Example of 2 Variances

A healthcare consultant wants to compare the patient satisfaction ratings of two hospitals. The consultant collects ratings from 20 patients for each of the hospitals.

The consultant performs a 2 variances test to determine whether the standard deviations in the patient ratings from the two hospitals differ.

  1. Open the sample data, HospitalComparison.MTW.
  2. Open the 2 Variances dialog box.
    • Mac: Statistics > 2-Sample Inference > Variances
    • PC: STATISTICS > Two Samples > Variances
  3. From the drop-down list, select Both samples are in one column.
  4. In Samples, enter Rating.
  5. In Sample IDs, enter Hospital.
  6. Click OK.

Interpret the results

The null hypothesis states that the ratio between the standard deviations is 1. Because the p-values are both greater than the significance level (denoted as α or alpha) of 0.05, the consultant fails to reject the null hypothesis. The consultant does not have enough evidence to conclude that the standard deviations between the hospitals are different.

Method
The Bonett and Levene's methods are valid for any continuous distribution.
Descriptive Statistics: Rating
Hospital
N
StDev
Variance
Ratio of Standard Deviations
Estimated Ratio
Test
Method
Test Statistic
DF1
DF2
P-Value
Bonett
Levene
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