Question

Analysis of variance is a widely used methodology, across various disciplines, to test more than two means. Citing scholarly articles, describe why such methodology is so useful and what kind of data can be analyzed using such methodology.

Answer 1

Analysis of variance is a widely used methodology, across various disciplines, to test more than two means. Citing scholarly articles, describe why such methodology is so useful and what kind of data can be analyzed using such methodology.

ANOVA is a tool to compare several treatment means. In comparing t treatments, the null hypothesis tested is that the t true means are all equal (H0: µ1 = µ2 = ... = µt).

ANOVA is tested through the F test.

If the F test is significant, one accepts the alternative hypothesis, which states that the true means are not all equal (i.e. at least one µ is different).

ANOVA is useful because of the following reasons:

1. It allows testing of difference between homogenous groups like treatments ( Fisher, 1925) Thus it has wide applications in the real world.

2. Testing is done in a conservative and easy to understand manner, by calculating the ratio of variance between the groups to variance within the groups. This ratio is independent of several possible alterations like adding a constant to all observations or multiplying all observations by a constant. So statistical significance result is independent of constant bias, units used in observations and scaling errors .

3. It allows computation through simple algebra and determination of significance through a readily available F distributation table. Therefore, it can be easily be used by a number of people

4. It can compare several groups based on one factor, two factors or three factors. It provides results for both direct effects of each factor as well interaction effects of two or more factors, which provides clear understanding about the role of different combination of factors .

ANOVA has wide applications in social science and medicine related experiments. It can be used to analyse how a specific outcome can vary across different groups. Some examples of the kind of data that can be analysed using ANOVA are the following:

1. Difference between religions based on number of children

2. Difference between gender based on  propensity for depression

3. Difference between several treatments for a disease based on health parameters

Fisher R.(1925), Statistical Methods for Research Workers.

Cochran, William G.; Cox, Gertrude M. (1992). Experimental designs (2nd ed.).

Cohen, Jacob (1988). Statistical power analysis for the behavior sciences (2nd ed.).

Gelman, Andrew (2005). "Analysis of variance? Why it is more important than ever". The Annals of Statistics.33: 1–53.

Montgomery, Douglas C. (2001). Design and Analysis of Experiments (5th ed.)