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F-Distribution Overview

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Definition of F-Distribution

Used to compare two variances and often in ANOVA.

F = \frac{\text{Variance between samples}}{\text{Variance within samples}}

Degrees of Freedom

Determined by the number of samples and data points. Formulas: $df_1 = n_1 - 1$ , $df_2 = n_2 - 1$

Shape of F-Distribution

Skewed to the right, depends on degrees of freedom. No fixed mean or mode.

Use in Analysis of Variance (ANOVA)

Determines if there are significant differences between group means.

F = \frac{MS_{\text{between}}}{MS_{\text{within}}}

Critical Values of F-Distribution

Values that define the rejection region in a hypothesis test. Dependent on $df_1$ , $df_2$ , and significance level.

Calculating P-value from F-Statistic

Shows the probability of obtaining an F-statistic as extreme or more extreme than the observed value. Use F-distribution tables or software.

Assumptions Behind F-Distribution

Populations from which samples are drawn should be normally distributed and have equal variances.

H_0: \sigma_1^2 = \sigma_2^2

When to Use F-Distribution

When comparing the variances of two independent samples or in the context of ANOVA for comparing means.

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