Example of Randomization Test for 2-Sample Means

A healthcare consultant wants to compare the patient satisfaction ratings of two hospitals. The consultant performs a randomization test for 2-sample means to determine whether there is a difference in the patient ratings between the hospitals.

  1. Open the sample data, HospitalComparison.MTW.
  2. Open the randomization test for 2-sample means dialog box.
    • Mac: Statistics > Resampling > Randomization Test for 2-Sample Means
    • PC: STATISTICS > Resampling > Randomization Tests > 2-Sample Means
  3. In Samples, enter Rating.
  4. In Sample IDs, enter Hospital.
  5. On the Options tab, enter 1 in Base for random number generator.
    Note

    Using Base for random number generator ensures that your results match the example.

  6. Click OK.

Interpret the results

The null hypothesis states that the difference in the patient ratings between the hospitals is equal to 0. Because the p-value is less than 0.002, which is less than the significance level of 0.05, the consultant rejects the null hypothesis and concludes that the difference in patient ratings between the hospitals is not equal to 0. The histogram shows that the bootstrap distribution appears to be normal, so the consultant can trust the results.

The difference in observed means is 21, indicating that hospital A has higher patient satisfaction ratings than hospital B.

Method
μ₁: mean of Rating when Hospital = A
μ₂: mean of Rating when Hospital = B
Difference: μ₁ - μ₂
Observed Samples
Hospital
N
Mean
StDev
Variance
Minimum
Median
Maximum
Difference in Observed Means
Randomization Test
Number of Resamples
Average
StDev
P-Value
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