Question

Are one way ANOVA, Bartletts test and Levene test parametric or non parametric hipothesis tests and why?

I need some explanation on this as i dont quite understand what it means to be a parametric or non parametric test. Thank you?

Answer 1

Parametric tests involve specific probability distributions (e.g., the normal distribution) and the tests involve estimation of the key parameters of that distribution (e.g., the mean or difference in means) from the sample data.

Nonparametric statistics are called distribution-free statistics because they are not constrained by assumptions about the distribution of the population.Nonparametric tests are based on fewer assumptions (e.g., they do not assume that the outcome is approximately normally distributed).It is best to use non-parametric test when data does not follow normal distribution

Now for one way ANOVA we assume that the data follows normal distribution. Hence it's a parametric hypothesis test.

Bartlett's test  is used to test if k samples are from populations with equal variances. Bartlett's test is sensitive to departures from normality. That is, if your samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality.If you have strong evidence that your data do in fact come from a normal, or nearly normal, distribution, then Bartlett's test has better performance. Hence a parametric test

Levene's test is an alternative to the Bartlett test. The Levene test is less sensitive than the Bartlett test to departures from normality. Levene's test assumes only that your data form random samples from continuous distributions. Hence it's a non-parametric test