How to use T-test in R to Compare Means

Introduction

One common test on samples is the mean test. The t-test is widely used in this regard. For example, maybe you know that the average sales for your company per a week is $500, and you just collected a couple of weeks of sales data. You would like to conduct a hypothesis test as to if your new sample is different than the avg$500. In this article, we will learn how to use the t-test to test the mean of a sample in R.

The Basic Test

Continuing from our example, let’s say we have collected five weeks of sales data. We know that the average sales per week is $500, so we will conduct a test to see if our recent samples differ. We can use the t.test method to perform this test.

recent.sales = c(400, 600, 850, 550)
avg.sales = 500

t.test(recent.sales, mu=avg.sales)

## 
##  One Sample t-test
## 
## data:  recent.sales
## t = 1.069, df = 3, p-value = 0.3634
## alternative hypothesis: true mean is not equal to 500
## 95 percent confidence interval:
##  302.3094 897.6906
## sample estimates:
## mean of x 
##       600

# One Sample t-test

# data:  recent.sales
# t = 1.069, df = 3, p-value = 0.3634
# alternative hypothesis: true mean is not equal to 500
# 95 percent confidence interval:
#  302.3094 897.6906
# sample estimates:
# mean of x 
#       600 

There is quite a bit of information here, but the focus for now will be on the p-value. Since this number is higher than .05, in this case we will fail to reject the null hypothesis. That means, we do not have enough evidence to say that our sample data is different from the average.

Viewing the T-test object

Now, that we have conducted our first t-test. Let’s take a look at the response object to see what other information is returned. We can use the names method to see which properties are on the return t-test.

result = t.test(recent.sales, mu=avg.sales)

names(result)

##  [1] "statistic"   "parameter"   "p.value"     "conf.int"    "estimate"   
##  [6] "null.value"  "stderr"      "alternative" "method"      "data.name"

You can see there are quite a bit of values returned. These are helpful for different reasons. Let’s extract the p.value and conf.int for an example.

result$p.value

## [1] 0.3634261

result$conf.int

## [1] 302.3094 897.6906
## attr(,"conf.level")
## [1] 0.95