The formula to calculate the Paired Difference Test statistic is:
\[ t = \frac{\bar{D} - \mu_D}{\frac{SD}{\sqrt{n}}} \]
Where:
A Paired Difference Test is a statistical procedure used to determine whether the mean difference between two sets of observations is zero. It is often used in before-and-after situations where the same subjects are measured twice, under different conditions. The test pairs each observation in one set with an observation in the other set, calculates the differences within each pair, and analyzes these differences. The test assumes that the differences in the entire population of pairs follow a normal distribution.
Let's assume the following values:
Step 1: Subtract the hypothesized mean difference from the mean of the differences:
\[ 1.5 - 0 = 1.5 \]
Step 2: Divide this result by the standard deviation of the differences divided by the square root of the number of pairs:
\[ t = \frac{1.5}{\frac{2.5}{\sqrt{10}}} = \frac{1.5}{0.79} \approx 1.90 \]
The Test Statistic (t) is approximately 1.90.