The Kolmogorov-Smirnov Goodness-of-fit Test

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Q. Fasting blood glucose determinations made on 36 non-obese, apparently healthy, adult males are shown below. We wish to know if we may conclude that these data are not from a normally distributed population with a mean of 80 and a standard deviation of 6.

The Kolmogorov-Smirnov test is used when one wishes to know how well the distribution of sample data conforms to some theoretical distribution.

When using the Kolmogrorov-Smirnov goodness-of-fit test, a comparison is made between some theoretical cumulative distribution function, (F_T (x)), and a sample cumulative distribution function, (F_S (x)). The sample is a random sample from a population with unknown cumulative distribution function F(x).

The difference between the theoretical cumulative distribution function and the sample cumulative distribution function is measured by the statistic D, which is the greatest vertical distance between F_S (x) and F_T (x).

"D equals the supreme (greatest), overall x, of the absolute value of the difference F_S (x) minus F_T (x)"