To perform a hypothesis test for two means you need to use the t.test()
function. You need to supply four pieces of information, data
, x
, and y
.
data
is the dataset from which the x
and y
variables reside.x
is a variable.y
is a variable.alternative
By default the alternative hypothesis is "two.sided", but you can also use "less", or "greater".There are two scenarios for which you may want to use the t.test()
function.
x
and y
variables in your dataset are listed in two columns you will want to use t.test()
like this.t.test(data = the.data, x = variable.1, y = variable.2, alternative="two.sided")
x
is a categorical variable and y
is a quantitative variable then you will want to use the t.test()
function like this.t.test(data = the.data, y ~ x, alternative="two.sided")
The steps for calculating a confidence interval are the same as those used for hypothesis testing. To calculate a confidence interval you need to specify conf.level
and make sure that alternative=two.sided
. By default, alternative = two.sided
so it is not necessary for you to include this, but it may help to remind you. By adding $conf.int
to the end of the function you will see only the confidence interval calculations.
t.test(data = the.data, x = variable.1, y = variable.2, alternative="two.sided")$conf.int
t.test(data = the.data, y ~ x, alternative="two.sided")$conf.int
The data for this example comes from the sleep
dataset. Suppose 20 individuals were randomized to one of two groups. Each group was given a set of tasks to perform. Participants recorded the amount of "extra" sleep they got after performing their tasks. Is the amount of extra sleep significantly different between the two groups?
# Hypothesis Test
t.test(data = sleep, extra ~ group, alternative = "two.sided" )
##
## Welch Two Sample t-test
##
## data: extra by group
## t = -1.8608, df = 17.776, p-value = 0.07939
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3.3654832 0.2054832
## sample estimates:
## mean in group 1 mean in group 2
## 0.75 2.33
# Confidence Interval
t.test(data=sleep, extra~group, conf.level = .95 )$conf.int
## [1] -3.3654832 0.2054832
## attr(,"conf.level")
## [1] 0.95
Mathematicss, Computer Science, and Statistics Department Gustavus Adolphus College