# Thread: Small sample: Descriptive or analytical? Adjust or not?

1. ## Small sample: Descriptive or analytical? Adjust or not?

Hi,
I need help with choosing which tests to use, as well as the goal of the testing. I am sure some of my questions are answered already on this forum (though I did not find all I needed when searching) or in a textbook. However, I need som help specific to my project.

I have a dataset of 29 observations and a range of variables. The observations are biological structures (within humans), and we are studying whether they have changed shape from time A to time B (a very unspecific explanation, but will do for now). The time span between time A and B is not the same for all structures. Information about whether each structure has changed is available in two ways: 1) One dichotomized variable "Changed" gives the value "1" for those structures that changed from A to B, and "0" for those that did not. 2) A few continuous variables describe factors X, Y, Z of the structures at point of time. Variables calculation the difference between e.g. factor X at time A and factor X at time B describe the amount of change.

Other available variables are continuous variables describing the structures, as well as a range of categorical variables describing the patients whose

Here is what I wish:
1. I want to test whether there is difference present at time A between factors X, Y, Z of those structures that subsequently changed, and those that did not;
2. I want to check whether the change is affected by time between A and B (e.g., do the structures that has a large time span between A and B change more than those with shorter, or do they not?);
3. I want to test whether the factors in (1.) adjusted for the time between A and B.

Here are my preliminary solutions:
• For (1), I guess a T Test is a good option (assuming parametric distribution). I have also tried using Logistic regression (with the dichotomized variable Changed as the dependent variable), but that gives me a higher p value. As far as I've understood, but not totally understood, that difference has something to do with the nature of those tests.
• For (3), a logistic regression would be best. Changed as the dependent variable, and because of sample size, restricting myself to two undependent variables: [Structure factor at time A] and [time between A and B]. However, in this small project, that seems to weaken results.
• For (2), I can use linear regression ([Amount of change between A and B for each structure] against [Time span between A and B for each structure]. Or I could present it graphically with a scatter plot.

Here are my problems/questions:
• Is the project to small to be analytical? In a larger project, I would jump right at Logistic regression, allowing me to adjust possible confounders. However, will Logistic regression just "blur" things in such a small project?
• Is it best to only be descriptive? Is it better to only report univariate statistics for [1], with a T test (e.g., "is there a difference between the mean of factor X at time A among those structures that did change versus those that did not?"), and only assess the impact of time between A and B graphically with a scatter plot?
• Have you got suggestions for any other tests or ways of describing the data?

2. ## Re: Small sample: Descriptive or analytical? Adjust or not?

Hi,
a quick partial reaction:

1. Depending on how many features you have (BTW I would not call them factors) you might want to use a correction for multiple tests with the t-tests (e.g. bonferroni, but there are better ones)

3. It is not really clear what the question is. The logistic regression will answer the question whether values of X , and the time between A and B make a change more or less likely.

Small sample size is a problem of course, but I would still present the analysis, with effect sizes and confidence intervals for the effects, even though they might not be significant. Just showing graphs communicates essentially the same information, but obfuscates the problems (e.g. some small effect might be visually apparent but not statistically significant, which info is missing from the graph).

regards

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