User-friendly rescaling

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 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=.

       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