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 one-line summary statistics. Bar charts are shown in Table 27.2. Detailed summary statistics in Table 27.3, 27.4, ...

 

TOTAL FOR ALL 14 NON-EXTREME TAP

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|          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                                                               |

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  MAXIMUM EXTREME SCORE: 3 TAP 16.7%

  MINIMUM EXTREME SCORE: 1 TAP 5.6%

 

TOTAL FOR ALL 18 EXTREME AND NON-EXTREME TAP

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|          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                                                              |

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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. Extreme persons and extreme items (minimum possible scores and maximum possible scores) have no infit nor outfit statistics, so those statistics are omitted from "extreme and non-extreme".

 

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)) 10

P.SD = Population standard deviation (when the sample is the entire population)

S.SD = Sample standard deviation (when the sample represents the population)

MAX. is its maximum value.

MIN. is its minimum value.

 

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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.

Real reliability while you are improving your results. This assumes misfit contradicts the Rasch model.

Model reliability when your results are as good as they can be. This assumes misfit is the randomness predicted by the Rasch model

 

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).