ANOVA Assumption of Homogeneity of Variance: Analysis & Implications

Introduction

Applying the approach of homogeneity of variance in a study, one has to understand the assumption that variance that exists between different populations has to be equal. This assumption is referred to as the analysis of variance which is commonly known as ANOVA. The study of variance is said to work correctly even in cases where the assumption has been violated or ignored (Blanca et al., 2017). However, the analysis of variance cannot work well in cases where there is the use of odd numbers of the subjects which are being used in different groups. In instances where variance is not homogenous, they are said to be heterogeneous. When the assumption of homogeneity is violated, there are four options which can be considered; the options include; the independent t-test might not be a right statistical test to be conducted in this procedure, in this case, there is a need to consider a lower nonparametric statistical analysis. The second option which is to be considered is that the t-test might not be the correct statistical test which can be done; for this reason, the test needs to be abandoned altogether. The third option is that the assumption will ignore the violation which has occurred and the test will be conducted as a parametric measure; this will also use the robust nature of the criteria which can be performed. The fourth option is to do a resample and increase the sample size that is being considered. This way, it will be possible to avoid the violations, and the test can be conducted as expected.

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In this case, each of the options that have been listed has pros and cons. Through the exploration of these pros and cons, one can be able to select the best option which he or she can use in his or her study. The first option, after the violation has occurred, the autonomous t-test is not considered as the proper statistical test, and a lower order non-parametric measure is used. The pros of this option include; the researcher is not limited to the type of analysis which he or she can do in the study, the non-parametric tests are free from assumptions that are made in the parametric analysis. However, the con for this option is that the non-parametric report is considered to be less potent as compared to the parametric study.

The second option is to consider the t-test as not the right tests for analysis since a violation has been done. This means that the test will be abandoned altogether. For this option, the advantage is that a different appropriate statistical test will be sought to make sure that a proper analysis is conducted. However, finding an appropriate conventional method for analytical testing might be time-consuming and, in some cases, the conservative methods that will be used instead of the t-test might be quite tricky to follow and find the required results. Another option is to ignore the violation which has been made and carry on using the parametric test in the research, in this case, the robust nature of the parametric tests is considered as a system of assuring that the tests will provide the required results for the study. In this option, the advantage is, using the robust nature of the parametric tests, it will be possible to determine ways of finding the best results for the study that is being done. However, the disadvantage of this option is that the researcher assumes normality (Jupiter, 2017). In this case, if the data on the variables is not transformed, it will be challenging to provide an interpretation of the results. The fourth option is to resample the study with a population which is much larger and then conduct a retest on the data. In this case, violations will be avoided, and the results which will be obtained for the study can be appropriately explained and also conclusive (Lane, 2016). However, this option will be time-consuming, by increasing the sample size, it also means that the resources which are used for the study have to be increased making it hard to complete the survey.

Conclusion

In my case, I will be conducting a study on high rates of dropouts in schools in the state as compared to surrounding school districts. Researching this field, it will be possible to understand the reason learners are dropping out of the public education system. This is aimed at ensuring that plans are established to close the gap of learners leaving school and increasing Florida State Assessment scores in studying1. Understanding the effects state testing have on student drop out. In this study, I will use the fourth option; this is because of the study aims at presenting findings which can be used to develop policies. Making violations and assumptions might lead to outcomes which are not representative of the real situation or results which will be difficult to explain. By increasing the sample size, it means that the analysis which will be done will not include any form of violations.

References

Blanca, M., Alarcon, R., Arnau, J., Bono, R., & Bendayan, R. (2017). Non-normal data: Is ANOVA still a valid option? Psicothema, 29(4), 552-557. http://www.psicothema.com/pdf/4434.pdf

Jupiter, D. C. (2017). Assumptions of statistical tests: What lies beneath. The Journal of Foot and Ankle Surgery, 56(4), 910-913. DOI: 10.1053/j.jfas.2017.05.022

Lane, D. (2016). The assumption of sphericity in repeated-measures designs: What it means and what to do when it is violated. Quantitative Methods for Psychology, 12, 114-122. http://www.tqmp.org/RegularArticles/vol12-2/p114/p114.pdf