Emily-Jane Bray

2020-10-26

When should i use the ANOVA test?
Remember that some tests, such as chi squared, can be used under various circumstances. The goal of the test changes based on the situation. Pay attention to the specific conditions noted in
parenthesis to ensure you are picking the correct goal.

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The ANOVA (analysis of variance) is a test used for comparing the means of several populations. The following are the assumptions and conditions that must be satisfied, if one wishes to use ANOVA:
Nature of data: The data on which the analysis is to be performed, must be in an interval or a ratio scale.
Independence: The observations are sampled independently of one another.
Normality: The residuals of the model must be normally distributed.
Homoscedasticity: The variances of the groups compared must not be significantly different. Nature of multicollinearity: The various categories to be compared using the test must be independent of one another, that is, there must be no multicollinearity among the categories. Remember that, ANOVA cannot be performed if normal distribution is not satisfied, or the variances of the categories are unequal. Moreover, it is not used to compare medians, but means. An ANOVA requires at least two different populations, it cannot be used to check whether the mean of a single population equals a constant. It cannot be used to check whether a data set fits a known discrete or continuous probability model using expected and observed frequencies. An ordinary ANOVA cannot be used to compared paired data, rather a repeated measures ANOVA may be used to compare paired data, provided the assumptions, especially that of normality and homoscedasticity are satisfied.
Hence, it can be observed that only Option I satisfies the requirement to perform ANOVA- that is, use ANOVA when more than two treatment groups are to be compares, provided normality can be assumed.
Additionally, it must be ANOVA is conventionally used for comparing the means of more than 2 categories. Although it is not exactly wrong if one uses it to compare 2 means, it must be remembered that if all the assumptions and conditions to conduct an ANOVA are already satisfied, then it is unnecessary to go through the comparatively complicated process of an ANOVA, rather, it would be preferable to use an independent samples t-test.

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