A student believes that there is an inverse relationship between sugar consumption and test scores. To test this hypothesis, he recruits several people to eat sugar, wait one hour, and take a short aptitude test afterwards. The student will compile the participants' sugar intake levels and test scores. How should the student conduct the experiment?

A single round of testing where each participant consumes a different level of sugar enables correlation analysis between independent variable (sugar intake) and dependent variable (test scores) while controlling for individual differences through random assignment.

Testing multiple sugar dosage levels across participants in one experimental session allows statistical evaluation of the hypothesized inverse relationship through regression analysis or correlation coefficients, with randomization minimizing confounding variables related to individual cognitive abilities or test-taking skills.

A) One round of testing, where each participant consumes a different level of sugar

This design creates variation in the independent variable (sugar consumption) necessary for detecting relationships with the dependent variable (test scores). By randomly assigning participants to different sugar dosages (e.g., 0g, 25g, 50g, 75g), the researcher establishes multiple data points along the sugar intake spectrum. Statistical analysis (Pearson correlation or linear regression) can then determine whether test scores decrease as sugar intake increases—testing the inverse relationship hypothesis directly. Random assignment helps distribute confounding variables (baseline cognitive ability, sleep quality, stress levels) evenly across dosage groups, while a single testing session minimizes practice effects or temporal variables that could distort results across multiple sessions. Control variables (testing environment, time of day, test version) remain constant across all participants.

B) Two rounds of testing: The first, where each participant consumes a different level of sugar, and the second, where each participant consumes the same level as they did in Round 1

Repeating identical conditions provides test-retest reliability data but adds no new information about the sugar-score relationship. Since sugar levels don't vary between rounds for any participant, no additional correlation data emerges—only measurement consistency assessment. This design wastes resources and introduces unnecessary complications: practice effects will likely elevate Round 2 scores independent of sugar consumption, creating confounding that obscures the true sugar-score relationship. If the hypothesis concerns acute sugar effects, repeated exposure might induce tolerance or sensitization, further complicating interpretation. Replication with identical conditions doesn't strengthen causal inference for dose-response relationships.

C) Two rounds of testing: The first, where each participant consumes the same level of sugar as each other, and the second, where each participant consumes the same level of sugar as each other but at higher levels than in Round 1

This design compares only two sugar levels (low vs. high) across the entire group but fails to establish individual dose-response relationships. All participants experience identical sugar exposure within each round, preventing correlation analysis at the individual level. Round 1 provides a single data point (one sugar level → group average score); Round 2 provides another single data point (different sugar level → new group average). While this allows comparison of two group means (via t-test), it cannot establish a continuous inverse relationship—only a binary difference. More critically, practice effects will almost certainly elevate Round 2 scores regardless of sugar level, creating a confound where improved performance might mask or reverse the expected sugar effect. Without counterbalancing (some participants receiving high sugar first), practice effects systematically bias results.

D) One round of testing, where each participant consumes the same level of sugar

Uniform sugar exposure eliminates variation in the independent variable, making relationship detection impossible. With identical sugar intake across all participants, any score variation reflects individual differences (intelligence, test anxiety, prior knowledge) rather than sugar effects. Correlation requires variation in both variables; without sugar dosage variation, the correlation coefficient becomes mathematically undefined (division by zero in standard deviation terms). This design might test whether that specific sugar level affects scores compared to a separate control group, but cannot evaluate the hypothesized inverse relationship across a dosage spectrum—only a binary comparison against an unstated baseline.

Conclusion:

Testing a dose-response hypothesis requires systematic variation in the independent variable across experimental units. Option A provides the necessary sugar dosage variation within a single controlled session, enabling direct correlation analysis while minimizing confounds from practice effects, temporal changes, or repeated exposure complications. Random assignment distributes individual differences evenly across dosage levels, allowing statistical isolation of sugar's effect. Options B and D fail to provide adequate independent variable variation, while option C introduces uncontrolled practice effects that systematically bias results. For initial hypothesis testing of an inverse sugar-score relationship, a single-session, multiple-dosage design (option A) represents the most efficient, statistically valid approach—though ideal methodology would include a true control group (zero sugar) and potentially counterbalanced repeated measures for stronger causal inference in follow-up studies.