Limitations and Requirements of ANOVA - Essay Example

PROJECT al Affiliation) ANOVA makes a comparison of the means between two samples or more. Where the number of samples are more than two ANOVA on its own is incomplete. It is impossible to determine with certainty whether the intermediates differ significantly from either extremes. For this reason the multiple comparison tests need to be used. Multiple comparison tests in association with ANOVA work efficiently, the latter is mostly reliable for differences detection. For data to be analyzed using ANOVA, the points of data must be autonomous from each other.

For distributions to be accommodated they must be normal, small departures may also be accommodated. The samples’ variances should not be different though some departures can be accommodated. All individuals used in the samples must be selected randomly from the population. All individuals of the samples must have equal probability for being selected. The sizes of the sample should be equal but there is an allowance of some differences. One of the limitations of ANOVA is that, when a significant data difference cannot be found, the samples cannot be said to be the same.

It only indicates differences between groups and not groups which are different. Normality assumes that the errors which are random within each group of treatment, the groups’ mean deviations, have a normal probability distribution. For normal data but variances which are heterogeneous, ANOVA is good for balanced designs but not for designs which are highly unbalanced. In normal data setting, heterogeneous variances and designs which are unbalanced, Welch’s ANOVA might be used for the accommodation of unequal variances.

With variances which are homogenous but data which is non-normal, ANOVA is good for designs which are balanced with large samples. It is not good for unbalanced designs with small samples. In non-normal data setting, variances which are homogenous and a small sample or unbalanced design, a non-parametric procedure is preferred. If the distribution of data is not normal and heterogeneity of variances exist, there might be transformation necessity. The importance of a design which is balanced and existence of a large sample must be put into consideration.

A common standard deviation is shared by all normal distributions. The different t-test options can be used around the equal variances assumptions or unequal variances assumption. The f-test, apart from being used to for t-tests, it can also be used to compare variations in two data sets in the CJ data. The test makes use of a calculated F stat and calculated F critical which are compared in a table of statistics. The F stat is calculated by dividing the large sample variance by the smaller sample variance.

In an F table, the column V is looked upon for the variance of the larger sample, and along the table top the row relating to the variance of the smaller sample is checked. If the degrees of freedom are not exactly given, an assumption that the critical value being less than highest next value is given. This would be the F critical. If the F stat and is less than the F critical, the variances of the samples are assumed to be equal. The F test applied on the CJ data requires the independent distribution of the two variances.

In variance analysis, the convention of putting the larger variance of the sample in the F statistic variance numerator cannot be applied. ReferenceSpiegel, M. R., & Stephens, L. J. (2011). Statistics (4th ed.). New York: McGraw-Hill.