A mathematically defined curve that is the comparison distribution used in ANOVA is called the:



- Normal distribution

- Chi Square distribution

- F distribution

- T distribution

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The mathematically defined curve that is the comparison distribution used in ANOVA is called the F distribution. To understand why, let me explain how to get to this answer.

ANOVA stands for Analysis of Variance. It is a statistical technique used to compare means of three or more groups to determine if there are any significant differences between them. In ANOVA, we compare the variation between the groups to the variation within the groups.

To do this comparison, ANOVA uses a test statistic called the F-statistic. This F-statistic follows the F distribution. The F distribution is a probability distribution that is skewed to the right, with values that can range from 0 to positive infinity. It is commonly used in hypothesis testing and is specifically designed for comparing variances.

The F distribution depends on two degrees of freedom: the degrees of freedom for the numerator (df₁) and the degrees of freedom for the denominator (df₂). df₁ represents the number of groups minus one, while df₂ represents the total number of observations minus the number of groups.

In ANOVA, the F distribution is used to calculate the p-value associated with the F-statistic. This p-value helps determine if the observed difference between the means of the groups is statistically significant or if it could be due to random chance.

So, in summary, the mathematically defined curve that is the comparison distribution used in ANOVA is the F distribution.