# Thread: Parametric or Non-Parametric and why?

1. ## Parametric or Non-Parametric and why?

I want to examine how three different treatments impact cytokine production in primary human cells (n=3) compared to an untreated control (example data attached).

I know that small data sets present a dilemma, with it being difficult to tell if the data the data is normally distributed, which is required for parametric test, while nonparametric tests tests lack statistical power with small samples.

Is it more appropriated to use parametric or non-parametric statistics?

2. ## Re: Parametric or Non-Parametric and why?

There is no easy answer to this question. It depends on your data. Generally non-parametrics are preferred when the data is not normal and/or is not linear (and can not be made so by a transformation). But that is a simplistic answer and I am sure there are a million exceptions to it. If your data is normal and linear than parametric methods are preferable ( i believe because they have more power although I am not certain).

A good starting point is seeing how normal your data is (perhaps through a QQ plot) and test for linearity (there are many ways to do this, Box-Tidwel is the simplest)

3. ## Re: Parametric or Non-Parametric and why?

Originally Posted by noetsi
A good starting point is seeing how normal your data is (perhaps through a QQ plot)
With a sample size of three unless one is a huge outlier this doesn't seem like it will be too informative (although it wouldn't be detrimental to look at a plot I would suggest a dot plot for this)
and test for linearity
It sounds like the OP is describing what would generally fall under ANOVA - what "linearity" are you referring to here?

4. ## Re: Parametric or Non-Parametric and why?

What I think the standard definition, if the relationship (the slope in regression) between the IV and DV remains constant at all levels of the IV controlling for other IV in the model. I understand they are talking something that might fall under ANOVA - but if the data is not linear I don't think ANOVA is appropriate. Wilcoxon or other non-parametric approaches would be.

I am not sure, as you noted but I missed if this discussion even matters with a sample size of 3. Can data be normal or linear with such a small sample? I am not sure why you would ever run an analysis with 3 points. Ignoring the statistical issues your ability to generalize at all with such data is essentially nil. And power would be beyond awful

5. ## Re: Parametric or Non-Parametric and why?

Time to clear up the same misconceptions we've dealt with in the past...

Originally Posted by noetsi
What I think the standard definition, if the relationship (the slope in regression) between the IV and DV remains constant at all levels of the IV controlling for other IV in the model.
Yeah sure this is fine.
I understand they are talking something that might fall under ANOVA - but if the data is not linear I don't think ANOVA is appropriate.
In ANOVA basically the model you fit says that each group has their own mean. You can fit this and think of it as "slopes" if you want but really it is IMPOSSIBLE for the "linearity" assumption (which isn't actually an assumption by the way - the underlying assumption is just that you fit the "true" model) to be broken. Just like with a t-test you don't check for linearity because it's always met - it's the same thing with one-way ANOVA.

Can data be normal or linear with such a small sample?
Yes - of course it can. Now to the question you meant to ask "can you actually tell in practice if data is normal or truly has a linear pattern with such a small sample size" the answer is no. But if you have reason to believe that these might be true you can make an assumption and use the models anyways. I'm not saying that is the best thing to do but we make assumptions all the time in statistics.

I am not sure why you would ever run an analysis with 3 points.
Because you have data that might have been quite costly to obtain and you want to say something. Plus if there is a strong effect you could find a significant difference even with a small sample size.

Ignoring the statistical issues your ability to generalize at all with such data is essentially nil.
Maybe but sometimes you just want to know if it's worth pursuing further investigation at all
And power would be beyond awful
Probably but you can't say for sure without specifying an effect size. Like I said with a large effect size the power might not be too terrible.

6. ## The Following User Says Thank You to Dason For This Useful Post:

noetsi (09-22-2014)

7. ## Re: Parametric or Non-Parametric and why?

Linearity is not an assumption for ANOVA. The DVs are either discrete or, if continuous, are treated as if they were discrete.

For the sake of argument take the attached sketch. The DV is continuous and has a nonlinear relationship with the DV. Levels A, B and C were selected for a 1-Way ANOVA. A continuous IV was treated as discrete. The ANOVA would likely show that the IV has a statistically significant effect on the DV. The nonlinear relationship might explain why Post hoc comparisons between B and C were not statistically significant.

8. ## Re: Parametric or Non-Parametric and why?

I always thought linearity was an assumption of General Linear Models generally of which I thought ANOVA was a form Oh well I will get that right someday.

Or maybe not...

9. ## Re: Parametric or Non-Parametric and why?

BTW dason one point I would quible with you about from you comments. Regardless of how large the effect size is I doubt you can generalize to a larger population from three cases. The results might be right by accident, but uncertainty would be very high that 3 cases represented accurately a population of any size. It is why analysis in the medical field spend so much time and money trying to get more cases. No one will take seriously studies with 3 cases. It is not a statistical issue per se.

10. ## Re: Parametric or Non-Parametric and why?

How many times do we need to tell you that the linear in "linear model" is referring to linearity in the parameters.

11. ## Re: Parametric or Non-Parametric and why?

Quite a few I guess since I simply don't run into this concept. All the discussions of linearity I run into (like the General Additive Models last week) bring up the concept of linearity as I mentioned it before, simply a relationship between the IV and DV. When they mention linearity as existing in the parameters (which is rare) they simply say that you can tranform non-linearity in some types of data and not in others. Obviously this is a distinction I don't get (that is what your comments mean in practice Dason).

Incidently Berry, who wrote the Sage monograph on regression assumptions, strongly disagrees that there even is a true model in the context of social science research At least one that is knowable and possibly at all. He list, as do many other authors, specific regression assumptions instead.

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