# Satisfying the normality condition for running parametric tests - more precision please

#### Protector999

##### New Member
1. Do ALL the samples (paired, before/after type) that are being compared need to be normally distributed; or is it sufficient if only the baseline values are normally distributed (see examples below)?
2. I´ve obtained kurtosis and skewness values for each time point using Excel. Do both values have to be within critical values? What if one is and one isn´t?
3. I´ve obtained the critical skewness value with the formula 2 x sqrt(6/n). Is this correct (I´ve often seen +/- 2 as the acceptable values)?
4. Is the same formula used to calculate the critical kurtosis value?
5. In a real-life research project is it normally sufficient and acceptable to base normality tests only on the skewness and kurtosis values (for the purpose of deciding whether parametric tests can be applied) or does one need to do a more formal test (such as Kolmogorov-Smirnov)?
6. To what extent does a sample size larger than ten offset non-normality when doing the students t-test or an ANOVA? Can this offset some sample data (in the time series) not being normally distributed?
7. I wish to compare each of 4 test phases with the baseline (I´m less interested in comparing say phase 3 with phase 2). Would 4 separate t-tests be robust enough (assuming sufficient normality) or would it be expected to do a repeated measures ANOVA? I ask because most studies in the literature use ANOVA).
Here´s the data that this request is about.
Outcome variable 1:

Outcome variable 2:

Background:
I have a test group with 19 subjects being tested on 4 outcome variables with 5 test phases for each subject: measure 1 (=baseline); treat 1; measure 2; treat 2; and measure 3. Data has been collected continuously (not sampled) for each of the phases, which range from 1 week (baseline) to 2 months (treat 2) in length. For each subject daily mean values of the outcome variables were calculated (from the raw data). For each subject the mean of these values for each test phase was calculated. The data samples comprise the respective phase means for each of the subjects.

Slight complication which leads to a supplementary question: Only 17 of the subjects also include "treat 2" data and only 15 of the subjects also include "measure 3" data. Whether via parametric or non-parametric tests can I compare the "measure 3" sample (n=15) with all 19 subjects in the baseline or should I compare the 15 "measure 3" subjects only with the same 15 subjects at baseline.

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#### Karabiner

##### TS Contributor
Do ALL the samples (paired, before/after type) that are being compared need to be normally distributed; or is it sufficient if only the baseline values are normally distributed (see examples below)?
Neither-nor. In case you want to perforn a dependent samples t-test. The dependent samples t-test assumes that the pre-post differences are sampled from a normally distributed population of pre-post-differences. Mind that this assumption is not important if sample size is large enough (n > 30 or so). With small samples, the normality assumption is hardly testable. Personally, I'd prefer Wilcoxon Signed Rank Test then. For an omnibus test, you could possibly use Friedman instead of repeated-measures ANOVA.

With kind regards

Karabiner

#### Protector999

##### New Member
Neither-nor. In case you want to perforn a dependent samples t-test. The dependent samples t-test assumes that the pre-post differences are sampled from a normally distributed population of pre-post-differences. Mind that this assumption is not important if sample size is large enough (n > 30 or so). With small samples, the normality assumption is hardly testable. Personally, I'd prefer Wilcoxon Signed Rank Test then. For an omnibus test, you could possibly use Friedman instead of repeated-measures ANOVA.

With kind regards

Karabiner
Thanks for that quick response Karabiner. Much appreciated. So the conclusion is: forget parametrics for this study if I understand you correctly.

I also have another study with identical design in which n=83. I guess I can then use the t-test without having to worry about normality?

Any comment on my supplementary question?: When comparing "measure 3" (n=15) with baseline do I include all 19 subjects in baseline or only the 15 subjects for which I have "measure 3" data?

Thanks in anticipation...