# T-tests

First we will conduct an independent two sample t-test i.e. the samples are from two different sets of participants. We simply use the two numeric vectors that we wish to test as the inputs to the `t.test()` function. In the example below we can see that the means are significantly different

``````
Input:
data <- data.frame(ID=seq(1,25,1), ScoreOne=rpois(25,20),ScoreTwo=rpois(25,35))
t.test(data\$ScoreOne,data\$ScoreTwo)

Output:
Welch Two Sample t-test

data:  data\$ScoreOne and data\$ScoreTwo
t = -8.4501, df = 36.02, p-value = 4.539e-10
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-18.55044 -11.36956
sample estimates:
mean of x mean of y
20.80     35.76
``````
``` ```

The most common way to visualise data relating to a t.test is to use a box plot as this plot type visualises the mean, range, quartiles and overlap of the data. Boxplots are created using the `boxplot()` function.

``````
Input:
boxplot(data\$ScoreOne,data\$ScoreTwo)

Output: ``````
``` ```

If we are comparing the means of data produced by the same participants we use a paired t-test. The only difference to the independent t-test is that we use the argument `paired=TRUE`. In the example below we can see that the means of the two numeric vectors that make up our data are not significantly different.

``````
Input:
dataP <- data.frame(ID=seq(1,25,1), Age=sample(18:99,25,replace=TRUE), Gender=sample(1:2,25,replace=TRUE), ScoreOne=sample(0:50,25,replace=TRUE), ScoreTwo=sample(0:50,25,replace=TRUE))
t.test(dataP\$ScoreOne,dataP\$ScoreTwo,paired=TRUE)

Output:
Paired t-test

data:  dataP\$ScoreOne and dataP\$ScoreTwo
t = -1.0953, df = 24, p-value = 0.2843
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-14.306582   4.386582
sample estimates:
mean of the differences
-4.96
``````
``` ```

Plotting our data as a boxplot confirms that the means are close together and there is a great deal of overlap in the data even though the inter-quartile spread of the data is different.

``````
Input:
boxplot(dataP\$ScoreOne,dataP\$ScoreTwo)

Output: ``````
``` ```