This article describes the **one sample t-test assumptions** and provides examples of R code to check whether the assumptions are met before calculating the t-test.

Contents:

#### Related Book

Practical Statistics in R II - Comparing Groups: Numerical Variables## Assumptions

The one-sample t-test assumes the following characteristics about the data:

**No significant outliers**in the data**Normality**. the data should be approximately normally distributed

In this section, we’ll perform some preliminary tests to check whether these assumptions are met.

## Check one-sample t-test assumptions in R

### Prerequisites

Make sure you have installed the following R packages:

`ggpubr`

for creating easily publication ready plots`rstatix`

provides pipe-friendly R functions for easy statistical analyses.`datarium`

: contains required data sets for this chapter.

Start by loading the following required packages:

```
library(ggpubr)
library(rstatix)
```

### Demo data

Demo dataset: `mice`

[in datarium package]. Contains the weight of 10 mice:

```
# Load and inspect the data
data(mice, package = "datarium")
head(mice, 3)
```

```
## # A tibble: 3 x 2
## name weight
## <chr> <dbl>
## 1 M_1 18.9
## 2 M_2 19.5
## 3 M_3 23.1
```

### Identify outliers

Outliers can be easily identified using boxplot methods, implemented in the R function `identify_outliers()`

[rstatix package].

`mice %>% identify_outliers(weight)`

```
## [1] name weight is.outlier is.extreme
## <0 rows> (or 0-length row.names)
```

There were no extreme outliers.

Note that, in the situation where you have extreme outliers, this can be due to: 1) data entry errors, measurement errors or unusual values.

In this case, you could consider running the non parametric Wilcoxon test.

### Check normality assumption

The normality assumption can be checked by computing the Shapiro-Wilk test. If the data is normally distributed, the p-value should be greater than 0.05.

`mice %>% shapiro_test(weight)`

```
## # A tibble: 1 x 3
## variable statistic p
## <chr> <dbl> <dbl>
## 1 weight 0.923 0.382
```

From the output, the p-value is greater than the significance level 0.05 indicating that the distribution of the data are not significantly different from the normal distribution. In other words, we can assume the normality.

You can also create a QQ plot of the `weight`

data. QQ plot draws the correlation between a given data and the normal distribution.

`ggqqplot(mice, x = "weight")`

All the points fall approximately along the (45-degree) reference line, for each group. So we can assume normality of the data.

Note that, if your sample size is greater than 50, the normal QQ plot is preferred because at larger sample sizes the Shapiro-Wilk test becomes very sensitive even to a minor deviation from normality.

If the data are not normally distributed, it’s recommended to use a non-parametric test such as the *one-sample Wilcoxon signed-rank test*. This test is similar to the one-sample t-test, but focuses on the median rather than the mean.

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