Support for PROX Method

Worksheet Functions

Real Statistics Functions: The Real Statistics Resource Pack contains the following functions:

PROX_SUBJ(R1): returns a summary of the PROX method for the data in R1 (with headings) consisting of 4 columns: subject labels for each of the subjects in R1, corresponding ability parameter estimates, standard errors, and % correct scores.

PROX_ITEM(R1): returns a summary of the PROX method for the data in R1 (with headings) consisting of 4 columns: item labels for each of the items in R1, corresponding difficulty parameter estimates, standard errors, and % correct scores.

These functions are employed by the PROX Method option of the Rasch Item Response Analysis data analysis tool described in Real Statistics Support for Rasch Analysis. For Example 1 of Building a Rasch Model, the data analysis tool returns the output shown in Figure 1.

Figure 1 – Output from PROX option

Range AJ3:AM12 contains the array formula =PROX_SUBJ(A3:K12) based on the input in A3:K12 shown in Figure 1 of PROX Model Example. Range AO3:AR13 contains the formula =PROX_ITEM(A3:K12).

More Worksheet Functions

As observed in PROX Model Example, we can obtain the ability level for any subject based on their total score even if they didn’t take the test. The following two functions implement this capability.

Real Statistics Functions: The Real Statistics Resource Pack contains the following functions:

PROXX_SUBJ(R1, R2): returns a two-column array consisting of ability parameter estimates and standard errors corresponding to the subject scores in the column array R2 based on the PROX method for the data in R1 (w/o headings).

PROXX_ITEM(R1, R2): returns a two-column array consisting of difficulty parameter estimates and standard errors corresponding to the item scores in the column array R2 based on the PROX method for the data in R1 (w/o headings).

E.g, range AU4:AV12 of Figure 2 contains the worksheet array formula for subjects =PROXX_SUBJ(B4:K12,AT4:AT12). Range AY4:AZ11 contains the corresponding worksheet array formula for items =PROXX_ITEM(B4:K12,AX4:AX11). These formulas refer to the range B4:K12 shown in Figure 1 of PROX Model Example.

Figure 2 – PROXX_SUBJ and PROXX_ITEM functions

We see from the figure, for example, that a subject who obtains a score of 8 correct items out of 10 has an ability of 2.260354 (cell AU11). This is the same as subject B (cell AK5 of Figure 1). A subject who obtains a score of 3 correct items out of 10 has an ability of -1.38152 (cell AU6). This is so even though no subject had such a score in the original data.

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Wright, B. D. and Stone, M. H. (1979) Best test design. MESA Press: Chicago, IL
https://research.acer.edu.au/measurement/1/

Wright, B. D. and Masters, J. N. (1982) Rating scale analysis. MESA Press: Chicago, IL
https://research.acer.edu.au/measurement/2/