Independent Samples T Tests with R
The data we shall use here were collected from students in my introductory statistics classes
from 1983 through Spring, 2015. Here is a description of the survey.
The data were in an SPSS file, but I wrote them from SPSS to a csv file. A csv file is a plain
text file that uses a comma as the delimiter. At first R did not want to work with this csv file. I
discovered that this was because I had SPSS set to use Unicode, but R was assuming the file was in
locale code. I went back into SPSS and changed the encoding to locale and all was well after that.
Below, on the left, is a snapshot of the first few lines of the csv file. On the right is how the data
appear in R.
Using commas as delimiters has the advantage of making it easier to deal with missing data.
Look at the data for the first two subjects, above, left. There is just white space between the commas
marking off the scores for SATM. Those two subjects were missing data on SATM. On the right,
notice that R replaces missing values with its missing values code, “NA.”
Here is the code used to read in the csv file:
introq <- read.table("C:/Users/Vati/Documents/StatData/IntroQ/IntroQ.csv", header=TRUE, sep=",")
I intent to use the “psych” package, so I activate it: library(psych)
Now for some basic descriptive statistics comparing men with women on height of ideal mate:
describeBy(introq$Ideal, introq$Gender)
group: 1
vars n mean sd median trimmed mad min max range skew kurtosis se
1 1 539 71.43 3.25 72 71.67 2.97 55 80 25 -0.97 2.82 0.14
------------------------------------------------------------
group: 2
vars n mean sd median trimmed mad min max range skew kurtosis se
1 1 180 66.59 3.27 66 66.42 2.97 55 78 23 0.44 1.23 0.24
Not surprisingly, the mean height of female students’ ideal mates is greater than that of male
students’ ideal mates.
Now for an independent samples t test, comparing the two genders on height of ideal mate.
t.test(introq$Ideal ~ introq$Gender)
Welch Two Sample t-test
data: Ideal by Gender
t = 17.218, df = 305.4, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
4.282968 5.388255
sample estimates:
mean in group 1 mean in group 2
71.43006 66.59444
It would be easier to deal with the output if I did not need to remember which numeric code
stands for male and which for female. Fortunately, SPSS will, upon request, write value labels to the
csv file, so I went back to SPSS and exported to csv with that request.
Gender Ideal Eye Statoph Nucoph SATM Year
1 Female 68.0 Other 8.0 50 NA 2105
2 Male 64.0 Other 4.0 40 NA 2105
3 Male 68.0 Other 5.0 30 430 2105
4 Female 72.0 Green 10.0 100 540 2105
As you can see, above, the csv file now has value labels, rather than numeric values, for the
categorical variables. When I read in the new csv file and run the t test again, I get
Welch Two Sample t-test
data: Ideal by Gender
t = 17.218, df = 305.4, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
4.282968 5.388255
sample estimates:
mean in group Female mean in group Male
71.43006 66.59444
Notice that, by default, R does a separate variances t test. This is, IMHO, a good idea, but if
you want a pooled variances t test, you can get it this way. Even though the sample sizes here differ
quite a bit, the sample variances are nearly identical, so I am comfortable with the pooled test.
t.test(introq$Ideal ~ introq$Gender, var.equal=TRUE)
Two Sample t-test
data: Ideal by Gender
t = 17.274, df = 717, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
4.286033 5.385189
sample estimates:
mean in group Female mean in group Male
71.43006 66.59444
Since the unit of measure for our scores is well known to folks in the US, it is perfectly
reasonable to use the simple difference between means (4.84 inches) as the effect size estimate.
We might want to convert that to cm for folks more familiar with the metric system. Suppose,
however, that our scores were estimates of political conservativism from the Überarschloch scale.
Unless we are very familiar with that scale, we are not going to know whether a difference of 4.84 is a
small difference or a large difference. In that case, it would be best to use Cohen’s d, the
standardized difference between group means. Here I shall use the “lsr” package to get Cohen’s d
library(lsr)
cohensD(introq$Ideal~ introq$Gender)
[1] 1.487092
To put a confidence interval around d, I am going to use the “compute.es” package.
install.packages("compute.es")
Installing package into ‘C:/Users/Vati/Documents/R/win-library/3.2’
(as ‘lib’ is unspecified)
trying URL 'http://cran.rstudio.com/bin/windows/contrib/3.2/compute.es_0.2-4.zip'
Content type 'application/zip' length 272294 bytes (265 KB)
downloaded 265 KB
package ‘compute.es’ successfully unpacked and MD5 sums checked
library(compute.es)
des(d=1.487092, n.1=539, n.2=180)
Mean Differences ES:
d [ 95 %CI] = 1.49 [ 1.3 , 1.67 ]
var(d) = 0.01
p-value(d) = 0
Presenting the Results
Students in Professor Karl’s undergraduate statistics classes completed a brief survey. They
were asked to indicate their sex/gender and the height, in inches, of their ideal mate. Mean height of
ideal mate was significantly greater for female students (M = 71.43, SD = 3.25, n = 539) than for male
students (M = 66.59, SD = 3.27, n = 180), t(717) = 17.27, p < .001, d = 1.49, 95% CI [1.30. 1.67].
Wuensch’s R Lessons
