Table 27.3+ Item subtotal detailed summary statistics 
(controlled by ISUBTOT=, UDECIMALS=)
These summarize the measures from the main analysis for all items selected by ISUBTOT=. Table 27.1 shows oneline summary statistics. Bar charts are shown in Table 27.2. Detailed summary statistics in Table 27.3, 27.4, ...
TOTAL FOR ALL 14 NONEXTREME TAP

 TOTAL MODEL INFIT OUTFIT 
 SCORE COUNT MEASURE S.E. MNSQ ZSTD MNSQ ZSTD 

 MEAN 16.9 35.0 .00 .71 .96 .0 .68 .1 
 P.SD 12.9 .0 3.48 .21 .28 .7 .58 .5 
 S.SD 13.3 .0 3.61 .22 .29 .7 .60 .6 
 MAX. 32.0 35.0 4.80 1.07 1.56 1.2 2.21 1.1 
 MIN. 1.0 35.0 4.40 .45 .59 1.3 .11 .6 

 REAL RMSE .77 TRUE SD 3.39 SEPARATION 4.41 TAP RELIABILITY .95 
MODEL RMSE .74 TRUE SD 3.40 SEPARATION 4.59 TAP RELIABILITY .95 
 S.E. OF TAP MEAN = .97 
 MEDIAN = .39 

MAXIMUM EXTREME SCORE: 3 TAP 16.7%
MINIMUM EXTREME SCORE: 1 TAP 5.6%
TOTAL FOR ALL 18 EXTREME AND NONEXTREME TAP

 TOTAL MODEL INFIT OUTFIT 
 SCORE COUNT MEASURE S.E. MNSQ ZSTD MNSQ ZSTD 

 MEAN 18.9 35.0 .76 .96 
 P.SD 14.0 .0 4.26 .51 
 S.SD 14.4 .0 4.39 .52 
 MAX. 35.0 35.0 6.13 1.85 
 MIN. .0 35.0 6.59 .45 

 REAL RMSE 1.10 TRUE SD 4.12 SEPARATION 3.73 TAP RELIABILITY .93 
MODEL RMSE 1.09 TRUE SD 4.12 SEPARATION 3.79 TAP RELIABILITY .93 
 S.E. OF TAP MEAN = 1.03 
 MEDIAN = 1.96 

