The results sheet contains the Kolmogorov-Smirnov statistic (0.475) that can be easily extracted (see further, the cumulative histograms chart). In the Charts tab, activate the Cumulative histograms option. In the Options tab, notice it is possible to select a one-tailed alternative hypothesis and/or an exact computation of the p-value. The Kolmogorov-Smirnov test allows samples to be unbalanced such as in our data: sample B contains fewer scores than sample A. Select the Brand A column in Sample 1 and the Brand B column in sample 2. Go to XLSTAT / Nonparametric tests / Comparison of two distributions. We will now use the Kolmogorov-Smirnov non-parametric test to compare the two distributions. Without making any theoretical assumption, we may say that the distribution of sample B is more skewed towards low values compared to the distribution of sample A. The histograms appear in the results sheet: This will force histograms to have the same lower bound on the x axis making their comparison easier. In the Options tab, activate the minimum option and enter 0 in the box. In the General tab, select both samples inside the Data cell range. Here, we are interested in comparing the distributions of the two samples.įirst of all, what do these distributions look like? Histograms are a good tool to visualize continuous distributions: XLSTAT / Visualizing data / Histograms. Part 1: Running a Kolmogorov-Smirnov test to compare two observed distributions in Excel In the second part, we use the Kolmogorov-Smirnov test to compare the distribution of one sample to a theoretical distribution.
We use the non-parametric Kolmogorov-Smirnov test, which is well suited in this case.
In the first part we compare the distributions of the two samples without making assumptions on underlying theoretical distributions (normal distribution for example). 15 customers have answered for brand A and 8 different clients for brand B. Scores were computed based on a survey addressed to customers using either brand. The data correspond to scores (0 – 30) measuring the quality of two brands of shoes (brand A and brand B).
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