Table 27.1 Item subtotal summaries on one line |
(controlled by ISUBTOT=, UDECIMALS=, REALSE=)
These summarize the measures from the main analysis for all items selected by ISUBTOT= (Table 27), including extreme scores.
Table
27.2 Measure sub-totals bar charts, controlled by ISUBTOT=
27.3 Measure sub-totals summary statistics, controlled by ISUBTOT=
Subtotal specification is: ISUBTOTAL=$S1W1
ALL ACT SCORES ARE NON-EXTREME
--------------------------------------------------------------------------------------------------------------------
| ACT MEAN MEAN MEAN S.E. MODEL MODEL TRUE MEAN |
| COUNT SCORE COUNT MEASURE MEAN P.SD S.SD MEDIAN SEPARATION RELIABILITY RMSE SD OUTFIT CODE |
|------------------------------------------------------------------------------------------------------------------|
| 25 95.0 75.0 .00 .29 1.41 1.43 .16 5.86 .97 .24 1.39 1.08 * |
| 4 90.5 75.0 .31 .73 1.27 1.47 -.11 5.89 .97 .21 1.25 1.41 F |
| 4 137.5 75.0 -2.24 .39 .67 .78 -2.26 1.62 .72 .36 .57 .94 G |
| 5 88.6 75.0 .32 .51 1.02 1.14 .42 4.81 .96 .21 1.00 .89 L |
| 1 83.0 75.0 .60 - .00 - .60 .00 .00 .19 .00 .95 M |
| 3 105.0 75.0 -.26 .34 .49 .60 -.48 2.14 .82 .21 .44 .63 R |
| 1 85.0 75.0 .53 - .00 - .53 .00 .00 .19 .00 .74 T |
| 7 76.6 75.0 .82 .45 1.10 1.19 1.10 5.29 .97 .21 1.08 1.37 W |
--------------------------------------------------------------------------------------------------------------------
SUBTOTAL RELIABILITY: inestimable
UMEAN=0 USCALE=1
Subtotal specification is: ISUBTOTAL=$S1W1 |
identifies the columns in the item label to be used for classifying the item by $S1W1 or whatever, using the column selection rules. |
EXTREME AND NON-EXTREME KID SCORES ALL SCORES ARE NON-EXTREME NON-EXTREME SCORES ONLY |
The items included in this summary table. Items with non-extreme scores (omits items with 0% and 100% success rates) |
ITEM COUNT |
count of items. "ITEM" is the name assigned with ITEM= |
MEAN SCORE |
weighted average item score by the persons |
MEAN COUNT |
weighted average of the count of responses by the persons |
MEAN MEASURE |
average measure of items |
S.E. MEAN |
standard error of the average measure of items. If only one item, then the S.E. of the item estimate |
P.SD |
population standard deviation of the item measures. |
S.SD |
sample standard deviation of the item measures. |
MEDIAN |
the measure of the middle item |
REAL/MODEL SEPARATION |
the separation coefficient: the "true" adjusted standard deviation / root-mean-square measurement error of the items (REALSE= inflated for misfit). |
REAL/MODEL RELIABILITY |
the item measure reproducibility = ("True" item measure variance / Observed variance) = Separation ² / (1 + Separation ²) |
RMSE |
Statistical average of the standard errors of the measures |
TRUE SD |
Observed population S.D. adjusted for measurement error |
MEAN OUTFIT |
Average outfit mean-square for the group. Expectation near 1.0 |
ITEM CODE |
the classification code in the item label. The first line, "*", is the total for all items. The remaining codes are those in the item columns specified by $S1W1 or whatever, using the column selection rules. |
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 inestimable = some subtotal counts are too small to estimate Reliability |
UMEAN=0 USCALE=1 |
Current user-scaling |
------------------------------------------------
| ITEM MEAN DIFFERENCE Welch-2sided |
| CODE CODE MEASURE S.E. t d.f. Prob. |
|----------------------------------------------|
| 0 1 -9.06 .57 -15.95 10 .000 |
| 0 2 -9.72 .87 -11.14 10 .000 |
| 0 4 -6.29 .94 -6.71 11 .000 |
| 1 2 -.66 .66 -1.00 2 .423 |
| 1 4 2.77 .75 3.71 3 .034 |
| 2 4 3.43 1.00 3.44 3 .041 |
------------------------------------------------
ITEM CODE |
the classification code in the item label for subtotal "1" |
CODE |
the classification code in the item 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. |
Welch2-sided |
2-sided t-test using Welch's adaptation of Student's t-test. |
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 |
|-------------------------------------------------------------|
| @TOPIC 1.70 1.00 1.70 1.89 .1761 |
| Error 26.91 30.00 .90 |
| Total 28.61 31.00 .92 |
|-------------------------------------------------------------|
| Fixed-Effects Chi-square: 1.7026 with 1 d.f., prob. .1919 |
---------------------------------------------------------------
Source |
the variance component. |
@TYPE (the specified ISUBTOTAL= classification) |
the variation of the subtotal mean measures around the grand mean. |
Error |
Error is the part of the total variation of the measures around their grand mean not explained by the @TYPE |
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 |
@TYPE Mean-Square / Error Mean-Square |
Prob>F |
the right-tail probability of the F-test value with (@TYPE, 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 item counts are too small and/or some variances are zero. |
Example: test the hypothesis "All the items have the same difficulty" with a "Fixed Effects" Chi-Square of Homogeneity:
ISUBTOTAL = $N ; each item is in its own group
then Table 27.1.
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