what is homoscedasticity and what is its relevance to statistical analysis?
In: Mathematics
Homoscedasticity is another word for homogeneity of variances. Let’s take a simple example: you have two groups of 10 people playing the same video game on a different console. In group 1, the fastest player to finish a particular part of the game does so in 30 minutes, while the slowest does so in 5 hours. In group 2, the fastest player to finish that same part does so in 32 minutes, while the slowest does so in 52 minutes. The variance of the times in group 1 is way bigger than in group 2. So the assumption of homoescedascity is violated in this case.
Why is this relevant for statistical analysis? You basically got two flavors of statistical tests: parametric and non-parametric tests. For paramatric tests to make sense, they have have the assumption of homoescedasticity. So when that assumption is violated (as in the example I just gave), on of the basic assumptions is violated, leading to nonsensical results. When 1 or multiple assumptions of parametric tests are violated, using the non-parametric variant is advised.
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