This is difficult in classical measurement approaches given the dependency on internal reliability (paradoxical) and baseline confounding (negative correlation).

IRT is the optimal approach for substantive indexing "gain scores" (See, Embretson & Poggio, 2011).

Hope this helps,

Matt

Good points by Matthew Kerry . Worth also looking at the Lord's paradox literature.

Hi,

You can use ANOVA (analyses of variance) for repeated measures in which you use your two scores (pre and post-test) as within-subjects variables (factor of the same score at two different moments) and number of minutes and number of words as covariates.

Thus, firstly you can confirm a significant gain (significant difference between the elements of your factor. E.g. here : score post>score pretest) by F value for factor and you potentially control that this gain depends on number of minutes and on number of words (by F values for factor*number of minutes or for factor*number of words). Here complete explanation: https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide.php

An example with R: https://www.r-bloggers.com/how-to-do-repeated-measures-anovas-in-r/

An example with SPSS: https://statistics.laerd.com/spss-tutorials/one-way-anova-repeated-measures-using-spss-statistics.php

Best

CH

With just two occasions (pre and post test) you may wish to look at my answer to this question

https://www.researchgate.net/post/Longitudinal_Mixed_Models_in_R_How_to_interpret_the_results

The effect of post-test gain can be analyzed using Po hoc comparison. Post hoc comparison are design to test each possible pair of means. There are five common multiple comparison tests you can use. These are; Fisher's LSD, Duncan's new multiple range test, Newman-Keuls, Tukey's HSD, and Scheffe's test