Do students who sleep less react more slowly?

In the week before our mock exams I slept badly, and in a hockey match that Saturday I was sure my reactions were slower than usual — I missed two interceptions I would normally make. I started wondering whether this was real or an excuse. Sleep is something every student in my year talks about, but usually as an opinion (“I function fine on five hours”), so I wanted to measure it.

The aim of this exploration is to find out whether there is a relationship between the number of hours students in my year slept the night before and their simple reaction time, and whether any relationship still holds once students who had caffeine that morning are considered separately.

I expected a negative relationship: less sleep, slower reactions. I also expected caffeine to be a problem for my analysis, because students who slept less might be more likely to drink coffee, which could hide the effect of sleep. Dealing with that possibility is a main part of this exploration.

Variables. \(h\) = hours of sleep the night before, self-reported to the nearest quarter of an hour; \(t\) = mean simple reaction time in milliseconds (ms), measured as described below; caffeine = whether the student had coffee, tea or an energy drink before the test that morning (yes/no).

Measuring reaction time. Every student used the same online reaction test on the same laptop and mouse in the library, between 8:30 and 9:00 on weekday mornings. The test shows a red screen that turns green after a random delay; the student clicks as soon as it turns green. Each student did one practice attempt and then five recorded attempts, and I used the mean of the five. Using one device matters because screens and mice add different delays; using the mean of five reduces the effect of one lucky or unlucky click.

Sample. My year group has 131 students. I asked every student in the four tutor groups whose tutor time fell on my free periods, which gave 48 students who agreed and gave consent (Appendix A shows the consent form). This is a convenience sample, not a random one, which I discuss in the conclusion. Around 40 is often suggested as a minimum for correlation to be meaningful, so 48 is adequate but not large.

Ethics. Participation was voluntary, no names were recorded (each student had a code), and I only asked about sleep and caffeine, not about health.

The scatter graph shows a downward trend: students who slept less tended to have slower reaction times. The points are quite spread out, so I expected a moderate rather than strong correlation. The caffeine group (triangles) seems to sit slightly lower, i.e. faster, at every amount of sleep.

Before fitting any line I measured the strength of the linear relationship. Pearson's product-moment correlation coefficient is \(r \approx −0.552\), a moderate negative linear correlation. Because \(h\) was self-reported and may not be precise, I also calculated Spearman's rank correlation coefficient, which only uses the order of the values: \(r_s \approx −0.556\). The two values are very close, which suggests the relationship is roughly linear and not caused by a few extreme values.

Since the relationship is reasonably linear, I used the least-squares regression line of \(t\) on \(h\):

\[ t \approx 341.0 −11.7h . \]

The gradient means that each extra hour of sleep is associated with a reaction time about 11.7 ms faster, on average. The intercept (about 341 ms at 0 hours of sleep) has no sensible meaning, because no one in the sample slept less than 5.00 hours; I would only use the line for \(4.5 \le h \le 9.5\). The residual plot (Figure 3) shows no curve or funnel shape, which supports using a straight line.

A difference of about 12 ms per hour sounds tiny, but it is about 5% of a typical reaction time. In hockey, a ball struck at 25 m s⁻¹ travels about \(25 \times 0.0117 \approx 0.29\) m in that time — so two hours less sleep could plausibly be the difference between an interception and a miss.

In my sample of 48 students there is a moderate negative relationship between sleep the night before and simple reaction time (\(r \approx −0.55\), \(r_s \approx −0.56\)): each extra hour of sleep is associated with reactions about 12 ms faster. Students who slept less than 7 hours were significantly slower than those who slept 7 or more (t-test and chi-squared test, both at the 5% level), and the relationship holds for students with and without caffeine that morning. So my slow reactions in the hockey match may not have been an excuse.

This does not prove that less sleep causes slower reactions. Students who sleep less might differ in other ways — for example, more screen time late at night or more stress before exams — and those could affect both. An experiment where the same students are tested after different amounts of sleep would be much stronger evidence.

The biggest weaknesses of my data are that sleep was self-reported (people tend to round and overestimate) and that my sample was a convenience sample from four tutor groups, which may not represent the whole year. If I repeated the study I would use sleep-tracking watches for a subset of students to check how accurate the self-reports are, and ask a random sample from the full year list. I would also like to test whether the effect is different for choice reaction time (deciding between two responses), which is closer to what happens in a real game.