Study Hours Matter, and Explain About a Quarter of the Difference

A real positive relationship, with two caveats that belong in any message to students.

To Course Leader

From Academic Analytics

Re Study hours and exam performance survey

Where this comes from

Chapter Chapter 170 · Pearson Correlation: Study Hours and Scores

Part Part XXVII · Capstone Projects: Statistical Testing

Dataset capstone-study-hours-and-scores.xlsx

Notebook View the analysis

Recommendation

Bottom line

Students who study more do score better, and the relationship is real rather than chance (correlation 0.48, n = 90). But hours explain only about 23% of the difference between students, so please avoid messaging that implies hours are the main lever. And because this is a survey rather than an experiment, we cannot say that studying more causes the higher scores.

What we found

Across 90 students, weekly study hours and final exam score move together positively. The correlation is 0.48, and we are 95 percent confident the true value lies between 0.31 and 0.63, comfortably away from zero. Squaring it gives the more useful figure: study hours account for roughly 23 percent of the variation in scores, leaving about three quarters explained by everything else, prior preparation, teaching, circumstances, and luck on the day.

Scatterplot of exam score against weekly study hours with an upward fitted line and one circled outlying student. — Figure 1. Each dot is a student. The line summarizes the upward trend. Note the circled student, who studied more than almost anyone and still scored near the bottom.

Stacked bar: study hours account for 23 percent of the variation between students and everything else for 77. — Figure 2. How much of the difference between students' exam scores is accounted for by study hours.

A caution about how much rests on one student

One student in the sample studied a great deal and scored poorly. That is a real person, not a data-entry error, so we have kept them in. It is worth knowing, though, that removing that single student would raise the correlation from 0.48 to 0.68. The headline number is therefore somewhat sensitive to one observation, which is a reason to describe the relationship as moderate rather than to quote the coefficient to two decimal places as though it were precise.

Two scatterplots showing the fitted line with all students and with the influential student removed. — Figure 3. The same students analyzed twice: with everyone on the left, and without that one student on the right. The line steepens noticeably.

What we cannot say

This was a survey taken at one point in time, so we cannot tell which way the arrow points. It is equally consistent with the data that studying raises scores, that students who find the material easy (and therefore score well) also find it pleasant to study more, or that something else such as prior preparation drives both. A message that says 'study five more hours to gain ten points' would be reading a cause into a pattern that cannot support one.

Suggested wording for students

Something like: students who put in more study hours tend to do better, though hours alone account for about a quarter of the difference in results, so how you study matters as much as how long. That is accurate, useful, and does not over-promise.

← Back to Chapter 170 📓 Companion notebook 📊 Download dataset

From Statistics, Data Science and AI: A Visual Handbook by John Fisher. Every statistic, table, and figure in this report is reproduced by the companion notebook.