# [non normal Multiple sample comparison] analysis and error bars for medians

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##### New Member
Dear all,

Background:
Treatment applied to 10 groups of different sizes. Each group treated with a different concentration. Groups 9 and 10 are control/sham and represent the negative outcome. Samples in each group are independent. Group numbers vary from 12 to 4 (I cannot increase the numbers). All data (numerical/cardinal) attached in .txt file for reference.

Objective:

o1. Statistical differences between groups?
o2. what is the error associated to the control groups (9 and 10) so I can define (with a certain degree of confidence) a number above which I can consider the treatment positive? this way I can represent the data in scatter X Y plot with an horizontal bar at that level for visualization reference.

What I have done:
Software used: Statgraphics Centurion XVI

1. Run Multiple sample comparisons to evaluate normality
2. Kruskal-Wallis (comparing more than 2 samples, non normal distributions, sample size equal/larger than 4): notched box visualization

Problems faced:

p1. 5 out of 10 groups fail normality tests (skewness, kurtosis); also Levene's p-value is less than 0.05
p2. Sample sizes between 12 and 4
p3. notched box interpretation

Questions:

1. From what I know, Kruskal-Wallis is a good/ideal method for my objectives, agreed?
2. Notched box: I have attached a .pdf with the graphs (one is simply the zoomed-in version). After the kruskal-willis (P-Value = 0,000150) the only way to know where the differences are with some confidence is by looking at the notches and see in which groups they do not overlap, correct?

2.1 this overlap, is it a complete overlap (both notches within the notched area of a group) or a partial overlap also counts (if only a part of the notched area overlaps another notched area). Somehow I cannot find a precise description of overlap in this case.
3. Mann-Whitney U two 2-by-2 comparisons would force me into type I error and is not the best approach, agreed? Because this would allow me to know exactly the inter-group statistical differences...
4. I am working with medians (non normal distributions). I would like to calculate/know the error bars associated with the groups... especially for the control groups (9 and 10). How can this be done?

I hope to have clearly exposed the problem.
Thank you very much for your help!
Comments with no definitive answers are also appreciated... knowledge is always good knowledge!

Best Regards,