Table 5 Measurable data summary 
Table 5 reports summary statistics about the data for the analysis.
++
 Cat Score Exp. Resd StRes 
+
 4.80 4.80 4.80 .00 .00  Mean (Count: 1152) 
 1.63 1.63 1.03 1.27 .99  S.D. (Population) 
 1.64 1.64 1.03 1.27 .99  S.D. (Sample) 
++
Column headings have the following meanings:
Cat = Observed value of the category as entered in the data file.
Score = Value of category after it has been recounted cardinally commencing with "0" corresponding to the lowest observed category.
Exp. = Expected score based on current estimates
Resd = Residual, the score difference between Step and Exp.
StRes = The residual standardized by its standard error. StRes is expected to approximate a unit normal distribution.
Mean = average of the observations
Count = number of observations
S.D. (Population) = standard deviation treating this sample as the entire population
S.D. (Sample) = standard deviation treating this sample as a sample from the population. It is larger than S.D. (Population).
The rawscore error variance % is 100*(Resd S.D./Cat S.D.)²
When the parameters are successfully estimated, the mean Resd is 0.0. If not, then there are estimation problems  usually due to too few iterations, or anchoring.
When the data fit the Rasch model, the mean of the "StRes" (Standardized Residuals) is expected to be near 0.0, and the "S.D." (sample standard deviation) is expected to be near 1.0. These depend on the distribution of the residuals.
Explained variance by each facet can be approximated by using the element S.D.^2 (^2 means "squared").
From Table 5:
Explained variance = Score Population S.D.^2  Resd^2
Explained variance % = Explained variance * 100 / Score Population S.D.^2
From Table 7:
+++++ +
 460.8 96.0 4.8 4.73 .00 .08  1.00 .1 .99 .2  .61   Mean (Cnt: 12) 
 29.5 .0 .3 .32 .19 .00  .23 1.8 .22 1.7  .05   S.D. (Population) 
 30.8 .0 .3 .33 .20 .00  .24 1.9 .23 1.8  .06   S.D. (Sample) 
+ +
v1 = (measure Population S.D. facet 1)^2
v2 = (measure Population S.D. facet 2)^2
v3 = (measure Population S.D. facet 3)^2
vsum = v1 + v2 + v3 + .... (for all facets)
Compute Explained variance for each facet:
Explained variance % by facet 1 = (Explained variance %) * v1 /vsum
Explained variance % by facet 2 = (Explained variance %) * v2 /vsum
Explained variance % by facet 3 = (Explained variance %) * v3 /vsum
For a Raschbased Generalizability Coefficient:
G = (Explained variance% by target facet) / 100
A more specific Generalizability Coefficient can be formulated by selecting appropriate variance terms from Table 5, Table 7, and Table 13.
Data loglikelihood chisquare = 3787.4307
Approximate degrees of freedom = 1093
Chisquare significance prob. = .0000
Count Mean S.D. Params
Responses after endoffile = 0 0.00 0.00 0 (only shown if not 0)
Responses only in extreme scores = 0 0.00 0.00 0 (only shown if not 0)
Responses in two extreme scores = 0 0.00 0.00 0 (only shown if not 0)
Responses with invalid elements = 0 0.00 0.00 0 (only shown if not 0)
Responses invalid after recounting = 0 0.00 0.00 0 (only shown if not 0)
Responses used for estimation = 1152 4.80 1.63 59
Responses in one extreme score = 0 0.00 0.00 0 (only shown if not 0)
All Responses = 1152 4.80 1.63 59
Identification 
Meaning 
Data loglikelihood chisquare 
This is a estimate of the global fit of the data to the model = 2 * loglikelihood of the empirical data. Likelihood = product of the probabilities of the observations. 
Approximate degrees of freedom 
The d.f. of the chisquare approximates the number of data points less the number of parameters estimated 
Chisquare significance prob. 
