Winsteps sets the zero point (local origin) at the mean item difficulty (including extreme items if UEXTREME=Yes). The unit of measurement is the logit. Changing the zero point and transforming logits into other units can be done with UIMEAN=, UPMEAN=, USCALE=. These transformed measurements can be more meaningful for particular applications, see Chapter 8 of BTD. Anchor values are treated according to UASCALE=
Table 20.1 suggests values for UIMEAN= and USCALE= which produce a more friendly range of measures.
The USCALE= Calculator in the Help menu can do many of the computations in these examples:
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=)
we observe the (current high) and (current low). We want (desired high) and (desired low) then
new USCALE = (current USCALE=) *(desired high-desired low)) / (current high-current low)
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 UIMEAN=, so the current values are USCALE=1, UIMEAN=0.
Therefore,
"wanted low" person measure = 0
"wanted high" person measure = 100
"wanted range" = "wanted high" - "wanted low" = 100 - 0 = 100
"current low" person measure = -4.53
"current high" person measure = 5.72
"current range" = "current high" - "current low" = 5.72 - -4.53 = 10.25
USCALE= (wanted range) / (current range) = 100 / 10.25 = 9.76
UIMEAN= ( 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
Double checking, when previous values are UIMEAN=0, USCALE=1:
low value = (current low)*(USCALE=) + (UIMEAN=) = (-4.53 * 9.76) + 44.20 = -0.01 = 0
high value = (current high)*(USCALE=) + (UIMEAN=) = (5.72 * 9.76) + 44.20 = 100.02 - 100
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 are USCALE=2, UIMEAN=1.5
Therefore,
"wanted low" person measure = 0
"wanted high" person measure = 100
"wanted range" = "wanted high" - "wanted low" = 100 - 0 = 100
"current low" person measure = -4.53
"current high" person measure = 5.72
"current range" = "current high" - "current low" = 5.72 - -4.53 = 10.25
"current UIMEAN" = 1.5
"current USCALE" = 2
USCALE= [(wanted range) / (current range)]/(current USCALE) = [100 / 10.25]/2 = 9.76/2 = 4.88
UIMEAN= ( wanted low ) - [(current low-current UIMEAN) * USCALE ] = 0 - [( -4.53-1.5) * 9.76] = 58.85
Required values are:
USCALE = 4.88
UIMEAN = 58.85
UDECIM = 0 to show no decimal places in report
Double checking is most easily done by looking at the new Table 20.
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 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
| P.SD 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
| P.SD 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
Example 8: Form 1 and Form 2 are obtained from an item bank. We rescale Form 1 and want to apply the same rescaling to Form 2.
Do the Form 1 analysis:
UASCALE= is the scaling of the item bank scale (1 if logits)
IAFILE= is the list of bank item difficulties for Form 1
No UIMEAN=, UPMEAN=, UMEAN= or USCALE= command.
We rescale Form 1 to have its own scale setting UIMEAN= and USCALE= with the scaling calculator.
Note down the values or list them with the Control Variable list from the Output Files menu.
In the Form 2 control file:
UASCALE= is the scaling of the item bank scale (1 if logits)
IAFILE= is the list of bank item difficulties for Form 2
No UIMEAN, UPMEAN or UMEAN command.
In the Form 2 control file, add these commands:
TFILE=*
; these are actioned after the analysis, at the beginning of the reporting
14.1 ; this will report the bank item anchor values as a check
3.1 ; summary statistics
UIMEAN= value from Form 1 ; the values used for the analysis are rescaled
USCALE= value from Form 1
14.1 ; rescaled items
3.1 ; summary statistics
18.1 ; rescaled persons
*
You can add these to an analysis of the Form 1 data to check that it works.
Do the analysis of Form 2.
