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F-Distribution Overview

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Degrees of Freedom

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

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

Definition of F-Distribution

Used to compare two variances and often in ANOVA.

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

When to Use F-Distribution

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

Use in Analysis of Variance (ANOVA)

Determines if there are significant differences between group means.

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

Shape of F-Distribution

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

Critical Values of F-Distribution

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

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