# Non-robustness of parametric statistics

Why is parametric test considered to be non-robust ?

Or, why is parametric test not considered to be robust?

• Why does your title refer to robustness of statistics, but your body refer to robustness of tests? Which should be discussed? Commented Feb 14, 2015 at 5:41
• Some context for the question might help guide answers. Commented Feb 14, 2015 at 7:28

Why is parametric test considered to be non-robust ? Or, why is parametric test not considered to be robust?

Strictly speaking, for this to apply you'd have to say which parametric tests and which kind of robustness you're looking at (robustness of what - level? power? -- and against what kind of departures from assumptions?)

As a generalization, it really isn't true; some parametric tests are quite robust.

Certainly some parametric tests really aren't robust - at least against some things.

The classic example is the F-test for normal variances, which is definitely not level-robust to deviations from normality.

But consider, for example, a two-sample parametric test for location in the logistic distribution (let's say we're dealing with a likelihood ratio test). It's pretty robust to departures from the parametric distributional assumptions; it can deal with lighter or heavier tails reasonably well - it's at least reasonably level-robust, especially against smooth, symmetric, equal-variance departures from the assumptions.

The t-test does fairly well for moderate departures from normality; however, it's not so (level-)robust to departures from equal variance unless sample sizes are equal or quite close to it. However the Welch test (which is still parametric) is reasonably robust against departures from equal variance and moderate departures from normality.

• What is LRT ? It seems i need some prerequisite learning for understanding your answer such as robustness(though i have read the Wikipedia,i need additional reading) and etc. Would you please give me some reference so that i can understood your answer thoroughly ?
– time
Commented Feb 14, 2015 at 7:06
• Sorry, I'll expand that abbreviation and give a link. LRT=Likelihood ratio test. I can't guess what you need, you need to identify specific things to ask about. It's similarly difficult for me to suggest books/resources -- I don't know how much stats background you have, whether you have calculus and linear algebra -- and if so, how much, nor what kind of explanations work for you. If you're trying to understand statistics from reading Wikipedia you'll have a difficult time. (It can be a valuable resource, but it isn't a good way to learn new things in any depth.) Commented Feb 14, 2015 at 7:13
• Many (parametric and nonparametric) tests assume independence and give wildly correct P-values in the presence of marked dependence. Box, Hunter, Hunter Statistics for experimenters Wiley, either edition and Miller Beyond ANOVA Wiley 1986 or later reprint are good on such matters. With a two hump distribution, even the median can be very unstable, etc. Commented Feb 14, 2015 at 10:09
• @Nick Agreed -- and it's important information to keep in mind when considering parametric vs nonparametric tests. I had considered addressing the sensitivity to assumptions of some nonparametric tests, but the question didn't mention them at all (only parametric tests) so after some debate I left them undiscussed. Commented Feb 14, 2015 at 10:12
• We agree, naturally. (I edited my comment while you were replying, I think.) Commented Feb 14, 2015 at 10:22