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716 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS
1.0
.9
Cumulative relative frequency
.8
.7
.6
.5
.4
.3
.2
.1
.2 .4 .5 .8 1.0
FIGURE 13.7.3 Graph of fictitious data showing correct calculation of D.
Advantages and Disadvantages The following are some important
points of comparison between the Kolmogorov–Smirnov and the chi-square goodnessof-fit
tests.
1. The Kolmogorov–Smirnov test does not require that the observations be grouped as
is the case with the chi-square test. The consequence of this difference is that the
Kolmogorov–Smirnov test makes use of all the information present in a set of data.
2. The Kolmogorov–Smirnov test can be used with any size sample. It will be recalled
that certain minimum sample sizes are required for the use of the chi-square test.
3. As has been noted, the Kolmogorov–Smirnov test is not applicable when parameters
have to be estimated from the sample. The chi-square test may be used in these
situations by reducing the degrees of freedom by 1 for each parameter estimated.
4. The problem of the assumption of a continuous theoretical distribution has already
been mentioned.
EXERCISES
13.7.1 The weights at autopsy of the brains of 25 adults suffering from a certain disease were as follows:
Weight of Brain (grams)
859 1073 1041 1166 1117
962 1051 1064 1141 1202
973 1001 1016 1168 1255
904 1012 1002 1146 1233
920 1039 1086 1140 1348