Complete the following steps to interpret a runs test. Key output includes the observed number of runs, the expected number of runs, and the p-value.

The observed number of runs is the number of groups of observations that are above or below the comparison criterion, K. The line represents K. This example contains five runs.

If the number of observed runs is substantially greater than or less than the number of expected runs, it is likely that the data are not in random order. To determine whether the order of your data is random, compare the p-value to the significance level.

Null hypothesis | H₀: The order of the data is random |
---|---|

Alternative hypothesis | H₁: The order of the data is not random |

Number of Runs | ||
---|---|---|

Observed | Expected | P-Value |

17 | 16.77 | 0.930 |

In these results, the value for the observed number of runs is very close to the value for the expected number of runs.

To determine whether the order of your data is random, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the order of your data is not random when it actually is random.

- P-value ≤ α: The order of the data is not random (Reject H
_{0}) - If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis and conclude that the order of the data is not random.
- P-value > α: Cannot conclude the order of the data is not random (Fail to reject H
_{0}) - If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the order of the data is not random.

Null hypothesis | H₀: The order of the data is random |
---|---|

Alternative hypothesis | H₁: The order of the data is not random |

Number of Runs | ||
---|---|---|

Observed | Expected | P-Value |

17 | 16.77 | 0.930 |

In these results, the null hypothesis states that the order of the data is random. Because the p-value is 0.930, which is greater than the significance level of 0.05, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the order of the data is not random.