# Thread: Skewness and non-normally distributed data - Question.

1. ## Skewness and non-normally distributed data - Question.

Hello everyone, this is actually my first post as I have just discovered this amazing forum for talking about statistics. I've read through the guidelines, and hopefully I am coming across as a new poster who is at least putting in some effort.

I am talking in slightly vague language because I do not want to give the problem away word for word, as I wish to attempt to interpret the answer on my own.

I am given a problem, where statistical analysis has revealed a significant "skew" in some hormonal data (so I know the data is not symmetrically distributed around the mean). In essence, the problem gives hormonal data for a certain cycle, and I am to suspect that there is a significant drop in these hormonal levels during mid-cycle (as there are high numbers at the start and end of the cycle). I am then asked how I would analyze this data (i.e. what test I would use) in order to test the hypothesis that there is a significant drop mid-cycle, and "how might the power of this experiment to detect differences have been improved?"

So because I am being told that I "suspect" a significant drop in the hormonal levels during the middle of the cycle, would I want to employ a chi-square test so I can compare this observed data with data that I would expect to obtain according to the hypothesis?

(I will note, I am not being asked to make any calculations whatsoever, just how I would approach such a problem)

Secondly, I am not sure about the second part of this problem. I was wondering if anyone could provide any insight as to the question overall, and any information that would help me for the second part of the problem. Any help is appreciated!

2. ## Re: Skewness and non-normally distributed data - Question.

I see that no one has responded to my question. In that case, is there anything I can do to make it easier to answer?

I do see that a lot of people have viewed it, so there must be something I can do.

3. ## Re: Skewness and non-normally distributed data - Question.

Is this a repeated-measures problem where each subject has been
measured three times during 1 circle? In that case the easiest way
would be to carry out two comparisons ("start" with "mid-cycle" and
"end" with "mid-cycle"), using a test for dependent measures (dependent
samples t-test or Wilcoxon signed rank test).

"how might the power of this experiment to detect differences have been improved?"
Usually by increasing number of subjects.

With kind regards

K.

4. ## Re: Skewness and non-normally distributed data - Question.

Originally Posted by Karabiner
Is this a repeated-measures problem where each subject has been
measured three times during 1 circle? In that case the easiest way
would be to carry out two comparisons ("start" with "mid-cycle" and
"end" with "mid-cycle"), using a test for dependent measures (dependent
samples t-test or Wilcoxon signed rank test).

Usually by increasing number of subjects.

With kind regards

K.
Hi Karabiner, thanks for the response.

The measurements were actually taken eight times throughout the whole cycle, with a varying amount of samples taken each subsequent day (ranging from 6 - 10 on various days). Would such a method still work?

Thank you!

5. ## Re: Skewness and non-normally distributed data - Question.

The measurements were actually taken eight times throughout the whole cycle,
Is there a clear definition which measures are "mid-cycle"?
with a varying amount of samples taken each subsequent day (ranging from 6 - 10 on various days).
Unfortunately I do not understand what you mean.

With kind regards

K.

6. ## Re: Skewness and non-normally distributed data - Question.

Originally Posted by Karabiner
Is there a clear definition which measures are "mid-cycle"?

Unfortunately I do not understand what you mean.

With kind regards

K.
Hi again Karabiner, thanks for taking the time to respond.

I am given a table that has the day the level of hormone was tracked (1, 5, 9, 13, 17, 21, 25, 29), a mean of the amount of hormone on each of those days, the standard deviation of each mean, and the number of samples that was taken on those days (so for example; 8 on day 1, 8 on day 5, but only 7 on day 9, etc).

Mid-cycle, I guess based on the days given, would be day 17, in which the mean was the lowest. However, I would imagine that "17" isn't exactly the mid-cycle, as it's just a sample set of data that we are given.

The question is only asking how we would analyze this data in order to test the hypothesis that "there is a significant drop in hormone levels at mid-cycle."

Thanks again.

7. ## Re: Skewness and non-normally distributed data - Question.

It is still not clear whether these are independent samples
or repeated measures. In the latter case, aggregate data
do not permit a test of significance. You would need to know
which data belong to which subject.

With kind regards

K.

8. ## Re: Skewness and non-normally distributed data - Question.

Originally Posted by Karabiner
It is still not clear whether these are independent samples
or repeated measures. In the latter case, aggregate data
do not permit a test of significance. You would need to know
which data belong to which subject.

With kind regards

K.
Unfortunately, I feel as though I'm giving all the information to you that I am being given myself. The question reads:

"In tracking the levels of a hormone across the menstrual cycle, you get the following results.

<then the table I described above is posted>

Statistical analysis reveals a significant “skew” in the hormone data. You suspect that there is a significant drop in hormone levels at mid-cycle, just after ovulation. How would you analyze the data to test this hypothesis? How might the power of this experiment to detect differences have been improved?"

Again, thanks for all the help you've provided already. If you can't help me further from here, that's alright. Just finding it difficult to answer this.

9. ## Re: Skewness and non-normally distributed data - Question.

As a last request for help, does anyone have any suggestions?

Should I just answer this question as if I am outlining an analysis? What kind of test would I need to employ to test such a hypothesis?

Thank you.

10. ## Re: Skewness and non-normally distributed data - Question.

Originally Posted by PBnJams
As a last request for help, does anyone have any suggestions?

Should I just answer this question as if I am outlining an analysis? What kind of test would I need to employ to test such a hypothesis?

Thank you.
Or rather, does an answer like this look okay?

1. State relevant null hypothesis.

3. Employ Levene's test of equality of variance, in order to assess the assumption that the variance of the populations from which these different samples have been drawn are equal.

4. Use a 1 way ANOVA to assess the assumption that the samples are drawn from populations with the same mean values, producing an F statistic.

4b. Do the 1 way ANOVA with a post hoc analysis in order to look for patterns that were not specified in the data before the experiment began.

5. Based on the F statistic, we can either reject or accept the null hypothesis, allowing us to determine if there is in fact a significant skew in the data.

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