EXTREME AND NONEXTREME SCORES 
All items with estimated measures 
NONEXTREME SCORES ONLY 
Items with nonextreme scores (omits items or persons with 0% and 100% success rates) 
ITEM or PERSON COUNT 
count of items or persons. "ITEM" is the name assigned with ITEM= : "PERSON" is the name assigned with PERSON= 
MEAN MEASURE 
average measure of items or persons. 
REAL/MODEL S.E. 
standard errors of the measures (REAL = inflated for misfit). 
REAL/MODEL RMSE 
statistical "rootmeansquare" average of the standard errors 
TRUE P.SD (previously ADJ.SD) 
The "true" population standard deviation is the observed population S.D. adjusted for measurement error (RMSE). This is an estimate of the measurementerrorfree S.D. 
REAL/MODEL SEPARATION 
the separation coefficient: G = TRUE P.SD / RMSE Strata = (4*G + 1)/3 
REAL/MODEL RELIABILITY 
the measure reproducibility 
S.E. MEAN 
standard error of the mean measure of items or persons 
For valid observations used in the estimation,
NONEXTREME persons or items  summarizes persons (or items) with nonextreme scores (omits zero and perfect scores).
EXTREME AND NONEXTREME persons or items  summarizes persons (or items) with all estimable scores (includes zero and perfect scores). Extreme scores (zero, minimum possible and perfect, maximum possible scores) have no exact measure under Rasch model conditions. Using a Bayesian technique, however, reasonable measures are reported for each extreme score, see EXTRSC=. Totals including extreme scores are reported, but are necessarily less inferentially secure than those totals only for nonextreme scores.
RAW SCORE is the raw score (number of correct responses excluding extreme scores, TOTALSCORE=N).
TOTAL SCORE is the raw score (number of correct responses including extreme scores, TOTALSCORE=Y).
COUNT is the number of responses made.
MEASURE is the estimated measure (for persons) or calibration (for items).
REAL/MODEL: REAL is computed on the basis that misfit in the data is due to departures in the data from model specifications. This is the worstcase situation. MODEL is computed on the basis that the data fit the model, and that all misfit in the data is merely a reflection of the stochastic nature of the model. This is the bestcase situation.
S.E. is the standard error of the estimate.
INFIT is an informationweighted fit statistic, which is more sensitive to unexpected behavior affecting responses to items near the person's measure level.
MNSQ is the meansquare infit statistic with expectation 1. Values substantially below 1 indicate dependency in your data; values substantially above 1 indicate noise.
ZSTD is the infit meansquare fit statistic t standardized to approximate a theoretical mean 0 and variance 1 distribution. ZSTD (standardized as a zscore) is used of a ttest result when either the ttest value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's tstatistic distribution value has been adjusted to a unit normal value. When LOCAL=Y, then EMP is shown, indicating a local {0,1} standardization. When LOCAL=L, then LOG is shown, and the natural logarithms of the meansquares are reported.
OUTFIT is an outliersensitive fit statistic, more sensitive to unexpected behavior by persons on items far from the person's measure level.
MNSQ is the meansquare outfit statistic with expectation 1. Values substantially less than 1 indicate dependency in your data; values substantially greater than 1 indicate the presence of unexpected outliers.
ZSTD is the outfit meansquare fit statistic t standardized to approximate a theoretical mean 0 and variance 1 distribution. ZSTD (standardized as a zscore) is used of a ttest result when either the ttest value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's tstatistic distribution value has been adjusted to a unit normal value. When LOCAL=Y, then EMP is shown, indicating a local {0,1} standardization. When LOCAL=L, then LOG is shown, and the natural logarithms of the meansquares are reported.
MEAN is the average value of the statistic.
P.SD is its standard deviation assuming that this sample of the statistic is the entire population. It is not, the corrected sample S.D. = (P.SD / √ (Count of statistic) / (Count of statistic  1))
MAX. is its maximum value.
MIN. is its minimum value.
MODEL RMSE is computed on the basis that the data fit the model, and that all misfit in the data is merely a reflection of the stochastic nature of the model. This is a "best case" reliability, which reports an upper limit to the reliability of measures based on this set of items for this sample. This RMSE for the person sample is equivalent to the "Test SEM (Standard Error of Measurement)" of Classical Test Theory.
REAL RMSE is computed on the basis that misfit in the data is due to departures in the data from model specifications. This is a "worst case" reliability, which reports a lower limit to the reliability of measures based on this set of items for this sample.
RMSE is the squareroot of the average error variance. It is the Root Mean Square standard Error computed over the persons or over the items. Here is how RMSE is calculated in Winsteps:
George ability measure = 2.34 logits. Standard error of the ability measure = 0.40 logits.
Mary ability measure = 3.62 logits. Standard error of the ability measure = 0.30 logits.
Error = 0.40 and 0.30 logits.
Square error = 0.40*0.40 = 0.16 and 0.30*0.30 = 0.09
Mean (average) square error = (0.16+0.09) / 2 = 0.25 / 2 = 0.125
RMSE = Root mean square error = sqrt (0.125) = 0.354 logits
TRUE P.SD is the population standard deviation of the estimates (assumed to be the population) after subtracting the error variance (attributable to their standard errors of measurement) from their observed variance.
(TRUE P.SD)² = (P.SD of MEASURE)²  (RMSE)²
The TRUE P.SD is an estimate of the unobservable exact standard deviation, obtained by removing the bias caused by measurement error.
SEPARATION coefficient is the ratio of the PERSON (or ITEM) TRUE P.SD, the "true" standard deviation, to RMSE, the error standard deviation. It provides a ratio measure of separation in RMSE units, which is easier to interpret than the reliability correlation. (SEPARATION coefficient)² is the signaltonoise ratio, the ratio of "true" variance to error variance.
RELIABILITY is a separation reliability (separation index). The PERSON (or ITEM) reliability is equivalent to KR20, Cronbach Alpha, and the Generalizability Coefficient. See much more at Reliability.
S.E. OF MEAN is the standard error of the mean of the person (or item) measures for this sample.
MEDIAN is the median measure of the sample (in Tables 27, 28).
Message 
Meaning for Persons or Items 
MAXIMUM EXTREME SCORE 
All nonmissing responses are scored correct (perfect score) or in the top categories. Measures are estimated. 
MINIMUM EXTREME SCORE 
All nonmissing responses are scored incorrect (zero score) or in the bottom categories. Measures are estimated. 
LACKING RESPONSES 
All responses are missing. No measures are estimated. 
DELETED 
Persons deleted with PDFILE= or PDELETE=. Items deleted with IDFILE= or IDELETE= 
IGNORED 
Entry numbers higher than highest reported entry number are deleted and not reported 
CUTLO= CUTHI= 
CUTLO= and CUTHI= values if these are active. They reduce the number of valid responses. 
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July 25  July 27, 2018, Wed.Fri.  PacificRim Objective Measurement Symposium (PROMS), (Preconference workshops July 2324, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org 
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