How to randomly select a plausible value

Chong Ho Yu, Ph.D.s



It is a common practice for large-scale assessments to report several test scores for every student (e.g. Trend for International Math and Science Study, Programme for International Student Assessment). Because it takes too long for every student to take a comprehensive exam, the test designer utilizes computerized adaptive testing (CAT) to present different testlets (item clusters) to different students. Afterwards, imputation methods are employed to estimate the propensity score for each student. Needless to say, any estimation results in uncertainty, and therefore these test scores are known as plausible values. What can we do in data analysis when every participant has multiple test scores?



There are different approaches to analyze these PVs. One way is to randomly select a single score out of 5 to 10 PVs. This selection process, which consists of three steps, can be implemented in Excel.

1. Use the function RANDBETWEEN(1, 5) to select a number within the range of the plausible values. In this example the range is between 1 and 5.

2. Use the function CHOOSE(the number selected by RANDBETWEEN, the range of five scores) to select a test score.

3. Grab the corner of the two cells, and then drag them down to populate the rest of the two columns.

Alternatively, you can copy the functions, select the rest of the cells by holding down the shift key while placing the cursor at the start and the end, and the paste the functions.

4. However, in Excel whenever any update is made, all functions would automatically re-calculate the values. As shown in the preceding graphs, the numbers in F2 and G2 keep changing because any new action result in new numbers. In order to fix the chosen score, one must copy Column G and paste the numbers in another column as values. By doing so the numbers are fixed and the column that contains functions can be removed.

 Last Updated: August 2016



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