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January 2012 Volume 15 Number 1 - Educational Technology ...

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2 .00 .05<br />

3 .02 .10<br />

1 .60 .40<br />

ECI 4 Z 2<br />

3<br />

.62<br />

.28<br />

.41<br />

.37<br />

2 6278.41*** .13 Both>High>Low<br />

INFIT Z<br />

1<br />

2<br />

3<br />

.00<br />

.00<br />

.00<br />

.02<br />

.01<br />

.01<br />

2<br />

1<br />

4.9<br />

.00 Both>High)>Low<br />

1 .64 .39<br />

OUTFIT Z 2 .73 .38 2 12214.40*** .23 Both>High)>Low<br />

3 .25 .35<br />

Note: a “spuriously high” aberrances, b “both spuriously high and low” aberrances, and c “spuriously low” aberrances.<br />

***p < .001.<br />

Regarding the condition of aberrant severity, Table 3 shows a summary of the results of a one-way MANOVA for<br />

the indices under the AS condition (Wilk’s Lambda = .604, p < .001, 2<br />

= .223). The NCI and ECI4z indices had<br />

large effect sizes (partial 2<br />

= .34, and .12, respectively). This may indicate that these two indices were more<br />

influenced by different levels of aberrant severity than other indices. Even though ECI2z and INFITz exhibited the<br />

lowest effect sizes of all indices, their detection rates were very low. This does not make much sense. On the other<br />

hand, the BW indices exhibited high detection rates (.95, .92, and .89 for different levels of aberrance severity,<br />

respectively) but low effect size (partial 2<br />

= .01). This indicates that the differences in detection rates among levels<br />

of aberrant sensitivity did not contain much practical meaning; furthermore, it reveals the strong detection power and<br />

stability of the BW indices across different levels of aberrant severity.<br />

Table 3. One-way MANOVA for the aberrant severity (AS) condition (N = 81,000)<br />

Index AS Mean SD df F partial 2<br />

Comparisons<br />

1<br />

SCI<br />

a .90 .23<br />

2 2 2822.87*** .07 30% >20% >10%<br />

b .98 .10<br />

3 c .99 .06<br />

1 .83 .30<br />

MCI 2 .95 .17 2 3271.02*** .07 30% >20% >10%<br />

3 .97 .13<br />

1 .32 .37<br />

NCI 2 .70 .36 2 20917.06*** .34 30% >20% >10%<br />

3 .89 .24<br />

1 .95 .16<br />

Wc&Bs 2 .99 .03 2 1990.97*** .05 30% >20% >10%<br />

3 .99 .03<br />

1 .95 .16<br />

BW 2 .92 .21 2 5<strong>15</strong>.97*** .01 10% >20% >30%<br />

3 .89 .26<br />

l z<br />

1<br />

2<br />

3<br />

.49<br />

.70<br />

.76<br />

.42<br />

.39<br />

.37<br />

2 3416.95*** .08 30% >20% >10%<br />

ECI 2 Z<br />

1<br />

2<br />

3<br />

.01<br />

.01<br />

.01<br />

.07<br />

.06<br />

.07<br />

2<br />

3.85<br />

.00 30% >20% >10%<br />

1 .30 .37<br />

ECI 4 Z 2<br />

3<br />

.56<br />

.65<br />

.41<br />

.41<br />

2 5782.52*** .12 30% >20% >10%<br />

1 .00 .00<br />

INFIT Z 2<br />

3<br />

.00<br />

.00<br />

.00<br />

.00<br />

2 22.84*** .00 30% >20% >10%<br />

OUTFIT 1 .41 .41 2 1987.38*** .05 30% >20% >10%<br />

Z<br />

34

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