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I am designing a correlational study experiment to test children on their performance on a task at $t_1$ and then at $t_2$ a year later, specifically using the balance-scale paradigm (Siegler, 1981). I'm not sure which statistical tests will be appropriate to run.

I want to find out if the early use of a sophisticated decision rule at $t_1$ is predictive of children using even more sophisticated rules in $t_2$. Namely, is a child who can deploy a complex decision rule quicker than most of her peers at $t_1$ more likely to use even more complex decision rules at $t_2$? I will compare these results with the $t_1$ vs $t_2$ results of children who failed to deploy that more complicated decision rule at $t_1$. These two decision rules will be operationalised as non-continuous binary variables.

What kind of statistical testing would be most appropriate here?

References

Siegler, R. S. (1981). Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development, 46(2), 84

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Although you have two times of testing, you really just have two binary variables and you'd like to know if they are associated, there are no repeated measures here. You'd like to know if the value of one binary variable depends on the value of the other binary variable. I'll call them A,B and X,Y.

If there is no relationship between A,B and X,Y, then you expect the ratio of X:Y to be the same for A as it is for B (this is your null hypothesis). You can examine your data by building a 2x2 contingency table with cells AX, AY, BX, and BY.

You can test the null hypothesis described with a chi-square test for independence, or Fisher's exact test if the sample size is fairly small.

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  • $\begingroup$ Thank you, Bryan! $\endgroup$
    – Max Moser
    Jan 6, 2021 at 21:02
  • $\begingroup$ Out of curiosity, is a 2x3 contingency table similarly possible? $\endgroup$
    – Max Moser
    Jan 6, 2021 at 21:17
  • $\begingroup$ @MaxMoser Yes, but the analysis can get more complicated depending on your research question. I would recommend collaborating with a statistician or someone in your field who is comfortable with statistics. $\endgroup$
    – Bryan Krause ♦
    Jan 6, 2021 at 22:18
  • $\begingroup$ Do you have other information about the participants as well though? You might want to consider a logistic regression scenario where 'rule use at t1' is just one of the predictors, alongside other relevant things you also know like age $\endgroup$
    – steveLangsford
    Jan 8, 2021 at 1:36

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