Inter-rater consistency: In the Table below, from a Facets analysis of the example "Essays.txt" data, the Correlation columns give the observed and expected correlations between the ratings given by each reader and the element measures. The element measures are based on the ratings given by all the readers, so this Point-Measure (PT-Biserial=Measure) correlation summarizes the agreement between this Reader and the consensus of all the readers. If you want the same correlation, but using the unadjusted ratings (not measures), then Pt-Biserial=Yes produces the column at the right of this table. The correlations are lower because they are not adjusted for rater leniency. BTW, this data is high quality, produced by ETS using their best raters for a special study.
AP English Essays (College Board/ETS) 8/24/2023 11:07:23 AM
Table 7.3.1 Reader Measurement Report (arranged by MN).
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| Total Total Obsvd Fair(M)| - Model | Infit Outfit |Estim.| Correlation | Exact Agree. | | Corr. |
| Score Count Average Average|Measure S.E. | MnSq ZStd MnSq ZStd |Discrm| PtMea PtExp | Obs % Exp % | Nu Reader | PtBis |
|--------------------------------+--------------+----------------------+------+-------------+--------------+---------------------|-------+
| 508 96 5.29 5.26 | -.30 .08 | 1.23 1.6 1.21 1.4 | .75 | .60 .62 | 20.8 20.4 | 8 8 | .32 |
| 485 96 5.05 5.00 | -.16 .08 | .52 -4.2 .53 -4.1 | 1.48 | .67 .62 | 21.2 21.7 | 4 4 | .39 |
| 484 96 5.04 4.99 | -.15 .08 | 1.02 .1 1.01 .0 | .97 | .64 .62 | 24.1 21.6 | 9 9 | .36 |
| 479 96 4.99 4.93 | -.12 .08 | 1.13 .9 1.13 .9 | .83 | .55 .62 | 28.8 21.7 | 7 7 | .29 |
| 473 96 4.93 4.86 | -.08 .08 | 1.06 .5 1.06 .4 | .93 | .56 .62 | 20.8 21.7 | 2 2 | .29 |
| 470 96 4.90 4.83 | -.06 .08 | 1.40 2.6 1.37 2.4 | .63 | .65 .62 | 27.8 22.0 | 12 12 | .33 |
| 466 96 4.85 4.79 | -.04 .08 | 1.14 .9 1.11 .8 | .81 | .62 .61 | 30.6 21.9 | 11 11 | .33 |
| 461 96 4.80 4.73 | .00 .08 | .71 -2.3 .71 -2.2 | 1.31 | .68 .61 | 42.4 21.9 | 10 10 | .36 |
| 444 96 4.63 4.55 | .11 .08 | .85 -1.1 .84 -1.1 | 1.14 | .60 .61 | 36.1 22.0 | 5 5 | .35 |
| 434 96 4.52 4.44 | .17 .08 | 1.04 .3 1.06 .4 | .93 | .65 .60 | 38.9 21.9 | 6 6 | .37 |
| 433 96 4.51 4.43 | .18 .08 | 1.06 .4 1.03 .2 | .99 | .64 .60 | 27.8 21.8 | 3 3 | .35 |
| 392 96 4.08 4.00 | .45 .08 | .79 -1.5 .79 -1.5 | 1.23 | .48 .59 | 19.7 19.8 | 1 1 | .27 |
|--------------------------------+--------------+----------------------+------+-------------+--------------+---------------------|-------+
| 460.8 96.0 4.80 4.73 | .00 .08 | 1.00 -.1 .99 -.2 | | .61 | | Mean (Count: 12) | .33 |
| 29.5 .0 .31 .32 | .19 .00 | .23 1.8 .22 1.7 | | .05 | | S.D. (Population) | .03 |
| 30.8 .0 .32 .33 | .20 .00 | .24 1.9 .23 1.8 | | .06 | | S.D. (Sample) | .04 |
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Model, Populn: RMSE .08 Adj (True) S.D. .17 Separation 2.17 Strata 3.22 Reliability (not inter-rater) .82
Model, Sample: RMSE .08 Adj (True) S.D. .18 Separation 2.28 Strata 3.38 Reliability (not inter-rater) .84
Model, Fixed (all same) chi-squared: 66.3 d.f.: 11 significance (probability): .00
Model, Random (normal) chi-squared: 9.4 d.f.: 10 significance (probability): .49
Inter-Rater agreement opportunities: 384 Exact agreements: 108 = 28.1% Expected: 82.6 = 21.5%
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Amother approach:
Use the Facets "Output Files" option to produce a Winsteps file.
Select the raters columns (items), and the relevant combinations of facets (e.g., examinees and tasks) as the rows.
This will produce a data file which can be used to produce inter-rater correlations in Excel.
If the inter-rater correlation computation is done in Winsteps,
In the Winsteps control file,
PRCOMP=Observation
ICORFILE=inter-rater-correlations.txt
Rasch estimates are not needed, so Ctrl+F soon after iteration starts.
inter-rater-correlations.txt contains a list of the inter-rater correlations based on the observations.
Otherwise, see Table 7 Agreement Statistics
