deviation, we can use
mean and
sd, but need to tell the functions
to ignore the NA values. (Having to tell the functions
to deal with the NA values differently is one of the disadvantages of
combining the columns.
mean(CommuteTimes$A1, na.rm=T)
sd(CommuteTimes$A1, na.rm=T)
22-2 d. Conducting the significance test
R makes two-sample t-tests very easy to compute.
Just call t.test with the two samples.
t.test(CommuteTimes$A1,CommuteTimes$A2)
22-2 f. Confidence intervals
We repeat the t-test, telling it to use a
different confidence level.
t.test(CommuteTimes$A1,CommuteTimes$A2, conf.level=.90)
22-2 k. More Computations
You should be able to figure out how to do these computations by
revisiting the Alex examples from above.
R notes for Activity 22-3
Since we ended up with very different sample sizes (I'm not sure why),
I've put the data into two files, Convenient.csv
and Inconvenient.csv.
Convenient = read.csv("/home/rebelsky/Stats115/Data/ConvenientSequence.csv")
Inconvenient = read.csv("/home/rebelsky/Stats115/Data/InconvenientSequence.csv")
Here are the commands you might use to build four windows with the
four separate displays.
library(BHH2, lib="/home/rebelsky/Stats115/Packages")
X11()
boxplot(Convenient,horizontal=T)
X11()
boxplot(Inconvenient,horizontal=T)
X11()
dotPlot(Convenient)
X11()
dotPlot(Inconvenient)
Are we doing a two-sided test or a one-sided test? If you're using
a one-sided test, which is the direction of the test? Use your answer
to figure out which of the following commands to select.
t.test(Convenient,Inconvenient)
t.test(Convenient,Inconvenient, alternative="greater")
t.test(Convenient,Inconvenient, alternative="less")
22-3 h. Confidence intervals
Add conf.level=.90 to your previous answer to compute
the confidence interval.