The probability of observing the chisquare value (or larger) when the data fit the model 


Response Type 
Responses not used for estimation: see Residual File 
Responses after endoffile 
A Facets internal workfile has too many responses. Please report this to Winsteps.com and rerun this analysis. 
Responses only in extreme scores 
The category of the rating scale cannot be estimated. 
Responses in two extreme scores 
These cannot be estimated nor used for estimating element measures. 
Responses with invalid elements 
Elements for these observations are not defined. See Table 2 with Build option. 
Responses invalid after recounting 
A dichotomy or rating scale has less than two categories, so it cannot be estimated. See Table 8 for missing or onecategory rating scales. 
Response Type 
Responses used for estimation: see Residual File 
Responses used for estimation 
This is the count of responses used in estimating nonextreme parameter values (element measures and rating scale structures). 
Responses in one extreme score 
These are only used for estimating the element with the extreme score 
All Responses 
Shown if there is more than one response type listed above 
Count of measurable responses = 1152
Rawscore variance of observations = 2.67 100.00%
Variance explained by Rasch measures = 1.06 39.57%
Variance of residuals = 1.61 60.43%
Variance explained by bias/interactions = 0.14 5.24%
Variance remaining in residuals = 1.47 55.06%
An approximate Analysis of Variance (ANOVA) of the data 

Identification 
Meaning 
Count of measurable responses 
All responses (including for extreme scores) with weighting (if any) 
Rawscore variance of observations 
Square of S.D. (Population) of Score 
Variance explained by Rasch measures 
Raw score variance  Variance of residuals. The size of the expected variance for 2facet models is shown in www.rasch.org/rmt/rmt221j.htm 
Variance of residuals 
Square of S.D. (Population) of Resd. 
Variance explained by bias/interactions 
The variance explained by the bias/interactions specified with "B" in your Models= statements 
Variance remaining in residuals 
Variance of residuals  Variance of interactions 
Nested models: Suppose we want to estimate the effect on fit of a facet.
Run twice:
First analysis: 3 facets
Models = ?,?,?, R
Second analysis: 2 facets:
Models = ?,?,X,R
We can obtain an estimate of the improvement of fit based on including the third facet:
Chisquare of improvement = Data loglikelihood chisquare (2 facets)  Data loglikelihood chisquare (3 facets) with d.f. (2 facets)  d.f. (3 facets).
If global fit statistics are the decisive evidence for choice of analytical model, then Facets is not suitable. In the statistical philosophy underlying Facets, the decisive evidence for choice of model is "which set of measures is more useful" (a practical decision), not "which set of measures fit the model better" (a statistical decision). The global fit statistics obtained by analyzing your data with loglinear models (e.g., in SPSS) will be more exact than those produced by Facets.
Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
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April 1012, 2018, Tues.Thurs.  Rasch Conference: IOMW, New York, NY, www.iomw.org 
April 1317, 2018, Fri.Tues.  AERA, New York, NY, www.aera.net 
May 22  24, 2018, Tues.Thur.  EALTA 2018 preconference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank WeissMotz), https://ealta2018.testdaf.de 
May 25  June 22, 2018, Fri.Fri.  Online workshop: Practical Rasch Measurement  Core Topics (E. Smith, Winsteps), www.statistics.com 
June 27  29, 2018, Wed.Fri.  Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org 
June 29  July 27, 2018, Fri.Fri.  Online workshop: Practical Rasch Measurement  Further Topics (E. Smith, Winsteps), www.statistics.com 
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 
Aug. 10  Sept. 7, 2018, Fri.Fri.  Online workshop: ManyFacet Rasch Measurement (E. Smith, Facets), www.statistics.com 
Sept. 3  6, 2018, Mon.Thurs.  IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org 
Oct. 12  Nov. 9, 2018, Fri.Fri.  Online workshop: Practical Rasch Measurement  Core Topics (E. Smith, Winsteps), www.statistics.com 
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