Calculation method for Mood’s Median Test

The calculation method for Mood's median test is:

1. Calculate the overall median of all the data.
2. Calculate the number of observations that are less than or equal to and greater than the overall median. If a factor has k levels, Minitab displays a 2 x k table of counts.
3. Perform a chi-square test for association on the 2 x k table of counts. A higher chi-square value provides stronger evidence against the null hypothesis. Only levels that contain two or more observations are included in the analysis. If the data have relatively few observations above the median because of ties with the median, then observations that are equal to the median may be counted with the observations that are above the median. The chi-square test statistics is given by:

   χ² = Σ(O_ij- E_ij)² / E_ij

• where,
• O_ij = Observed number of observations in cell (i,j)
• E_ij = Expected number of observations in cell (i,j)

For each factor level, Minitab displays the median, the interquartile range, and the number of observations that are above and below the median.

The confidence intervals are the nonlinear interpolation intervals that a 1-sample sign test calculates. The confidence level is less than 95% for a factor level that has fewer than six observations. For more information, go to 1-sample sign confidence interval.