(controlled by PSUBTOT=, UDECIMALS=, REALSE=)
These summarize the measures from the main analysis for persons selected by PSUBTOT= (Table 28), including extreme scores. PSUBTOTAL= is useful for quantifying the impact of a test on different types of test-takers.
Table
28.2 Measure sub-totals bar charts, controlled by PSUBTOT=
28.3 Measure sub-totals summary statistics, controlled by PSUBTOT=
Subtotal specification is: PSUBTOTAL=@GENDER
Subtotals
EXTREME AND NON-EXTREME KID SCORES
--------------------------------------------------------------------------------------------------------------------
| KID MEAN MEAN MEAN S.E. MODEL MODEL TRUE MEAN |
| COUNT SCORE COUNT MEASURE MEAN P.SD S.SD MEDIAN SEPARATION RELIABILITY RMSE SD OUTFIT CODE |
|------------------------------------------------------------------------------------------------------------------|
| 74 31.4 25.0 .90 .14 1.22 1.22 .67 2.88 .89 .40 1.15 1.08 * |
| 18 35.7 25.0 1.62 .38 1.56 1.61 1.43 3.05 .90 .49 1.49 .74 F |
| 56 30.0 25.0 .67 .13 .97 .98 .49 2.47 .86 .37 .90 1.19 M |
--------------------------------------------------------------------------------------------------------------------
SUBTOTAL RELIABILITY: .00
UMEAN=0 USCALE=1
Subtotal specification is: PSUBTOTAL=@GENDER
|
identifies the columns in the Person label to be used for classifying the Person by @GENDER or whatever, using the column selection rules.
|
EXTREME AND NON-EXTREME SCORES
|
All persons with estimated measures
|
NON-EXTREME SCORES ONLY
|
Persons with non-extreme scores (omits Persons with 0% and 100% success rates)
|
PERSON COUNT
|
count of Persons. "PERSON" is the name assigned with PERSON=
|
MEAN SCORE
|
weighted average person score on the items
|
MEAN COUNT
|
weighted average of the count of responses to the items
|
MEAN MEASURE
|
average measure of Persons
|
S.E. MEAN
|
standard error of the average measure of Persons
|
P.SD
|
population standard deviation of the Persons.
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S.SD
|
sample standard deviation of the Persons.
|
MEDIAN
|
the measure of the middle Person
|
REAL/MODEL SEPARATION
|
the separation coefficient: the "true" adjusted standard deviation / root-mean-square measurement error of the Persons (REAL = inflated for misfit).
|
REAL/MODEL RELIABILITY
|
the Person measure reproducibility = ("True" Person measure variance / Observed variance) = Separation ² / (1 + Separation ²)
|
RMSE
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Statistical average of the standard errors of the measures
|
TRUE SD
|
Observed population S.D. adjusted for measurement error
|
MEAN OUTFIT
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Average outfit mean-square for the group. Expectation near 1.0
|
CODE
|
the classification code in the Person label. The first line, "*", is the total for all Persons. The remaining codes are those in the Person columns specified by @GENDER or whatever, using the column selection rules. In this example, "F" is the code for "Female" in the data file. "M" for "Male". It is seen that the two distributions are almost identical.
|
SUBTOTAL RELIABILITY
|
the reliability (reproducibility) of the means of the subtotals = true variance / observed variance = (observed variance - error variance) / observed variance.
Observed variance = variance of MEAN MEASURES
Error variance = mean-square of the S.E. MEAN
|
Independent-samples t-test of pairs of subtotal means
------------------------------------------------
| PERSON MEAN DIFFERENCE Welch |
| CODE CODE MEASURE S.E. t d.f. Prob. |
|----------------------------------------------|
| F M -.62 .77 -.81 33 .424 |
------------------------------------------------
PERSON CODE
|
the classification code in the Person label for subtotal "1"
|
CODE
|
the classification code in the Person label for subtotal "2"
|
MEAN DIFFERENCE
|
difference between the mean measures of the two CODE subtotals, "1" and "2"
|
MEASURE
|
size of the difference between "1" and "2"
|
S.E.
|
standard error of the difference =
sqrt ( (S.E. Mean "1")² + (S.E. Mean "2")² )
|
t
|
Student's t = MEASURE / S.E.
|
d.f.
|
Welch's degrees of freedom
|
Prob.
|
two-sided probability of Student's t. See t-statistics.
|
One-way ANOVA of subtotal means and variances
This reports a one-way analysis of variance for the subtotal means. Are they the same (statistically) as the overall mean?
---------------------------------------------------------------
| ANOVA - KID |
| Source Sum-of-Squares d.f. Mean-Squares F-test Prob>F |
|-------------------------------------------------------------|
| @GENDER 3.41 1.00 3.41 .67 .5743 |
| Error 169.12 33.00 5.12 |
| Total 172.53 34.00 5.07 |
|-------------------------------------------------------------|
| Fixed-Effects Chi-square: .6565 with 1 d.f., prob. .4178 |
---------------------------------------------------------------
Source
|
the variance component.
|
@GENDER (the specified PSUBTOTAL= classification)
|
the variation of the subtotal mean measures around the grand mean.
|
Error
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Error is the part of the total variation of the measures around their grand mean not explained by the @GENDER
|
Total
|
total variation of the measures around their grand mean
|
Sum-of-Squares
|
the variation around the relevant mean
|
d.f.
|
the degrees of freedom corresponding to the variation (= number of measures - 1)
|
Mean-Squares
|
Sum-of-Squares divided by d.f.
|
F-test
|
@GENDER Mean-Square / Error Mean-Square
|
Prob>F
|
the right-tail probability of the F-test value with (@GENDER, Error) d.f. A probability less than .05 indicates statistically significant differences between the means.
|
Fixed-Effects Chi-Square (of Homogeneity)
|
a test of the hypothesis that all the subtotal means are the same, except for sampling error
|
d.f.
|
degrees of freedom of chi-square = number of sub-totals - 1
|
prob.
|
probability of observing this value of the chi-square or larger if the hypothesis is true. A probability less than .05 indicates statistically significant differences between the means.
|
inestimable
|
some person counts are too small and/or some variances are zero.
|
