# MSA Interval Level Output

The output for a Measurement Systems Analysis for Interval/Ratio level data is shown below.

Several unique diagnostic assessments are performed. Pair-wise comparisons are made for each set of measures for each appraiser. Pair-wise comparisons are also made between each appraiser. The following two-sample dependent tests are performed.

- Pearson Correlation between the measures [r], with the p-value of the
*r*statistic [p(r)] - The two-sample dependent (matched-pairs) t-test for variances (t(Var)), with the p-value for that
*t*statistic [p(Var)] - The two-sample dependent t-test [t(Means)], with the p-value for the
*t*statistic [p(Means] - The two-sample dependent t-test on ranges [t(ranges)], with the p-value for that
*t*statistic [p(Ranges]

If there is no correlation, the system or study would be suspect. The system would have no ability to see differences between specimens.

If the two-sample matched-pairs t-test for variances is significant, there may be a linearity problem. This could be seen on a scatter plot. This test is sensitive to non-linearity.

If there is a difference in sample means within appraiser, then something has changed during the study, and the system is not in statistical control.

If there is a difference in appraiser means, then there is a bias from one appraiser/system to another.

Testing for differences in ranges, using the t-test (normally for means), assess differences in measurement error from one appraiser to another.

Finally, the standard calculations are made for measurement error and for "Equipment Variation" (EV) and "Appraiser Variation" (AV), and "%R&R"

## Sample Output

# Measurement Systems Analysis - Interval/Ratio Data

File: C:\DATA\GAUGE\Gauge Potential Example Data.mvp Confidence Level = 95.00%

## Variables

Jack1 [Jack1,Jack2] Jill1 [Jill1,Jill2]

## Specifications

Range = 9.0

## Repeatability (Within Appraiser)

### Jack1 - Repeatability Analysis

Trials n r p(r) t(Var) p(Var) Diff t(Means) p(Means)m1 vs m2 10 0.841 0.002* -0.949 0.367 -1.65 -4.107 0.003*

### Jill1 - Repeatability Analysis

Trials n r p(r) t(Var) p(Var) Diff t(Means) p(Means)m1 vs m2 10 0.988 0.000* -2.566 0.030* -0.94 -2.825 0.022*

### System - Repeatability Analysis

Appraisers n r(R) p(r) t(Var R) p(Var R) Rmin/Rmax t(Ranges) p(Ranges)Jack1 vs Jill1 10 -0.119 0.744 0.657 0.528 0.594 1.236 0.252Appraiser Measures n Avg(R) Std Dev(E) NT(EV) EVJack1 2 10 1.65 1.42 7.33 81.4% Jill1 2 10 0.98 0.85 4.35 48.4% Overall 2 10 1.32 1.17 6.00 66.7%

## Reproducibility (Between Appraisers)

### Appraiser vs Appraiser - Reproducibility Analysis

Appraisers n r p(r) t(Var) p(Var) Diff t(Means) p(Means)Jack1 vs Jill1 10 0.623 0.054 -3.647 0.005* -3.82 -2.975 0.018*

### System - Reproducibility Analysis

Group Range Std Dev NT(AV) AVOverall 3.82 2.71 13.97 155.2%

## System - Measurement Error

Group EV AV NT(E) %R&ROverall 66.7% 155.2% 15.21 168.9%