Minitab uses a normal approximation to the binomial distribution to calculate the p-value for samples that are larger than 50 (n > 50). Specifically:
is approximately distributed as a normal distribution with a mean of 0 and a standard deviation of 1, N(0,1).
where S, the number of observations that are above the median, has the binomial distribution with n as the number of trials and p = 0.5 as the probability of success under the null hypothesis, B(n, 0.5).
The normal approximation p-value for the three alternative hypotheses uses a continuity correction of 0.5.
|H1: Median > Hypothesized median
|H1: Median < Hypothesized median
|H1: Median ≠ Hypothesized median
|n||the observed number of data points after omitting any observations that are equal to the hypothesized median value|
|s||the observed number of data points that are greater than the hypothesized median|
|S||a random variable that has the binomial distribution with n as the number of trials and p = 0.5 as the probability of a success, B(n, 0.5)|