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

-------------------------------------------------------------------------------

|    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    |

-------------------------------------------------------------------------------

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

 

------------------------------------------------

| 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-squared: .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

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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