I have run an experiment where i measure different soil properties along a transect ( Bulk density, porosity, EC, pH, CaCO3). the sample size is 16. and i want to evaluate the spatial dependance between these parameter, through autocorrelation. i have compute the Skewness and Kurtosis of the results i found only pH and CaCo3 that have a skewness near zero! so i suspect that some of these parameter don't know follow a normal distribution. so any advice will be welcomed.
Kind regards Louadj yacine
This paper might be useful:
D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183–189.
I'm not aware off the top of my head of a limit for skewness tests. Playing around with randomly-generated data now, though, skewness tests for n=16 seemed to give reasonable-looking results. It wouldn't hurt to also look at your data distribution (e.g., with a histogram) to visually confirm.
Dear Louadj,
For normality tests the limits in sample size exist. Let us say for Chi-Square test the minimum sample size is 16. But it is recommended a value greater than 30. For small samples is better to use other normality tests, such as the Kolmogorov-Smirnov test. With small sample sizes of 10 or fewer observations it’s unlikely the normality test will detect non-normality. If you know the distribution is normal you should still use a parametric test, as it’s more powerful, but if you’re unsure a non-parametric alternative is usually more conservative.
The answer is 2. The problem is that the level of error in a sample size of 2 is typically larger than anyone will accept. Power increases with increasing sample size. The real problem is that failing to reject the null hypothesis is not the same as proving the null hypothesis true. This is what you are doing if you fail to reject the hypothesis that the distribution is normal, and then run the data through analyses that require normally distributed data. So the real question is whether the violations of the normality assumption are bad enough to seriously affect the outcome of the statistical methods.
An alternative is to use a variety of tests and see if they give the same answer. If they do, state which tests were tried in the methods but report the simplest method in the results. If they do not, then you have to figure out why. This may take considerable effort (time). If the data were worth collecting, why ruin good data with a bad analysis?
Another issue may be that the models don’t require normal distributions of the independent or dependent variable. The assumption is that the residuals are normally distributed. The reply in the first paragraph was written to apply to the variables, but is more appropriate when applied to the residuals.
To test for normality, I suggest either Shapiro Wilk or Smirnov test. If the data turns out to be normally distributed proceed with parametric analysis, otherwise use nonparametric.
I am not sure I fully understand what is being suggested: So failing to reject the null hypothesis is sufficient to prove that the null hypothesis is true? As in both Shapiro Wilk and Smirnov tests fail to reject the null hypothesis that the data are normally distributed so we will now use parametric tests because we have proven that the data are normally distributed? While this is common practice, that does not mean that it is logically sound. This strategy leads to a great argument for use of small sample sizes, because the smaller the sample size the more normally distributed everything becomes.
Are you sure you want to go down this road?
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