Help!! a little confused with ANOVA, should be easy

Dear all,

I would like to ask for your help in determining which test I should run for my samples. Here is my data: I have 4 water samples of Nitrite (mg/l) from 3 sites.

Site1:.00171, .00206, .00031, .00066
Site3:.00136, .00206, .00415, .00275
Site4:.02193, .02298, .02681, .01531

My objective: is to objectively analyze the quality between sites.
My question: What test should I run in SPSS to determine a significance difference (in SPSS)? ANOVA with Turkey HSD?

I appreciate your help!



Well-Known Member
A one way anova type test is usual for data like this, but in this case site 4 has variance about 20 time the others and the variance for all groups should be much the same. A Kruskal-Wallis test would be more appropriate, but even the KW test has some assumptions which aren't fully satisfied here. I suggest that you do three t tests with unequal variance, and use a Bonferroni type adjustment and set your p value for significance at say 0.02 instead of 0.05 to keep your risk of a false positive down to about 5%. Use Excel. =TTEST(data,data,2,3) Easy to do, easy to explain, easy to justify, and no need for post hoc tests.
Cheers Kat
Welcome John.

My first question would be why you would want to do testing with so very little data and high variability. Can you get more data?

Just eyeballing it seems like site 4 clearly has a higher mean than the other two, but the difference between site1 and site3 is uncertain.

If you do want to do testing, you should definitely use a non-parametric test and not a t-test, since you can't assume the mean is normally distributed with n=4 (unless you know that this particular variable is normally distributed).

You can use the Kruskal-Wallis test and some post-hoc test. It does not necessarily assume that the distributions are equal; this is only if you want to say something about the medians. If you just want to be able to say that a random sample from site4 is higher than a random sample from site1 it works.

A simpler alternative is to do three Mann-Whitney U's, with multiple comparisons Bonferroni correction (alpha=0.05/3). You could easily do them by hand if you wanted to, it gives you some insight in how the procedure works.

But if this is important, I would really look for ways to get more data.


Well-Known Member
Yes and no, Junes. When you are looking for a difference in level between groups, both those non-parametric tests assume that the distributions are the same except for level. This is clearly not the case here because of the difference in spread, so a low KW p value may either indicate a difference in shape (which we can see already) or a difference in location (which is also pretty obvious) or both (probably both, but we can't be certain).
Junes is right - get more data if it is important, say for a paper or a prosecution. If it part of a regular monitoring scheme. you are probably lucky to get four samples analysed, so you will need to just do what you can.
Another alternative you could try is to negative log the values first, a sort of p(Nitrite) which is often appropriate in this sort of situation. That settles things down a lot. The data isn't obviously non normal, and so anova t test stuff should work, and that is what is used in most comparative lab work.
Cheers Kat