# 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
 σ₁: standard deviation of Rating when Hospital = A σ₂: standard deviation of Rating when Hospital = B Ratio: σ₁ / σ₂
 The Bonett and Levene's methods are valid for any continuous distribution.
 Descriptive Statistics: Rating
 Hospital N StDev Variance 95% CI for σ A 20 8.1828 66.958 (5.8931, 12.5966) B 20 12.4313 154.537 (8.6927, 19.7093)
 Ratio of Standard Deviations
 Estimated Ratio 95% CI for Ratio Bonett 95% CI for Ratio Levene 0.658241 (0.37247, 1.21499) (0.37779, 1.29619)
 Test
 Null hypothesis H₀: σ₁ / σ₂ = 1 Alternative hypothesis H₁: σ₁ / σ₂ ≠ 1
 Method Test Statistic DF1 DF2 P-Value Bonett 2.09 0.1485 Levene 1.60 1 38 0.2141
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