Describe how you understand ANOVA - Case Study Example

Understanding the ANOVA When attempting to examine the potential differences between three or more groups of scores; it is necessary to examine thesegroups simultaneously. Pair wise comparisons are not only tedious and time consuming; but also prone to error. Since we have to accept a minimum possibility of error for each comparison made; the chances for type I error to occur across a large number of comparisons keeps increasing exponentially with the number of comparisons (Guilford, & Fruchter, 1973).

For three groups, there will be 3 comparisons; for four groups there will be six comparisons and so on. In order to contain the error and compare all groups simultaneously, the Analysis of Variance or ANOVA may be used.The ANOVA is a statistical method that compares the variance associated with groups of scores and the variance associated with individual differences among scores in order to test the significance of the difference between groups (Guilford, & Fruchter, 1973). According the Bass (2007), the ratio of the variance between groups (which occurs due to differences in the treatments) and the variance within groups (due to individual differences) tells us the extent to which the total variance may be attributed to the treatments or group distinctions.

The null hypothesis for the ANOVA is that “the means for each group are the same at a given level of significance”, while the alternate hypothesis states that “the means are significantly different from each other”. The alternate hypothesis is true when the variations in the treatment levels are not due to error or individual differences but due to the differences in the treatment levels. This concept is explained very well by Bass (2007).The ANOVA is a parametric statistic; and thus requires that certain assumptions about the population from which the data is collected be met.

These assumptions are that the Population from which data is taken should be normal.The variance of each group be equal.All samples should be collected randomly so that they can come from any part of the population.All samples should be independent of each other (Bass, 2007). Although it is important that these criteria be met in order for the statistic value to be strong and reliable; a slight deviation from the ideal is acceptable as the ANOVA is quite a robust statistic. The ANOVA statistic is calculated as the F statistic, and is based on the F distribution of scores (Bass, 2007).

If the calculated value of the ANOVA is equal to or higher that the F statistic presented at the stated level of significance; then we reject the null hypothesis. On the other hand, if the F value calculated is lower to the tabulated value, we accept the null hypothesis. References:Bass, I. (2007). Analysis of variance. Six sigma statistics with Excel and Minitab. New York : McGraw-Hill.Guilford, J. P., & Fruchter, B. (1973). Fundamental statistics in psychology and education. (5th ed.). New York: McGraw-Hill.