"Parametric" and "non-parametric" tests are not simply interchangeable. They test different hypotheses. You should make up your mind what hypothesis you really want to test. If there is no neat parametric test that can serve, then you might have to use a bootstrap approach.

If you use ANOVA (on linear or on log-transformed values) you should have a look at the residuals. Make some diagnostic plots to see if everything is ok. This is only to see if there are huge problems. Small "problems" are not relevant, since the ANOVA is quite robust.

A final note: if you have data and then you select the test or transformation by looking at the data and do the actual test on the same data, you won't keep the type-I error-rate.

Edit: One more thing: using a log-transformed response changes your model. It means that the errors are modelled multiplicatively rather than additively. It's also worth a thought if this is what you want (or if an additive contribution of errors is really what you want to model).

Parametric tests, like ANOVA, are expected to be more powerful - of course provided the required assumptions are fulfilled. On this basis, if logY-based ANOVA residuals are normally distributed and have constant variance, you could choose ANOVA over the K-W test. Note that you will need to back-transform your results. If treatment differences (which you find significant on logY scale) based on back-transformed means are not practically useful, the 'statistical' significance you see will only of academic interest!

I would agree with Eduard. Note that GLM is a parametric approach to analysis which, as I mentioned, is expected to be more powerful than a non-parametric approach. 

"Parametric" and "non-parametric" tests are not simply interchangeable. They test different hypotheses. You should make up your mind what hypothesis you really want to test. If there is no neat parametric test that can serve, then you might have to use a bootstrap approach.

If you use ANOVA (on linear or on log-transformed values) you should have a look at the residuals. Make some diagnostic plots to see if everything is ok. This is only to see if there are huge problems. Small "problems" are not relevant, since the ANOVA is quite robust.

A final note: if you have data and then you select the test or transformation by looking at the data and do the actual test on the same data, you won't keep the type-I error-rate.

Edit: One more thing: using a log-transformed response changes your model. It means that the errors are modelled multiplicatively rather than additively. It's also worth a thought if this is what you want (or if an additive contribution of errors is really what you want to model).

Nice points from everyone above. Let me add two. Do I understand correctly that there are 3 cases per cell? Depending on the standard deviation within the cells, this might be too small a sample to yield powerful comparisons. Second, Jochen's point that you cannot look at data in a few ways and then choose the way to report based on which you like is critical (you've used up your 5%). You could do things like try a bunch of transformations and choose based on which produces the least skewed residuals, since that would not be using up your p-value for that particular hypothesis. This is why IRB proposals and the various schemes for registration ask about the statistical procedures to use (but it is also helpful in that it sometimes people change their designs when they realized that the stats they thought they might want to do are not well suited for the design).

Dear all,

Thanks a lot for your responses, the data that I am analyzing is  NMR-peak intensities. Actually when I log transformed my data, residuals would normally as I see in scatter plot, then I run one-way ANOVA followed by  Dunnett's hoc-post test to compare all 3 groups vs my treatment group. and finally show my "back-transformed" plot.

I guess minimum 3 samples per each group is sufficient for stats analysis! Am I wrong?

Thanks again for your cooperation!

Mojtaba - it's hard to say without seeing your results, but it's likely that an n of 3 is far too small for a robust analysis. In fact, at very small n (for example, less than 5), the Kruskal-Wallis test statistic distribution no longer follows an approximate chi-square distribution... Which could explain why you are having problems with this test.

With n=3 per sample, no statistical analysis is required and reasonably applicable.

With so small samples, only a graphical representation can be considered and should exhibit a clear trend to be interpreted, i.e. very similar intra-sample values with (comparatively) strong inter-sample differences. 

The best way to valid our data is then to carry out independent experiments to verify that the data exhibit the same trend.

1) Note, With n=3, the 95%CI will slitly broader then if you got n=4 per sample - when  nonparametric 95%CI = Range (min-max)! Sems to me, the 4 is minimum minimorum per sample in task for 2 sample comparison, since N(tot)=12, then for model that contrasting {a}-{b,c,d} you have 10 df for residuals that may be enough: log(y)=b0+b1X1+e

imho, just try the model selection via BIC/AIC in GLM with apropriate link (log-, invers?, ...) among all models {a,b,c,d} ... {a}{b}{c}{d} coding by dumy ;-)

my virtual example with 3 sample only:

№ Модель К -2LL G2(K-1) ΔAIC w(AIC) ΔCAIC w(CAIC)

1. {1}, {2, 3} 2 77.460 7.12 0.65 0.79

2. {1}, {2}, {3} * 3 77.446 7.13 1.99 0.24 4.39 0.09

3. {2}, {1, 3} 2 82.698 1.88 5.24 0.05 5.24 0.06

4. {3}, {1, 2} 2 83.186 1.39 5.73 0.04 5.73 0.04

5. {1,2,3} # 1 84.579 7.12 0.02 7.12 0.02

Note: # – H0, * – satureted model;

minAIC=81.46, minCAIC=86.26