Whether to interpret based on descriptive or infferential statistics in present case?

In our study which is already completed, I have three groups: Drug A(n=87), Drug B(=62) and Drug C(n=5). The Shapiro-Wilk test, Histograms and Side-by-side Box plots were used to assess normality of the data of the individual group with respect to all the parameters used separately (weight, BMI, blood sugar, total cholesterol, triglycerides, LDL-cholesterol, HDL-cholesterol, clinical/illness/adverse effect/quality of life etc scores). So, ultimately looking to non-normal distribution, outliers, unequal sample size (n=5 in Drug C group), in addition to descriptive statistics (mean ± SD and proportion of % wherever applicable), nonparametric tests were carried out for the inferential statistics. For between-group comparisons, Kruskal Wallis H and subsequently for the therapeutic where p<0.05 obtained in Kruskal Wallis H, Mann Whitney U test as post-hoc test were used. And in case of within-group comparison, Freidman’s test (for five evaluable visits data) and subsequently for p<0.05 for the therapeutic where p<0.05 obtained in Freidman’s test, Wilcoxon-signed rank test as post-hoc test were done. And in case of p<0.05 obtained in Wilcoxon-signed rank test in two (out of three) groups further to ascertain the between-group significance difference, Mann Whitney U test was also done.
Kindly advise me: 1) First of all, have done the right choice of tests and am I in the right direction? 2) As regarding present analytical sample of total N=154, for arriving at final conclusion should I depend on descriptive or inferential statistics or both? 3) In case where the mean ± SD changes and proportion of percentage (%) are found comparatively higher in case of Drug C which has sample power n=5 compared to other two drug groups but in case of between-group and/or within group inferential statistical analysis, (wherever) found non-significant difference/change in case
of Drug C, can it be ‘said’ superior to other two drugs ‘on the basis of descriptive statistics’ or can I at least make a statement that mean± SD and proportion of % changes at endpoint (or at other time-point) compared to baseline were found higher in case of Drug C compared to other two or other one ? So, what should be the (cautious) interpretation/statement in case of Drug C compared to other two drugs? I shall be thankful and appreciate your prompt reply.
Re: Whether to interpret based on descriptive or infferential statistics in present c

Hey saurin.

When you mention that you only have five samples for Drug C this raises a few red flags (not just statistically or probabilistically speaking). One question I have for you is why you have a massive sample size for the other groups but an extremely low count for Drug C?

If you are trying to do a genuine comparison between things, you really want to make sure that you do a fair comparison between those things and part of doing the best possible comparison is to get enough data to facilitate this.

If for some reason you can't get a more balanced set of observations, it might be wise to outline why this is the case.

With regards to statistical and probabilistic stuff, the normality condition on a low sample size is really going to be a volatile thing. Also if you have a small sample size, you typically want to look at expert information and possibly consider the Bayesian framework for Inference which is often used when you have really small sample sizes (and is used in medical areas for this very reason).

To me if I saw a study with sample sizes being used for inference in something like this, alarm bells would be going off left right and centre because if you are providing an argument for something and the process is biased, then this is going to screw things up.
Re: Whether to interpret based on descriptive or infferential statistics in present c

Hi Chiro.
Thanks for the reply. In third therapeutic group, the drug selected for mono-therapy is used only in resistant cases, most of the times being used as an add on therapy. Because of inclusion criteria, it was not feasible to select patients on this drug receiving other similar drugs at the same time. So, the sample size in this naturalistic study in third group is ought to be low. Since it was not found prudent to keep 3rd group out of comparison while using non-parametric tests (as all the 3 groups were individually tested for different parameters for different tests of normality), between-group and within-group comparison was based on non-parametric tests. Although there was apparent difference found in descriptive statistics for 3rd group in some parameters (as 3rd group due to its low sample power is sensitive) in inferential statistics (including post-hoc tests), such difference was shown eliminated.