﻿ Two-sample Kolmogorov-Smirnov Test

Two-sample Kolmogorov-Smirnov Test

Statistics > Nonparametric Tests > Two Kolmogorov

Performs Kolmogorov-Smirnov Goodness-of-Fit Test for Independent-Samples.

This procedure performs a two-sample Kolmogorov-Smirnov test to compare the distributions of values in two data sets. For each potential value x, the Kolmogorov-Smirnov test compares the proportion of values in the first sample less than x with the proportion of values in the second sample less than x. The null hypothesis is that the two samples have the same continuous distribution. The alternative hypothesis is that they have different continuous distributions.

Assumptions:

samples are random

two samples are mutually independent

measurement scale is at least ordinal

Dialog box items

Samples in one column:
Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oSamples: Enter the columns containing the sample data.

oFactor and Levels: Enter the columns containing the sample factor, and select the levels.

Samples in different columns:
Choose if the data of the two samples are in separate columns.

oFirst Sample: Enter the column containing one sample.

oSecond Sample: Enter the column containing the other sample

Report:
The display of outputs of VisualStat.

Data

Data can be entered in one of two ways:

Both samples in a single numeric column with another grouping column (called factor) to identify the population. The grouping column may be categorical, numeric or text.

Each sample in a separate numeric column.

The sample sizes do not need to be equal. Missing values are ignored.

Charts

Displays a histogram, a histogram with a normal curve, and a boxplot.

Histogram:
Choose to display a histogram for each variable

Histogram with Normal Curve:
Choose to display a histogram with a normal curve for each variable

Boxplot of data:
Choose to display a boxplot for each variable

Options:
Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.

Options

Confidence Level: Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

Example

1.Open the DataBook nonparam.vstz

2.Select the sheet k2

3.Choose the tab Statistics, the group Nonparametric Tests and the command Two Kolmogorov

4.Select group Samples in different columns

5.In First Sample, select Process 1 (Old). In Second Sample, select Process 2 (New).

6.Click OK

Report window output

Two-sample Kolmogorov-Smirnov Test

Kolmogorov-Smirnov test to compare the distributions of values in two data sets

alternative hypothesis: true the two samples have different continuous distributions

N1  N2  Critical Value  alpha      ks  p-value  Alt Hypothesis

Process 1 (Old) : Process 2 (New)  11   9          0.5672   0.95  0.4545   0.1870          Reject

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