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5.3 DETERMINING A REASONABLE SAMPLE SIZE FOR DRAWING STATISTICAL CONCLUSIONS ABOUT THE AUTO BODY GROUP

5.3.1 Sample Size Needed to Benchmark an Individual State’s Sector Performance

The Massachusetts ERP “sample-size calculator” was used to calculate the sample sizes that would be required to benchmark each state’s performance at various confidence levels, confidence intervals and assumptions about the observed compliance rates. The chart below shows the results of the analysis.

85

85

+/- 5%

+/- 10%

80%

50%

135

47

85

42

118

49

95

45

90

90

90%

95%

95%

95%

+/- 10%

+/- 10%

+/- 5%

+/- 15%

+/- 10%

+/- 7%

50%

80%

80%

50%

80%

90%

40

129

39

55

62

37

100

36

49

54

42

150

41

58

66

38

114

38

52

58

Confidence Level: % certainty that the observed result reflects actual conditions/ is not due to chance

Confidence Interval/Margin of Error: the actual percentage of facilities in compliance falls somewhere within + or - the listed percentage points of the observed percent compliance

Observed “Good Performance” Rate of the Sample

Auto Body Universe Size

500 –750 (used 500)

235

1096 – 1514 (used 1096)

336

116

49

130

51

41

145

41

58

65

43

168

42

61

70

900 (Regions 4 and 9)

6000 (entire state)

The highlighted columns show the level of certainty (confidence level) and precision (confidence interval) that can be achieved for a “realistic” number of inspections per state

  • (e.

    g., between 36 – 70 inspections):

    • o

      Column 6 presents the lowest range of inspections per state at the most conservative observed “good performance” level (50%): a minimum of 36 for Vermont, the state with the smallest universe and a maximum of 42 inspections for New York, the state with the largest. This number of inspections would allow a state to be 95% confident that the actual result has a margin of error of +/- 15% of the observed result, however this 30% confidence interval may be a little too broad for some states. Alternatively, as shown in column 4, with just one more inspection per state, and IF the observed performance level turned out

The States Common Measures Project Final Report

93

217

165

146

120

284

201

179

142

269

193

361

236

+/-

+/-

5%

5%

95%

95%

50%

80%

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