Transforming logits into other units using UIMEAN=, UPMEAN=, USCALE=. These can be more meaningful for particular applications, see Chapter 8 of BTD. Anchor values are treated according to UASCALE=

 

 

Example 0: we observe the (current mean) and (current S.D.) of a set of measures. We want (desired mean) and (desired S.D.) then

new USCALE = (current USCALE=) *(desired S.D.) / (current S.D.)

new UIMEAN = desired mean - (current mean - current UIMEAN=)*(new USCALE=) / (current USCALE=)

 

Example 1: CHIPs are a useful transformation, in which 1 logit = 4.55 CHIPs. In this user-scaling system, standard errors tend to be about 1 CHIP in size. The recommended control variable settings are:

USCALE = 4.55

UIMEAN = 50

UDECIM = 1

MRANGE = 50

 

The probability structure of this relationship is:

 

Probability of Success

 Difference between Person Ability Measure and Item Difficulty Measure in CHIPs

.10 -10

.25 -5

.50 0

.75 5

.90 10

 

Example 2: WITs are one tenth the size of CHIPs, enabling the elimination of decimals from your output tables.

USCALE = 45.5

UIMEAN = 500

UDECIM = 0

MRANGE = 500

 

Example 3: You want the lowest reportable person measure to be 0 and the highest to be 100. Looking at Table 20, you see the extreme values are -4.53 and +5.72. You have not used USCALE= and UMEAN=, so USCALE=1, UMEAN=0.

 

USCALE= (wanted range) / (current range)

USCALE= (100 - 0)  / (5.72 - -4.53) = 100 / 10.25 = 9.76

UMEAN= ( wanted low ) - ( current low * USCALE= ) = 0 - ( -4.53 * 9.76 ) = 44.20

 

Required values are:

USCALE = 9.76

UIMEAN = 44.20

UDECIM = 0 to show no decimal places in report

 

Example 4: You want the lowest reportable person measure to be 0 and the highest to be 100. Looking at Table 20, you see the extreme values are -4.53 and +5.72. The current values in the output are USCALE=1 and UIMEAN=0.

 

USCALE= (previous USCALE=) * (wanted range) / (current range) = 1* (100 - 0)/ (5.72 - -4.53) = 1 * 100 / 10.25 = 9.76

UMEAN= (wanted low) - (current low - previous UMEAN=)*(wanted range)/(current range) = 0 - (-4.53 - 0)*100/10.25 = 44.20

UDECIM = 0 to show no decimal places in report

 

Double checking, when previous UMEAN=0, USCALE=1:

low value = (current low)*(USCALE=) + (UMEAN=) = (-4.53 * 9.76) + 44.20 = -0.01

high value = (current high)*(USCALE=) + (UMEAN=) = (5.72 * 9.76) + 44.20 = 100.02

 

Example 5: You want the lowest reportable person measure to be 100 and the highest to be 900. Looking at Table 20, you see the extreme values are -4.53 and +5.72. Looking at the second page of output, you see the current values are USCALE=1 and UMEAN=0.

 

USCALE= (previous USCALE=) * (wanted range: 900 - 100) / (reported range: 5.72 - -4.53) = 1 * 800 / 10.25 = 78.05

UMEAN= (wanted low) - (reported low - previous UMEAN=)*(wanted range)/(reported range) = 100 - (-4.53 - 0)*800/10.25 = 453.56

UDECIM = 0 to show no decimal places in report

 

Example 6: You want norm-referenced user-scaling, such that the person mean is 0.0, and the person sample standard deviation is 1.0.

 

In a standard analysis, set:

UDECIM=4

USCALE=1

UMEAN=0

 

Look at Table 18

 +------------------------------

 |ENTRY    RAW                  

 |NUMBER  SCORE  COUNT  MEASURE 

 |------------------------------

 | MEAN     6.7   14.0  -.3728  

 | S.D.     2.4     .0  2.2202  

 +------------------------------

 

Set (either in a new analysis, or using the "Specification" pull-down menu

USCALE = 1/person S.D. = 1/2.2202 = 0.4504

UMEAN = - person mean/person S.D. = - (-.3728)/2.2202 = 0.1679

Look at Table 18

 +------------------------------

 |ENTRY    RAW                  

 |NUMBER  SCORE  COUNT  MEASURE 

 |------------------------------

 | MEAN     6.7   14.0   .0000  

 | S.D.     2.4     .0  1.0000  

 +------------------------------

 

Example 7: You want to give your pass-fail point the value 400 and 100 to the lowest reported measure. Inspecting your output you see that the pass-fail point is at 1.5 logits, and that -3.3 logits is the lowest reported measure.

 Then 400-100 new units = 1.5 - (-3.3) logits, so

 USCALE = 300 / 4.8 = 62.5

 UMEAN = 400 - (1.5) * 62.5 = 306.25

 Then: 1.5 logits = 306.25 + 1.5*62.5 = 400

  -3.3 logits = 306.25 - 3.3*62.5 = 100