Table 3.1 Summaries of persons and items

(controlled by REALSE=, UMEAN=, USCALE=, ISUBTOTAL=, PSUBTOTAL=)

This table summarizes the person, item and structure information.

 

Table 3.1: Gives summaries for all persons and items.

Table 3.2: Summary of rating categories and probability curves

Table 27.3: Gives subtotal summaries for items, controlled by ISUBTOT=

Table 28.3: Gives subtotal summaries for persons, controlled by PSUBTOT=

 

   SUMMARY OF 34 MEASURED (NON-EXTREME) KID

-------------------------------------------------------------------------------

|          TOTAL                         MODEL         INFIT        OUTFIT    |

|          SCORE     COUNT     MEASURE    S.E.      MNSQ   ZSTD   MNSQ   ZSTD |

|-----------------------------------------------------------------------------|

| MEAN       9.9      18.0        -.19    1.01       .99    -.2    .68    -.1 |

| P.SD       2.1        .0        1.97     .10       .94    1.2   1.29     .7 |

| S.SD       2.1        .0        2.00     .10       .95    1.2   1.30     .7 |

| MAX.      14.0      18.0        3.73    1.11      4.12    2.5   6.07    2.2 |

| MIN.       5.0      18.0       -4.32     .82       .18   -1.5    .08    -.7 |

|-----------------------------------------------------------------------------|

| REAL RMSE   1.18 TRUE SD    1.58  SEPARATION  1.34  KID    RELIABILITY  .64 |

|MODEL RMSE   1.01 TRUE SD    1.69  SEPARATION  1.67  KID    RELIABILITY  .74 |

| S.E. OF KID MEAN = .34                                                      |

-------------------------------------------------------------------------------

 MINIMUM EXTREME SCORE:      1 KID 2.9%

 

    SUMMARY OF 35 MEASURED (EXTREME AND NON-EXTREME) KID

-------------------------------------------------------------------------------

|          TOTAL                         MODEL         INFIT        OUTFIT    |

|          SCORE     COUNT     MEASURE    S.E.      MNSQ   ZSTD   MNSQ   ZSTD |

|-----------------------------------------------------------------------------|

| MEAN       9.7      18.0        -.37    1.03                                |

| P.SD       2.4        .0        2.22     .17                                |

| S.SD       2.4        .0        2.25     .18                                |

| MAX.      14.0      18.0        3.73    1.85                                |

| MIN.       3.0      18.0       -6.62     .82                                |

|-----------------------------------------------------------------------------|

| REAL RMSE   1.21 TRUE SD    1.86  SEPARATION  1.55  KID    RELIABILITY  .70 |

|MODEL RMSE   1.05 TRUE SD    1.96  SEPARATION  1.87  KID    RELIABILITY  .78 |

| S.E. OF KID MEAN = .38                                                      |

-------------------------------------------------------------------------------

KID RAW SCORE-TO-MEASURE CORRELATION = 1.00

CRONBACH ALPHA (KR-20) KID RAW SCORE "TEST" RELIABILITY = .75  SEM = 1.17

 

    SUMMARY OF 14 MEASURED (NON-EXTREME) 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                                                      |

-------------------------------------------------------------------------------

 MAXIMUM EXTREME SCORE:      3 TAP 16.7%

 MINIMUM EXTREME SCORE:      1 TAP 5.6%

 

    SUMMARY OF 18 MEASURED (EXTREME AND NON-EXTREME) 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      14.2        .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                                                     |

-------------------------------------------------------------------------------

TAP RAW SCORE-TO-MEASURE CORRELATION = -.99

Global fit: please see Table 44.

UMEAN=.0000 USCALE=1.0000

 

EXTREME AND NON-EXTREME SCORES

All items with estimated measures

NON-EXTREME SCORES ONLY

Items with non-extreme 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 "root-mean-square" 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 measurement-error-free S.D.

REAL/MODEL SEPARATION

the separation coefficient: G = TRUE P.SD / RMSE

Strata = (4*G + 1)/3

REAL/MODEL RELIABILITY

the measure reproducibility
= ("True" item measure variance / Observed variance)
= Separation ² / (1 + Separation ²)

S.E. MEAN

standard error of the mean measure of items or persons

 

For valid observations used in the estimation,

 

NON-EXTREME persons or items - summarizes persons (or items) with non-extreme scores (omits zero and perfect scores).

 

EXTREME AND NON-EXTREME 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 non-extreme 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 worst-case 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 best-case situation.

 

S.E. is the standard error of the estimate.

 

INFIT is an information-weighted fit statistic, which is more sensitive to unexpected behavior affecting responses to items near the person's measure level.

 

MNSQ is the mean-square infit statistic with expectation 1.  Values substantially below 1 indicate dependency in your data; values substantially above 1 indicate noise.

 

ZSTD is the infit mean-square fit statistic t standardized to approximate a theoretical mean 0 and variance 1 distribution. ZSTD (standardized as a z-score) is used of a t-test result when either the t-test value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's t-statistic 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 mean-squares are reported.

 

OUTFIT is an outlier-sensitive fit statistic, more sensitive to unexpected behavior by persons on items far from the person's measure level.

 

MNSQ is the mean-square 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 mean-square fit statistic t standardized to approximate a theoretical mean 0 and variance 1 distribution. ZSTD (standardized as a z-score) is used of a t-test result when either the t-test value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's t-statistic 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 mean-squares 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 square-root 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 signal-to-noise ratio, the ratio of "true" variance to error variance.

 

RELIABILITY is a separation reliability (separation index). The PERSON (or ITEM) reliability is equivalent to KR-20, 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 non-missing responses are scored correct (perfect score) or in the top categories. Measures are estimated.

MINIMUM EXTREME SCORE

All non-missing 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.

 

PERSON RAW SCORE-TO-MEASURE CORRELATION is the Pearson correlation between raw scores and measures, including extreme scores. When data are complete, this correlation is expected to be near 1.0 for persons.

 

CRONBACH ALPHA (KR-20) KID RAW SCORE "TEST" RELIABILITY is the conventional "test" reliability index. It reports an approximate test reliability based on the raw scores of this sample. It is only reported for complete data. See more at Reliability. Cronbach Alpha is an estimate of the person-sample reliability (= person-score-order reproducibility). Classical Test Theory does not usually compute an estimate of the item reliability (= item-value-order reproducibility), but it could. Winsteps reports both person-sample reliability (=person-measure-order reproducibility) and item reliability (= item-measure-order-reproducibility). Cronbach Alpha is computed for both dichotomous and polytomous data. Cronbach Alpha is the same as KR-20 when the data are dichotomous. KR-20 is not defined for polytomous data.

SEM this is the "standard error of measurement" (the averaged S.E. of the person raw-scores) reported by Classical Test Theory = raw score S.D. * √(1-Cronbach Alpha)

 

ITEM RAW SCORE-TO-MEASURE CORRELATION is the Pearson correlation between raw scores and measures, including extreme scores. When data are complete, this correlation is expected to be near -1.0 for items. This is because higher measure implies lower probability of success and so lower item scores.

 

Global fit: please see Table 44.

 

UMEAN=.000 USCALE=1.000 are the current settings of UMEAN= and USCALE=.


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