The formula to calculate the F-statistic is:
\[ f = \frac{ \left( \frac{S_1 \times S_1}{\sigma_1 \times \sigma_1} \right)}{ \left( \frac{S_2 \times S_2}{\sigma_2 \times \sigma_2} \right)} \]
Where:
The F-statistic is a statistical measure used to compare the variances between two or more groups. It determines whether the differences observed between the group means are statistically significant or simply due to chance. This is important because it helps us understand if there are true differences between groups, allowing for more confident conclusions and informed decision-making.
Let's assume the following values:
Step 1: Calculate the variance ratios:
\[ \frac{S_1 \times S_1}{\sigma_1 \times \sigma_1} = \frac{2 \times 2}{1.5 \times 1.5} = \frac{4}{2.25} \approx 1.78 \]
\[ \frac{S_2 \times S_2}{\sigma_2 \times \sigma_2} = \frac{2.5 \times 2.5}{2 \times 2} = \frac{6.25}{4} = 1.56 \]
Step 2: Calculate the F-statistic:
\[ f = \frac{1.78}{1.56} \approx 1.14 \]
The F-Statistic (f) is approximately 1.14.