I am trying to statistically answer whether these two data sets have normal distribution. It seems obvious from the bar chart which I created in Excel that they do not, but I've attempted a Kolmogorov-Smirnov test with various online calculators and they find that the data does not differ significantly from that which is normally distributed. I guess I'm overlooking something obvious here - can anyone explain..?
Hello Roxanne,
Having a sample of 25 cases map exactly onto a normal distribution would be quite extraordinary, even when you are sampling from a parent population that is normal. So, sampling variation alone will explain a lot of instances wherein your plot apparently looks non-normal, or computed skewness and/or kurtosis differ from zero.
The plot that is needed (but not shown) would be a frequency distribution (e.g., horizontal axis is score bins, and vertical axis is frequency or percent of all cases). Note that for your yearly data, the closer the correlation of value with year is to 1.0, the more closely the scores (when correctly displayed) would resemble a uniform (rectangular) distribution.
For skew and kurtosis, you should compare computed values against their standard errors, and start worrying only when the ratio (value/SE) exceeds about 2.5 or 3, depending on your personal threshold.
Some may quibble as to whether the K-S (with the adjustment proposed by Lilliefors) is the best possible goodness of fit test for evaluating normality. There are many others available: Anderson-Darling, Shapiro-Wilks, et al.
You may find this resource helpful for your query: Article Normality Tests for Statistical Analysis: A Guide for Non-St...
Good luck with your work.
Simply check your data for skewness and kurtosis. If these two tests show not normal, then it is not normal. Look for non-normal data testing.
I think, It's due to small skewness value of your data. I suggest using Jarque-Bera normality test.
- Badges
- Science topic