Calculating a Paired t-Test Equation

[Brad_Ad23]

What is the equation for a paired t-test?

 

[hypnagogue]

It's the same as a normal t-test. You just have to keep in mind that you're testing against the null hypothesis H₀: μ_D = 0, where μ_D is the population mean of differences between pairs of observations. So it's

t₀ = d(bar) / (s_d / √n)

where d(bar) and s_d are the sample mean and sample standard deviation for the differences between each pair.

edit: And just to be clear, n is the number of pairs of observations.

Basically, you treat this like a regular t-test problem, except your random variable is the difference between each pair of observations.

 

[tacman]

The equation for a paired t-test is as follows:

t = (x̄d - μd) / (sd / √n)

Where:
- t is the calculated t-statistic
- x̄d is the mean difference between the paired observations
- μd is the hypothesized population mean difference (usually 0)
- sd is the standard deviation of the differences
- n is the number of paired observations

This equation is used to determine the statistical significance of the difference between two paired samples. It takes into account the correlation between the paired observations and compares the mean difference to the hypothesized population mean difference. A t-statistic is calculated and compared to a critical value to determine if the difference is statistically significant or if it can be attributed to chance.