The Friedman chi-square tests the null hypothesis that the ranks of the variables do not differ from their expected value. For a constant sample size, the higher the value of this chi-square statistic, the larger the difference between each variable's rank sum and its expected value.

- For these rankings, the chi-square value is 10.3. Degrees of freedom are equal to the number of variables minus 1. Because four health plans were being ranked, there are three degrees of freedom.

- The asymptotic significance is the approximate probability of obtaining a chi-square statistic as extreme as 10.3 with three degrees of freedom in repeated samples if the rankings of each health plan are not truly different.

Because a chi-square of 10.3 with three degrees of freedom is unlikely to have arisen by chance, the insurer concludes that the 12 employers do not have equal preference for all four health care plans.