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 VariablesFormula
The paired t-test statistics value can be calculated using the following formula:
\[
t = \frac{m}{s/\sqrt{n}}
\]
where,
mis the mean differencesnis the sample size (i.e., size of d).sis 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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