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Runs

The one sample runs test is a non-parametric test to determine if the distribution of observations in a sample are random.

The requirements of the test are:  

  • A dichotomous sample measured on a nominal or ordinal scale.


Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain a nominal or ordinal scale variable containing two groups.

When entering new data we recommend using New Dataset to create a new 1 variable (categorical) dataset ready for data entry.

Using the test 

To start the test:

  1. Excel 2007:
    Select any cell in the range containing the dataset to analyse, then click Distribution on the Analyse-it tab, then click Runs
  2. Excel 97, 2000, 2002 & 2003:
    Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyse-it toolbar, click Distribution then click Runs.

  3. Click Variable then select the variable to compare.
  4. Click Alternative hypothesis and select the alternative hypothesis to test.
  5. X ≠ random to test if the observations are not randomly distributed.
    X > random to test if the observations are not randomly distributed due to too many runs.
    X < random to test if the observations are not randomly distributed due to few runs
  6. Click OK to run the test.

The report shows the number of observations analysed, the number of missing values excluded, and summary statistics for each group.

The Runs statistic (the number of contiguous runs) and hypothesis test are shown. The p-value is the probability of rejecting the null hypothesis, that the observations are randomly distributed, when it is in fact true. A significant p-value implies the observations of the sample are not randomly distributed.

METHOD  For a sample size of ≤ 25 observations an exact p-value is calculated (see [2]), otherwise a Normal approximation is used (see [1]).

Further reading & references

  1. Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)
    David J. Sheskin, ISBN 1-58488-440-1 2003; 337.
  2. Practical Non-parametric Statistics (1st edition)
    Conover W.J. out of print; 353-6.

(click to enlarge)