Final answer:
When calculated, a large F ratio suggests greater variability between the groups than within them, indicating a likely real effect between the groups. The F statistic is a key component of ANOVA, used to compare means and decide if differences are statistically significant.
Step-by-step explanation:
When the F ratio has a large value, it indicates that the variability between the groups is greater than the variability within the groups. The F statistic is calculated as the ratio of the variance measured between the groups to the variance within the groups. If the F ratio is significantly greater than 1, it suggests the presence of a real effect, meaning that the means of the different groups are not all the same. In such cases, the null hypothesis (which usually states that the group means are equal) is likely to be rejected.
The F distribution is always right-skewed and its shape can vary depending upon the degrees of freedom in the numerator and the denominator. The degrees of freedom for the numerator are based on the number of groups minus one, while the denominator's degrees of freedom are based on the total number of observations minus the number of groups. When using ANOVA ({Analysis of Variance}), this F statistic can be used to compare the means across different groups.