Interpreting the tests for randomnessmain topic see also
Interpreting the tests for randomnessA normal pattern for a process in control is one of randomness. If only common causes of variation exist in your process, the data exhibit random behavior.
The following table illustrates what the two tests for randomness can tell you. See Interpreting the test for number of runs about the median and Interpreting the test for number of runs up or down for more details.
|
Test for randomness |
Condition |
Indicates |
|
Number of runs about the median |
More runs observed than expected |
Mixed data from two population |
|
|
Fewer runs observed than expected |
Clustering of data |
|
Number of runs up or down |
More runs observed than expected |
Oscillation - data varies up and down rapidly |
|
|
Fewer runs observed than expected |
Trending of data |
Both tests are based on individual observations when the subgroup size is equal to one. When the subgroup size is greater than one, the tests are based on either the subgroup means (the default) or the subgroup medians.
With both tests, the null hypothesis is that the data have a random sequence. Run Chart converts the observed number of runs into a test statistic that is approximately standard normal, then uses the normal distribution to obtain p-values. See [1] for details. The two p-values correspond to the one-sided probabilities associated with the test statistic. When either is smaller than your a-value (significance level), reject the hypothesis of randomness. Assume the test for randomness in the examples is significant at an a-value of 0.05.