The formula to calculate the t-value in a dependent t-test is:
\[ t = \frac{M - \mu}{\frac{s}{\sqrt{n}}} \]
Where:
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.
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.
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.