Question

A median run test if performed on a C-Chart. It is determined that of the 16 samples, there were 6 "runs" above and/or below the mean. What is the z-value (z_test) to test whether or not this is in control with respect to runs? Round to 2 decimal places.

Answer 1

Median run test

Sample size, N = 16

Number of observed runs = 6

Expected number of runs = (N/2) + 1 = (16/2) + 1 = 9

Variance = (N/2)*((N/2) - 1)/(N - 1) = 8*(8 - 1)/(16 - 1) = 3.7333

Note: An alternate formula for variance is (N - 1) / 4 which will come = (16 - 1)/4 = 3.75 in this case

So,

Stdev = √3.7333 = 1.932

z-score = (Observed runs - Expected runs) / Stdev = (6 - 9)/1.932 = -1.55