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. Choose Stat > Basic Statistics > 2 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.


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

HospitalNStDevVariance95% CI for σ
A208.18366.958(5.893, 12.597)
B2012.431154.537(8.693, 19.709)

Ratio of Standard Deviations

95% CI for Ratio
using Bonett
95% CI for Ratio
using Levene
0.658241(0.372, 1.215)(0.378, 1.296)


Null hypothesisH₀: σ₁ / σ₂ = 1
Alternative hypothesisH₁: σ₁ / σ₂ ≠ 1
Significance levelα = 0.05
Bonett2.091 0.148