Example of Mood's median test
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One hundred seventy-nine participants were given a lecture with cartoons to illustrate the subject matter. Subsequently, they were given the OTIS test, which measures general intellectual ability. Participants were rated by educational level: 0 = preprofessional, 1 = professional, 2 = college student. The Mood's median test was selected to test H0: h1 = h2 = h3, versus H1: not all h's are equal, where the h's are the median population OTIS scores for the three education levels.

1    Open the worksheet CARTOON.MTW.

2    Choose Stat > Nonparametrics > Mood's Median Test.

3    In Response, enter Otis. In Factor, enter ED. Click OK.

Session window output

Mood Median Test: Otis versus ED

 

 

Mood median test for Otis

Chi-Square = 49.08    DF = 2    P = 0.000

 

                           Individual 95.0% CIs

ED  N≤  N>  Median  Q3-Q1  ----+---------+---------+---------+--

0   47   9    97.5   17.3  (-----*-----)

1   29  24   106.0   21.5           (------*------)

2   15  55   116.5   16.3                           (----*----)

                           ----+---------+---------+---------+--

                            96.0     104.0     112.0     120.0

 

Overall median = 107.0

Interpreting the results

The participant scores are classified as being below or above the overall median, and a chi-square test for association is performed. The c2 value of 49.08 with a p-value of < 0.0005 indicates that there is sufficient evidence to reject H0 in favor of H1 at commonly used a levels.

For each factor level, Minitab prints the median, interquartile range, and a sign confidence interval for the population median. The confidence interval is the nonlinear interpolation interval done by the one-sample sign procedure  (see methods and formulas - 1-sample sign). Test scores are highest for college students. (You might conjecture that it is the college student whose intellect is most stimulated by cartoons.)

If a level has less than six observations, the confidence level would be less than 95%. When there are only two factor levels, Minitab displays a 95% two-sample confidence interval for the difference between the two population medians.