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.
Interpret the results
The null hypothesis states that the ratio between the standard deviations is 1. Because the pvalues 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 

Descriptive Statistics: Rating 

A  20  8.1828  66.958  (5.8931, 12.5966)  B  20  12.4313  154.537  (8.6927, 19.7093) 

Ratio of Standard Deviations 

0.658241  (0.37247, 1.21499)  (0.37779, 1.29619) 


Null hypothesis  H₀: σ₁ / σ₂ = 1  Alternative hypothesis  H₁: σ₁ / σ₂ ≠ 1 



Bonett  2.09    0.1485  Levene  1.60  1  38  0.2141 

