Wald wolfowitz run test example
The Wald-Wolfowitz two sample runs test is used to determine whether two samples come from the same distribution. Determine whether the following samples come from the same distribution.
Sample 1: 23 42 36 27 48 52 35 31
Sample 2: 43 56 38 20 46 51 36
http://www.real-statistics.com/non-parametric-tests/two-sample-runs-test/
Procedure:
- Nonparametric
- Two Samples (Unpaired).
- Wald-Wolfowitz Runs Test.
- Significance Level = 5%
- OK
DATA TABLE No Gr1 Gr2 --------------------------------- 1 23 43 2 42 56 3 36 38 4 27 20 5 48 46 6 52 51 7 35 36 8 31 --------------------------------- Mean 36.75 41.43 Mededian 35.5 43 SD 10.05 11.75 Skewness 0.26 -0.86 Kurtosis -0.98 1.12 DOT PLOTS +---+-----------+-----------+-----------+-----------+---+ | | | | | | | | | | | | | | | * * * ** * * * | Gr1 +---+-----------+-----------+-----------+-----------+---+ | | | | | | | | | | | | | | | * * * * * * * | Gr2 +---+-----------+-----------+-----------+-----------+---+ 20 29 38 47 56 BOX-AND-WHISKER PLOTS +---+-----------+-----------+-----------+-----------+---+ | | | +--------+-----------+ | | |-------| |* |---------| | Gr1 | +--------+-----------+ | | +-------+------+ | | |----------------------| * | |---------| | Gr2 | +-------+------+ | | | +---+-----------+-----------+-----------+-----------+---+ 20 29 38 47 56 WALD-WOLFOWITZ RUNS TEST (two samples) Hypotheses Ho: The two populations have the same distribution. Ha: The two populations have different distributions. (They differ in central tendency, variances, skewness, or any other distribution pattern.) (Significance Level = 0.05) COMBINED DATA TABLE (sorted) -------------------------------------------------- Minimum Runs Maximum Runs ------------ ------------ No Data Sample Run Sample Run -------------------------------------------------- 1 20 2 1 2 1 2 23 1 2 1 2 3 27 1 1 4 31 1 1 5 35 1 1 6 36 1 2 3 7 36 2 3 1 4 8 38 2 2 5 9 42 1 4 1 6 10 43 2 5 2 7 11 46 2 2 12 48 1 6 1 8 13 51 2 7 2 9 14 52 1 8 1 10 15 56 2 9 2 11 -------------------------------------------------- 8 7 9 8 7 11 Runs = 9 Runs = 11 PROBABILITY TABLE (N1 = 8, N2 = 7) Run Prob. CP -------------------------------- 1 0.0000 0.0000 2 0.0003 0.0003 3 0.0020 0.0023 4 0.0131 0.0154 5 0.0359 0.0513 6 0.0979 0.1492 7 0.1469 0.2960 8 0.2176 0.5136 9 0.1904 0.7040 10 is recommended.) N2 = 7 (N2>10 is recommended.) Runs = 9 (# of minimum possible runs) Mu = 8.47 (expected mean of runs) Sigma = 1.86 (expected standard deviation of runs) Z = 0.29 (test statistic) P(10 is recommended.) N2 = 7 (N2>10 is recommended.) Runs = 11 (# of maximum possible runs) Mu = 8.47 (expected mean of runs) Sigma = 1.86 (expected standard deviation of runs) Z = 1.36 (test statistic) P(
