Table 5 reports summary statistics for the analysis.

 

Table 5. Measurable Data Summary.

+-----------------------------------------------------------+

|Cat   Step   Exp. Resd  StRes|                             |

|-----------------------------+-----------------------------|

| 1.26  1.26  1.26   .00  .06 | Mean (Count: 1850)          |

|  .77   .77   .55   .54 1.03 | S.D. (Population)           |

|  .77   .77   .55   .54 1.03 | S.D. (Sample)               |

+-----------------------------------------------------------+

 

Column headings have the following meanings:

Cat  = Observed value of the category as entered in the data file.

Step = Value of category after it has been recounted ordinally 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 and truncated. A value of 1.6 is reported as 1. See Residuals file for a more exact value. 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).

 

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.

 

---

 

Data log-likelihood chi-square = 2658.0383

Approximate degrees of freedom = 99

Chi-square significance prob. = .0000

                                         Count   Mean   S.D.   Params

Responses used for estimation      =      1850   1.26   0.77       99

Responses in one extreme score     =        25   2.00   0.00        1

All Responses                      =      1875   1.27   0.77      100

 

Data log-likelihood chi-square =
This is a estimate of the global fit of the data to the model.

 

Approximate degrees of freedom =
The d.f. of the chi-square approximates the number of data points less the number of parameters estimated.

 

Chi-square significance prob. =
The probability of observing the chi-square value (or larger) when the data fit the model.

 

Responses used for estimation =
This is the count of responses used in estimating non-extreme parameter values (element measures and rating scale structures).

 

Params =
the number of parameters that the responses were used to estimate.