a mathematically defined curve that is the comparison distribution used n ANOVA is called the?
The mathematically defined curve used as a comparison distribution in ANOVA (Analysis of Variance) is called the F-distribution. This distribution is used to test the null hypothesis that the means of multiple groups are equal.
The mathematically defined curve that is used as the comparison distribution in ANOVA (Analysis of Variance) is called the F-distribution. The F-distribution is named after the British statistician Sir Ronald Fisher, who developed the ANOVA method.
To understand how to obtain the F-distribution for ANOVA, here are the steps:
1. Calculate the sum of squares between groups (SSbetween): This represents the variability between the means of different groups or treatments. It is obtained by summing the squared deviations of each group mean from the overall mean, multiplied by the number of observations in each group.
2. Calculate the sum of squares within groups (SSwithin): This represents the variability within each group or treatment. It is obtained by summing the squared deviations of each observation from its respective group mean.
3. Calculate the degrees of freedom (dfbetween and dfwithin): Degrees of freedom represent the number of independent pieces of information available for estimation. dfbetween is equal to the number of groups minus one, and dfwithin is equal to the total number of observations minus the number of groups.
4. Calculate the F-ratio: The F-ratio is the ratio of the mean squares for the groups (MSbetween = SSbetween / dfbetween) to the mean squares within the groups (MSwithin = SSwithin / dfwithin).
5. Use the F-distribution: The F-distribution is a probability distribution that provides critical values for the F-ratio, which can be used for hypothesis testing in ANOVA. These critical values depend on the chosen significance level (e.g., alpha = 0.05). By comparing the obtained F-ratio to the critical value from the F-distribution, you can determine if the differences between the group means are statistically significant or not.
In summary, the F-distribution is the comparison distribution used in ANOVA, and it helps to assess the statistical significance of differences between group means.