Can you compare 3 small groups <4 participants using Multiple Mann-Witney?

#1
Hi,
I am very new to statistics but have found myself doing a small master desgree research project with very little statistics background so I am finding it very difficult. I have had a go at a mann-whitney but am just not confident that it is the correct test to use or whether there is something I should know about it's use in this instance.

I would really appreciate any help anyone can give.

My project is comparing the speech (3 different acoustic measures) of 3 different subtypes of patients.

I only have 2 participants in subgroup 1, 3 in subgroup 2, and 2 participants in subgroup 3. Disappointing!

Each participant has multiple trials for each speech stimulus which is then accoustically analysed and turned into data.

I have had a go at trying to compare the outcomes of one of the measures between the groups.
What I did was put all the data points from each participant within the subgroup together (eg. group one has 2 participants, each with 6 data points which makes 12 data points.)
Using the mann-Whitney test I have then tried to compare these 12 data points in group 1 to the 18 data points in group 2 (3 participants each with 6 data points).

I then went on to do multiple comparisons between the groups e.g group 1-group 2, group 1-group 3, group 2-group 3.

Is Mann-Whitney the correct test to use in this instance?
Should I use the Boniferroni correction given that I am doing multiple comparisons?

I really appreciate any help or direction people can give me. I realise this is a big ask and I value your time you may spare to answer this.

kindest regards
 
#2
Hey Nysnos.

Are you trying to assess means or medians as a reference for comparison?

Typically medians are useful when you have really skewed or highly asymmetric data, but if you have enough data and wish to assess the means (where they provide a good indicator with respect to the distribution for comparison), then you can use the Central Limit Theorem which is the basis for most of the frequentist statistical results that people take for granted.

Now an ANOVA is basically a way to compare means for an arbitrary number of groups: if you did a t-test for multiple groups beyond 2, then you would introduce all kinds of errors when it comes to significance levels and so this procedure provides a way to keep these significance levels in take for an arbitrary number of groups.

Based on this, the next thing to do is to get an idea of what the data looks like to see if you can use these assumptions and even before we do that, we need to assess what the data actually represents non-mathematically.

So could you please provide a brief description of what this data represents physically, what else it relates, some kind of context for the numeric representation, what the typical range for this data is, and ultimately what you want to use this for and what kinds of questions you are trying to answer with responses that are completely non-mathematical or non-statistical.

It's important that these are discussed as opposed to statistical ones because all the test rely on assumptions and also because the point of statistics in situations like yours is but one tool to get advice for decision making and not the whole process itself.