4.3

STATISTICAL ANALYSIS OF SQG PERFORMANCE RESULTS

4.3.1

Interpreting Observed SQG Results

The data in the above charts represent observed SQG performance levels in each state. Had all of the SQGs in each state been evaluated, these results could provide definitive information about each state’s SQG performance and any differences among them. However, as is often the case, only a portion of the SQGs could be inspected. Since the facilities were randomly selected, statistical methods were used to generalize the field observation findings to the sector as a whole and to determine if the observed differences among states are likely to be due to chance, or reflect actual differences in performance.

When statistics are used to estimate the performance of an entire population from a sample, the conclusions are presented as a range rather than as a point (e.g. 75% + or – a confidence interval of 10% which means that the estimated achievement rate is between 65% and 85%).

# 4.3.2 Statistically Significant Differences in SQG Mean Facility Scores

Exhibit 4.1 below presents statistically significant differences in mean facility achievement scores, at a 90% confidence level with the associated confidence interval, across all states and categorized by group, (i.e., all indicators, regulatory indicators and beyond compliance indicators):

HOW TO READ THESE CHARTS: The chart below presents the number of facilities that were evaluated, the observed performance score and associated confidence interval range in each state. States are listed from highest to lowest SQG performance and statistically significant differences between states are shown by arrows. An arrow connecting a state to another state below on the list indicates the existence of a statistically significant difference. The lack of an arrow between any two states means the observed differences may be due to chance. A state may use these charts to compare its SQG performance with any other state’s SQG performance.

## The States Common Measures Project Final Report

67