```
# Create sample data
<- tibble::tribble(
pressure ~SBPbefore, ~SBPafter,
120, 128,
124, 131,
130, 131,
118, 127,
140, 132,
128, 125,
140, 141,
135, 137,
126, 118,
130, 132,
126, 129,
127, 135
)
```

# Paired t-test

**Paired t-test in R**

The Paired t-test is used when two samples are naturally correlated. In the Paired t-test, the difference of the means between the two samples is compared to a given number that represents the null hypothesis. For a Paired t-test, the number of observations in each sample must be equal.

In R, a Paired t-test can be performed using the Base R `t.test()`

from the **stats** package or the `proc_ttest()`

function from the **procs** package.

## Normal Data

By default, the R paired t-test functions assume normality in the data and use a classic Student’s t-test.

### Data Used

The following data was used in this example.

### Base R

#### Code

The following code was used to test the comparison in Base R.

```
# Perform t-test
t.test(pressure$SBPbefore, pressure$SBPafter, paired = TRUE)
```

```
Paired t-test
data: pressure$SBPbefore and pressure$SBPafter
t = -1.0896, df = 11, p-value = 0.2992
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
-5.536492 1.869825
sample estimates:
mean difference
-1.833333
```

### Procs Package

#### Code

The following code from the **procs** package was used to perform a paired t-test.

```
library(procs)
# Perform t-test
proc_ttest(pressure,
paired = "SBPbefore*SBPafter")
```

```
$Statistics
VAR1 VAR2 DIFF N MEAN STD STDERR MIN MAX
1 SBPbefore SBPafter SBPbefore-SBPafter 12 -1.833333 5.828353 1.682501 -9 8
$ConfLimits
VAR1 VAR2 DIFF MEAN LCLM UCLM STD
1 SBPbefore SBPafter SBPbefore-SBPafter -1.833333 -5.536492 1.869825 5.828353
LCLMSTD UCLMSTD
1 4.128777 9.895832
$TTests
VAR1 VAR2 DIFF DF T PROBT
1 SBPbefore SBPafter SBPbefore-SBPafter 11 -1.089648 0.2991635
```

Viewer Output:

## Lognormal Data

The Base R `t.test()`

function does not have an option for lognormal data. Likewise, the **procs** `proc_ttest()`

function also does not have an option for lognormal data.

One possibility may be the `tTestLnormAltPower()`

function from the **EnvStats** package. This package has not been evaluated yet.