The F Distribution and the F Ratio Quiz

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and one for the denominator. For example, if F follows an F distribution and the number of degrees of freedom for the numerator is 4, and the number of degrees of freedom for the denominator is 10, then F ~ F4,10. NOTE The F distribution is derived from the Student’s t-distribution. The values of the F distribution are squares of the corresponding values of the t-distribution. One-way ANOVA expands the t-test for comparing more than two groups. The scope of that derivation is beyond the level of this course. It is preferable to use ANOVA when there are more than two groups instead of performing pairwise t-tests because performing multiple tests introduces the likelihood of making a Type 1 error.

PDF page 771: To calculate the F ratio, two estimates of the variance are made.

PDF page 771: sizes are the same. If the samples are different sizes, the variance between samples is weighted to account for the different sample sizes. The variance is also called variation due to treatment or explained variation.

PDF page 771: variance. When the sample sizes are different, the variance within samples is weighted. The variance is also called the variation due to error or unexplained variation.

PDF page 771: To find a sum of squares mean, add together squared quantities which, in some cases, may be weighted. We used sum of squares to calculate the sample variance and the sample standard deviation in Descriptive Statistics. MS means mean square. MSbetween is the variance between groups, and MSwithin is the variance within groups.

PDF page 772: within If MSbetween and MSwithin estimate the same value, following the belief that H0 is true, then the F ratio should be approximately equal to 1. Mostly, just sampling errors would contribute to variations away from 1. As it turns out, MSbetween