Hi all,
I want to conduct a correlation analysis, to check whether changes in learning outcomes correlate with the number of lessons students attend. Learner outcomes are measured at baseline and endline, and the measurement is ordinal. To be specific, students get assessed and assigned to one of 5 learning categories (for example for literacy, this would be Beginner, Letter, Word, Sentence, or Paragraph). The number of lessons students attended is measured quantitatively.
Since we are interested in the changes in learning outcomes, I was initially planning to calculate a difference score between endline and baseline, and correlate that with the number of lessons attended. However, having discovered that learner outcomes are measured ordinally, this does not make any sense. What would be the best way to compute a correlation between changes in learner outcomes (between baseline and endline) and the number of lessons students attend?
Thank you in advance for your responses!
Best,
Sharon
To compute the correlation between ordinal progress in learner outcomes and attendance, you can use a rank correlation coefficient such as Spearman's rank correlation coefficient or Kendall's rank correlation coefficient. These methods take into account the ordinal nature of the data and can still provide a measure of the strength and direction of the relationship between the two variables.
To use Spearman's rank correlation coefficient, you would rank both the learning outcome categories and the attendance scores and then calculate the correlation coefficient using a formula. To use Kendall's rank correlation coefficient, you would count the number of times pairs of observations are in agreement or disagreement and use that to calculate the correlation coefficient.
Both methods are widely used in research and are appropriate for analyzing ordinal data. However, it is important to note that correlation does not imply causation, and other factors may be influencing the relationship between attendance and learning outcomes. As with any statistical analysis, careful interpretation and consideration of the context are critical.
Hi Ajit, thank you so much for your response! I appreciate it. In terms of the ordinal progress in learner outcomes, how should I calculate that?
Since I have both baseline and endline values for the learner outcomes, does it make any sense to calculate the absolute difference between them to estimate progress? It feels like it does not, because the data is ordinal, so the intervals between the different categories of learner outcomes are not the same.
Alternatively, would it make sense to correlate the endline scores only with the number of attended lessons? In this case, I would assume I would have to control for the baseline values, or is this not needed?
Please let me know how you think it would be best to estimate the progress in learner outcomes. Thank you so much in advance!
Dear Sharon,
When determining the measures of association, we can apply Spearman’s rho (a statistic gives the degree of association between two set of ordinal variable), Kendall’s Tau (a statistic gives the degree of association between one continuous and one ordinal variable) and a point biserial correlation (a statistic gives the degree of association between one continuous variable and one nominal, dichotomous variable) for non-parametric data and the Pearson product moment correlation (a statistic gives the degree of association between two set of interval or ratio variables) for parametric data.
For example, using Spearman rank order correlation the relationship between the results from two ratings scales or two different rank order positions of two variables can be determined. Using Pearson’s correlation we can find out the relation between two different test scores. Likewise a point biserial is useful for determining the association between gender – male and female and mathematic test scores.
It is important to note that correlation tests do not yield any important findings other than the strength and direction of a relationship that exists between two set of variables. Moving from correlation to causality which gives us some usable statistics to examine whether change in one variable is the cause of the change in other variable, we can reduce the effect of confounding variables that is very common in correlation studies.
You can refer the following link for further explanation.
https://journals.sagepub.com/doi/pdf/10.1177/8756479308317006#:~:text=If%20one%20variable%20is%20continuous,%2Dsub%2Db%2C%20%CF%84b%20.
Administer same test at the beginning (pre-test) and do same at the end (post-test) and find the difference between pre-test and post-test.
- Badges
- Science topic