Complete the following steps to interpret a Mood's median test. Key results include the median estimates, the p-value, and the confidence intervals.

To determine whether any of the differences between the medians are statistically significant, compare the p-value to your significance level to assess the null hypothesis. The null hypothesis states that the population medians are all equal. 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 a difference exists when there is no actual difference.

- P-value ≤ α: The differences between some of the medians are statistically significant
- If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that not all the population medians are equal. Use your specialized knowledge to determine whether the differences are practically significant. For more information, go to Statistical and practical significance.
- P-value > α: The differences between the medians are not statistically significant
- If the p-value is greater than the significance level, you do not have enough evidence to reject the null hypothesis that the population medians are all equal. Verify that your test has enough power to detect a difference that is practically significant. For more information, go to Increase the power of a hypothesis test.

Temp | Median | N <= Overall Median | N > Overall Median | Q3 – Q1 | 95% Median CI |
---|---|---|---|---|---|

38 | 19 | 4 | 3 | 4.00 | (17.4667, 22.5333) |

42 | 19 | 3 | 3 | 9.50 | (15.3571, 25.6429) |

46 | 22 | 2 | 4 | 7.25 | (15.7857, 26.5714) |

50 | 18 | 4 | 2 | 4.25 | (14.4286, 20.6429) |

Overall | 19 |

Null hypothesis | H₀: The population medians are all equal |
---|---|

Alternative hypothesis | H₁: The population medians are not all equal |

DF | Chi-Square | P-Value |
---|---|---|

3 | 1.44 | 0.697 |

In these results, the median weights for the four groups are 19.0, 19.0, 22.0, and 18.0. The null hypothesis states that the population medians are all equal. Because the p-value is greater than the significance level of 0.05, you fail to reject the null hypothesis. The differences between the median weights are not statistically significant.

Use the confidence intervals (95% Median CI) to assess the estimate of the population median for each group. The confidence intervals are ranges of values that are likely to contain the population median.

For example, with a 95% confidence level, you can be 95% confident that the confidence interval contains the group median. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

Temp | Median | N <= Overall Median | N > Overall Median | Q3 – Q1 | 95% Median CI |
---|---|---|---|---|---|

38 | 19 | 4 | 3 | 4.00 | (17.4667, 22.5333) |

42 | 19 | 3 | 3 | 9.50 | (15.3571, 25.6429) |

46 | 22 | 2 | 4 | 7.25 | (15.7857, 26.5714) |

50 | 18 | 4 | 2 | 4.25 | (14.4286, 20.6429) |

Overall | 19 |

The intervals show that a temperature of 38 has a median of 19.0 and the confidence interval extends from approximately 17.5 to 22.5.