Which of the following is not typically calculated when performing a one-way ANOVA?

In a one-way ANOVA, the primary focus is on comparing the means of different groups to determine if there are any statistically significant differences between them. To achieve this, several statistics are calculated, including the mean, variance, and sum of squares.

The mean is calculated for each group to provide a measure of central tendency. Variance is also calculated since it helps in understanding the dispersion of the data points within each group. The sum of squares is crucial in ANOVA because it quantifies the total variability in the data: it divides this total variability into components associated with the different groups and the error.

While standard deviation is important in statistics as it provides a measure of dispersion, it is derived from the variance and thus is not specifically calculated as a separate value during a one-way ANOVA. Instead, variance serves as the foundational statistic from which standard deviation is derived (the square root of variance). Since standard deviation is not a primary component in the process of conducting a one-way ANOVA, it is the correct answer to the question regarding what is not typically calculated.