P/S 01 · Arousal, anxiety and research design
Pressure and Performance
Read a randomized experiment and a survey on arousal, sleep and anxiety.
Passage
Psychologists use the word arousal for the overall level of physiological and mental activation of a person, from drowsy and relaxed to alert and agitated. Arousal rises with sympathetic nervous system activity and can be changed by the surroundings, for example through noise, time pressure or the chance of a penalty. Researchers wanted to know how arousal affects performance, and whether the answer depends on how hard the task is.
Part 1. Sixty university students were recruited with flyers and randomly assigned, 20 per group, to one of three conditions. In the low-arousal condition, participants worked in a quiet, dimly lit room with slow music. In the moderate-arousal condition, they worked in a normal classroom. In the high-arousal condition, they worked with loud, unpredictable noise, a visible countdown timer and a small cash penalty for each error. Every participant then completed an easy task (simple word matching) and a hard task (novel logic puzzles). Heart rate was measured as a check on the manipulation. Table 1 shows the group means.
Table 1. Group means for each arousal condition (n = 20 per group).
| Condition | Heart rate (bpm) | Easy task (% correct) | Hard task (% correct) |
|---|---|---|---|
| Low arousal | 68 | 55 | 50 |
| Moderate arousal | 76 | 75 | 80 |
| High arousal | 92 | 85 | 55 |
Part 2. The researchers also wondered whether everyday sleep habits are related to anxiety. They sent an online survey to 200 students at the same university. Students reported their average nightly sleep and completed a 20-item trait anxiety scale, on which a higher score means greater anxiety. Across all 200 students, the correlation between nightly sleep and anxiety score was r = −0.45. Table 2 shows the mean anxiety score for students grouped by nightly sleep.
Table 2. Mean anxiety score by average nightly sleep (n = 200).
| Nightly sleep | Students | Mean anxiety score |
|---|---|---|
| Under 6 hours | 40 | 52 |
| 6 to 7 hours | 60 | 46 |
| 7 to 8 hours | 70 | 41 |
| Over 8 hours | 30 | 38 |
Questions
Question 1 of 6
The researchers conclude that performance on the hard task is best at moderate arousal, while performance on the easy task is best at high arousal. Which interpretation of the high-arousal group’s results is most consistent with this conclusion?
The easy-task result is the highest of the three conditions, so the data show no general impairment. The effect depends on task difficulty.
Performance changes systematically with arousal on both tasks, and the heart rates confirm the groups differed in arousal. The data do not suggest that arousal has no effect.
Random assignment makes the groups similar in ability on average. A group difference in ability would not explain why the high-arousal group did well on one task and poorly on the other.
Why the answer is what it is
This is the pattern predicted by the Yerkes–Dodson relationship: performance follows an inverted U with arousal, and the peak sits at a lower level of arousal for hard tasks than for easy ones. The high-arousal group is past its peak on the hard task (55%) but still near its peak on the easy task (85%).
Review: Emotion, Stress, and Motivation
Question 2 of 6
In Part 1, which statement correctly identifies the variables?
These are reversed. The researchers assigned the arousal condition, and percent correct is the outcome they measured.
Heart rate was measured as a check that the manipulation worked. It was not assigned by the researchers.
Sleep was not measured in Part 1, and the cash penalty was only one of several features of the high-arousal condition.
Why the answer is what it is
The independent variable is what the researchers manipulate (the arousal condition), and the dependent variable is what they measure to see the effect (percent correct). Heart rate is a manipulation check that confirms the groups really did differ in arousal.
Review: Social Structure, Inequality, Health, & Research Methods
Question 3 of 6
Why was it important that participants in Part 1 were randomly assigned to the three conditions?
Random assignment is about how participants are placed in groups. Generalizing to other students depends on how the sample was recruited, not on assignment.
The effect on heart rate comes from the manipulation, which the researchers checked separately. Random assignment does not guarantee anything about an individual’s response.
The comparison between conditions is the whole design. Random assignment makes the comparison fairer, not unnecessary.
Why the answer is what it is
Random assignment makes the groups roughly equivalent before the manipulation, on both measured and unmeasured characteristics. Any difference that appears afterward is then more plausibly caused by the manipulation than by pre-existing differences between the people.
Review: Social Structure, Inequality, Health, & Research Methods
Question 4 of 6
Which conclusion is best supported by the Part 2 data?
The fraction of variation explained is r², which is about 0.20, or 20%. The value r = −0.45 is the strength and direction of the relationship.
A correlation does not show which variable, if either, causes the other. This was a survey, and the researchers did not control sleep.
This is a possible explanation, but the data cannot tell it apart from the reverse. It is not supported more than the opposite claim.
Why the answer is what it is
The negative correlation (r = −0.45) and the pattern across the four groups in Table 2 show an association: less sleep goes with higher anxiety. Direction of cause cannot be read from a correlation, and r² ≈ 0.20 means sleep accounts for about a fifth of the variation in anxiety scores.
Review: Social Structure, Inequality, Health, & Research Methods
Question 5 of 6
Which of the following is an example of a confounding variable that could explain the Part 2 correlation without sleep affecting anxiety, or the reverse?
This is a case where anxiety causes poor sleep, which is reverse causation. A confound is a third variable that affects both.
This would add some noise to the measurement, but it would not create a relationship between sleep and anxiety.
A shorter scale could be less precise, but it does not provide a third variable that links sleep and anxiety.
Why the answer is what it is
A confound is a third variable that influences both of the measured variables and can produce a correlation between them. A heavy workload could reduce sleep and raise anxiety at the same time, so the two would be correlated even if neither caused the other.
Review: Social Structure, Inequality, Health, & Research Methods
Question 6 of 6
Which new study would best test whether limited sleep causes higher anxiety?
A larger sample makes the estimate of the correlation more precise, but it is still a survey and cannot show the direction of cause.
Beliefs about cause are not evidence of cause, and the answers are open to bias.
This is another comparison of groups that formed on their own, so the same confounds could explain it.
Why the answer is what it is
To test a causal claim, the researchers need to manipulate the cause and assign it at random, as they did with arousal in Part 1. Measuring anxiety afterward in a restricted-sleep group and a normal-sleep group would let differences be attributed to sleep rather than to pre-existing differences. The restriction would need to be short and safe, and approved by an ethics board.
Review: Social Structure, Inequality, Health, & Research Methods · Emotion, Stress, and Motivation