Minitab uses the binomial distribution to calculate the p-value for samples up to size 50 (n ≤ 50). For a sample size n (after omitting any observations that are equal to the hypothesized median value) and a probability of occurrence of p = 0.5 under the null hypothesis, the calculation of the p-value depends on the alternative hypothesis.
Alternative hypothesis | P-value |
---|---|
H_{1}: Median > Hypothesized median | |
H_{1}: Median < Hypothesized median | |
H_{1}: Median ≠ Hypothesized median |
Term | Description |
---|---|
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 follows a binomial distribution with n trials and a 0.5 probability of an event, B(n, 0.5) |
k |
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.
Alternative hypothesis | P-value |
---|---|
H_{1}: Median > Hypothesized median | |
H_{1}: Median < Hypothesized median | |
H_{1}: Median ≠ Hypothesized median |
Term | Description |
---|---|
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) |
k |
B has a binomial distribution with parameters sample size n and probability of occurrence p = 0.5.
The lower endpoint of the interpolation interval is given by:
The upper endpoint is given by: