Dependent T-Test Calculator









Formula

The formula to calculate the t-value in a dependent t-test is:

\[ t = \frac{M - \mu}{\frac{s}{\sqrt{n}}} \]

Where:

What is a Dependent T-Test?

A Dependent T-Test, also known as a paired sample T-Test, is a statistical procedure used to determine whether the mean difference between two sets of observations is zero. It is used when the observations are dependent; that is, when there is a meaningful relationship between the two sets of data, such as a before-and-after scenario or when the same subjects are measured more than once under different conditions.

Example Calculation 1

Let's assume the following values:

Step 1: Subtract the hypothesized population mean difference from the mean difference score:

\[ M - \mu = 2.5 - 0 = 2.5 \]

Step 2: Divide the standard deviation of the difference scores by the square root of the total number of pairs:

\[ \frac{s}{\sqrt{n}} = \frac{1.2}{\sqrt{30}} \approx 0.219 \]

Step 3: Divide the first result by the second result to get the t-value:

\[ t = \frac{2.5}{0.219} \approx 11.42 \]

Therefore, the t-value is approximately 11.42.

Example Calculation 2

Let's assume the following values:

Step 1: Subtract the hypothesized population mean difference from the mean difference score:

\[ M - \mu = 1.8 - 0 = 1.8 \]

Step 2: Divide the standard deviation of the difference scores by the square root of the total number of pairs:

\[ \frac{s}{\sqrt{n}} = \frac{0.9}{\sqrt{25}} = 0.18 \]

Step 3: Divide the first result by the second result to get the t-value:

\[ t = \frac{1.8}{0.18} = 10 \]

Therefore, the t-value is 10.