This article describes the **paired t-test formula**, which is used to compare the means of two related groups or samples. The paired t-test formula is also referred as:

*dependent t test formula*,*paired sample t test formula*,*paired samples t test formula*,*formula for paired t test*,*paired t test equation*and*dependent t test equation*

The procedure of the paired t-test analysis is as follow:

- Calculate the difference (\(d\)) between each pair of value
- Compute the mean (\(m\)) and the standard deviation (\(s\)) of \(d\)
- Compare the average difference to 0. If there is any significant difference between the two pairs of samples, then the mean of d (\(m\)) is expected to be far from 0.

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#### Related Book

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

The paired t-test statistics value can be calculated using the following formula:

\[

t = \frac{m}{s/\sqrt{n}}

\]

where,

`m`

is the mean differences`n`

is the sample size (i.e., size of d).`s`

is the standard deviation of d

We can compute the p-value corresponding to the absolute value of the t-test statistics (|t|) for the degrees of freedom (df): \(df = n - 1\).

If the p-value is inferior or equal to 0.05, we can conclude that the difference between the two paired samples are significantly different.

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