## Using R in Psychology

## Simple descriptive statistics and the t-test

An investigator believes that caffeine facilitates performance on a simple spelling test. Two groups of subjects are given either 200 mg of caffeine or a placebo. The data are:

Placebo Drug 24 24 25 29 27 26 26 23 26 25 22 28 21 27 22 24 23 27 25 28 25 27 25 26

To describe the differences between these two groups, we can use basic descriptive statistics (means and standard deviations), and graph the results. To see how likely a difference of this magnitude would happen by chance if, in fact, the two groups were sampled from the same population, we can do a t-test.

The next few lines show how this is done in R.

## Data entry and descriptive statistics

library(psych) #make sure the psych package is installed and loaded #now, copy the data into the clipboard and then read it into R experiment.1 <- read.clipboard() experiment.1 #show the data, to make sure we got it summary(experiment.1) #basic descriptive statistics describe(experiment.1) #another way to get descriptive statistics #now some simple descriptive graphics #The boxplot shows the Tukey 5 numbers boxplot(experiment.1,main="Effect of Caffeine on a spelling test",ylab="Spelling Performance") #a stripchart shows the actual data points stripchart(experiment.1,method="jitter",jitter=.05,vertical=T,add=T) #show the raw data as well added to the boxplot multi.hist(experiment.1) #show the histograms if we want with(experiment.1, t.test(Placebo,Drug,equal.var=TRUE) ) #the t-test

The code above produces this output:

> experiment.1 #show the data, to make sure we got it Placebo Drug 1 24 24 2 25 29 3 27 26 4 26 23 5 26 25 6 22 28 7 21 27 8 22 24 9 23 27 10 25 28 11 25 27 12 25 26 > > summary(experiment.1) #basic descriptive statistics Placebo Drug Min. :21.00 Min. :23.00 1st Qu.:22.75 1st Qu.:24.75 Median :25.00 Median :26.50 Mean :24.25 Mean :26.17 3rd Qu.:25.25 3rd Qu.:27.25 Max. :27.00 Max. :29.00 > describe(experiment.1) #another way to get descriptive statistics var n mean sd median trimmed mad min max range skew kurtosis se Placebo 1 12 24.25 1.86 25.0 24.3 1.48 21 27 6 -0.33 -1.33 0.54 Drug 2 12 26.17 1.85 26.5 26.2 2.22 23 29 6 -0.22 -1.33 0.53 > #now some simple descriptive graphics > boxplot(experiment.1,main="Effect of Caffeine on a spelling test",ylab="Spelling Performance") #show some basic descriptive graphics > stripchart(experiment.1,method="jitter",jitter=.05,vertical=T,add=T) #show the raw data as well added to the boxplot > > multi.hist(experiment.1) #show the histograms if we wantand produces the following two graphs:

## The t-test (equal sample sizes)

In the case that the samples sizes are equal for the two conditions, we read the data into a 12 x 2 data frame and do the t-test on that data.frame.> with(experiment.1, t.test(Placebo,Drug,equal.var=TRUE) ) #the t-test Welch Two Sample t-test data: Placebo and Drug t = -2.5273, df = 21.999, p-value = 0.01918 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -3.4894368 -0.3438965 sample estimates: mean of x mean of y 24.25000 26.16667

## t-test, unequal sample sizes -- two ways

But if the sample sizes are not equal, we need to either specify the missing data, or enter the responses and conditions as separate variables.If the number of observations in the two groups are unequal, you can either enter missing value codes (NA) for the condition with the fewer observations, or you can "string out the data" by specifying the condition and the observations.### Missing values are specified by NA

Missing values are specified by NA Placebo Drug 1 24 24 2 25 29 3 27 26 4 26 23 5 26 25 6 22 28 7 21 27 8 22 24 9 23 27 10 25 28 11 25 27 12 25 26 13 22 NA 14 25 NA #copy the data into the clipboard, read the clipboard, and then do the normal t-test. exp.1 <- read.clipboard() #make sure the data are in the clipboard with(exp.1, t.test(Placebo,Drug,equal.var=TRUE) ) Produces this output: > exp.1 <- read.clipboard() > with(exp.1, t.test(Placebo,Drug,equal.var=TRUE) ) Welch Two Sample t-test data: Placebo and Drug t = -2.7917, df = 23.327, p-value = 0.01028 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -3.5223056 -0.5253134 sample estimates: mean of x mean of y 24.14286 26.16667

### or, if the data are strung out

spelling conditions 1 24 Placebo 2 25 Placebo 3 27 Placebo 4 26 Placebo 5 26 Placebo 6 22 Placebo 7 21 Placebo 8 22 Placebo 9 23 Placebo 10 25 Placebo 11 25 Placebo 12 25 Placebo 13 22 Placebo 14 25 Placebo 15 24 Drug 16 29 Drug 17 26 Drug 18 23 Drug 19 25 Drug 20 28 Drug 21 27 Drug 22 24 Drug 23 27 Drug 24 28 Drug 25 27 Drug 26 26 DrugCopy the data into the clipboard, read the clipboard, and then run t.test using a formula:

exp.3 <- read.clipboard() with(exp.3, t.test(spelling~conditions)Produces this output

> exp.3 <- read.clipboard() > with(exp.3,t.test(spelling~conditions)) Welch Two Sample t-test data: spelling by conditions t = 2.7917, df = 23.327, p-value = 0.01028 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.5253134 3.5223056 sample estimates: mean in group Drug mean in group Placebo 26.16667 24.14286

part of a short guide to R

Version of March 28, 2010

William Revelle

Department of Psychology

Northwestern University