﻿ Table 28.1 Person subtotal summaries on one line

Table 28.1 Person subtotal summaries on one line

(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

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|    KID    MEAN    S.E.                            MODEL      MODEL          |

|  COUNT  MEASURE   MEAN    P.SD    S.SD  MEDIAN  SEPARATION RELIABILITY CODE |

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

|     35    -.37     .38    2.22    2.25    -.26     1.87        .78     *    |

|     18    -.68     .47    1.93    1.98    -.26     1.61        .72     F    |

|     17    -.05     .61    2.45    2.53    -.26     2.04        .81     M    |

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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 MEASURE average measure of Persons S.E. MEAN standard error of the average measure of Persons P.SD population standard deviation of the Persons. 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) 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

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| 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?

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| 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-squared: .6565 with 1 d.f., prob. .4178   |

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 Source the variance component. @GENDER (the specified PSUBTOTAL= 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 @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.

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