Difficulty: Intermediate | Prerequisites: Core Concepts study notes (Doc 1). Familiarity with ANOVA, chi-square tests, and basic experimental design.
This set of notes covers the two empirical studies from Perez's paper on social loafing and anchoring at Florida International University. Study One establishes the basic social loafing effect using a math task with three conditions (Individual, Group Total, Group Average). Study Two adds the anchoring heuristic as a second independent variable, creating a 2x2 factorial design. Together they test whether identifiability drives effort and whether a reference point (anchor) can shift both performance and self-perception. If you have not reviewed the core concepts (social loafing, anchoring, social facilitation), do that first.
Study One showed that participants in the individual condition solved more math problems than those in either group condition, confirming social loafing. Study Two added anchoring and found that a high anchor boosted performance, particularly for group-condition participants. Across both studies, everyone believed they outperformed the average, regardless of their actual score or condition.
One-way ANOVA
A statistical test that compares the means of three or more independent groups to determine whether at least one group mean differs significantly from the others.
Think of it as: "Are these groups meaningfully different, or could the differences be down to chance?"
Factorial ANOVA (2x2)
An extension of ANOVA that examines the effects of two or more independent variables simultaneously, including their interaction.
In simple terms, it lets you ask two questions at once and also check whether the answer to one depends on the other.
Tukey post hoc test (Tukey HSD)
A follow-up test run after a significant ANOVA to identify which specific group pairs differ from each other.
Think of it as: ANOVA tells you "something is different"; Tukey tells you "which ones."
Chi-square test
A statistical test that determines whether there is a significant association between two categorical variables.
In simple terms, it checks whether the pattern you see in a crosstab table is real or just noise.
Cramer's V
An effect size measure for chi-square tests, ranging from 0 (no association) to 1 (perfect association).
Think of it as the chi-square's way of saying how strong the relationship is, not just whether it exists.
Independent variable (IV)
The variable the researcher manipulates. In Study One: condition (Individual Total, Group Total, Group Average). In Study Two: condition (Individual vs Group) and anchor level (High vs Low).
Dependent variable (DV)
The variable the researcher measures. Here: Total Math Score and self-rating on "I completed more math problems than average" (1 to 7 scale).
High anchor / Low anchor
The reference point given to participants about how many problems a prior pilot group supposedly completed. High anchor = 40 problems. Low anchor = 20 problems.
Sample: 195 FIU students (44.6% male, 50.8% female, 0.5% non-binary, 4.1% other). Mean age 31.15 (SD = 12.45). Predominantly Latino/a (66.2%).
Design: Between-subjects, one-way with three conditions: Individual Total, Group Total, Group Average.
Task: Participants solved multiplication problems (1x1 through 42x42). They were told it was acceptable not to solve all of them.
Manipulation: Instructions varied by condition. Individual participants were told their personal score determined "best performance." Group participants were told their score would be pooled with two others (as either a total or an average).
Self-report measure: Six statements rated on a 1 (strongly disagree) to 7 (strongly agree) scale, including "I completed more math problems than average."
Manipulation check: Participants recalled which scoring method applied to their condition.
Total Math Score (DV1): Significant one-way ANOVA, F(2, 192) = 6.50, p < .001.
Individual condition: M = 28.68, SD = 11.18
Group Total condition: M = 22.32, SD = 11.00
Group Average condition: M = 22.98, SD = 10.98
Tukey post hoc: Individual > Group Total and Individual > Group Average. The two group conditions did not differ from each other.
"More math problems than average" (DV2): Non-significant ANOVA, F(2, 192) = 0.60, p = .55. All three conditions rated themselves similarly (around 5.7 out of 7).
Manipulation check: Chi-square significant, X²(4) = 240.15, p < .001. Most participants correctly recalled their condition (Individual: 99%, Group Total: 75%, Group Average: 79%). Cramer's V = .785.
The first hypothesis (individual condition outperforms group conditions) was supported.
The second hypothesis (all participants believe they outperformed the average) was also supported: ratings did not differ by condition, and all groups rated themselves above the midpoint.
Sample: 458 FIU students (41.5% male, 56.1% female). Mean age 26.42 (SD = 10.42). Predominantly Latino/a (62.2%).
Design: 2 x 2 between-subjects factorial. IV1: Loafing condition (Individual vs Group). IV2: Anchor level (High vs Low).
Four conditions: (1) Individual + High Anchor, (2) Group + High Anchor, (3) Individual + Low Anchor, (4) Group + Low Anchor.
Anchor manipulation: Participants were told a prior pilot study's participants completed either 40 problems (high anchor) or 20 problems (low anchor).
Task and self-report: Same as Study One.
Total Math Score (DV1), 2x2 ANOVA:
Significant main effect of loafing condition: F(1, 454) = 37.98, p < .001. Individual M = 29.87 vs Group M = 23.64.
Significant main effect of anchor: F(1, 454) = 20.08, p < .001. High anchor M = 29.00 vs Low anchor M = 24.51.
Significant interaction: F(1, 454) = 10.91, p = .001.
Simple effects (unpacking the interaction):
Individual condition: high anchor (M = 30.48) vs low anchor (M = 29.28), F(1, 227) = 0.63, p = .427. No significant difference.
Group condition: high anchor (M = 27.56) vs low anchor (M = 19.62), F(1, 227) = 33.53, p < .001. Large significant difference.
Low anchor: individual (M = 29.28) vs group (M = 19.62), F(1, 227) = 52.69, p < .001. Large significant difference.
High anchor: individual (M = 30.48) vs group (M = 27.56), F(1, 227) = 3.56, p = .061. Marginal, not significant at .05.
"More math problems than average" (DV2), 2x2 ANOVA:
No significant main effect of loafing condition: F(1, 454) = 0.04, p = .840.
No significant main effect of anchor: F(1, 454) = 0.04, p = .840.
No significant interaction: F(1, 454) = 0.16, p = .684.
All four cell means clustered around 4.3 to 4.4.
Manipulation check: Chi-square significant, X²(1) = 159.03, p < .001. Individual participants: 73.4% correctly recalled. Group participants: 85.2% correctly recalled.
Anchoring significantly affected actual performance but only in the group condition. Individual participants were already motivated by personal accountability, so the anchor added little.
Anchoring did not affect self-perception. Regardless of condition or anchor, everyone rated themselves similarly on the "better than average" item.
The interaction is the key finding: the combination of group context and low anchor produces the worst performance (M = 19.62), while individual context with either anchor produces the best (around M = 29 to 30).
Students often assume a significant ANOVA means every group differs from every other group. It does not. A significant omnibus F only tells you that at least one pair differs. You need the post hoc test (here, Tukey) to identify which pairs.
A common error is reading the interaction result in Study Two as "anchoring always matters." The simple effects show it mattered only in the group condition, not the individual condition. The interaction is precisely about that difference.
Students sometimes think a non-significant result on the "better than average" DV means the measure failed. It did not fail. The consistent ratings across conditions are themselves a finding: self-perception of effort is remarkably stable regardless of actual effort or experimental manipulation.
Confusing p values with effect sizes is another frequent mistake. A result can be statistically significant (low p) with a modest effect size, or vice versa. The paper reports F values and means, so focus on the size of the mean differences alongside the p values.
⚠️ Know the specific F values and p values for the main effects and interaction in Study Two. The loafing main effect (F = 37.98), anchor main effect (F = 20.08) and interaction (F = 10.91) are the headline statistics.
⚠️ Be ready to interpret the interaction: why did anchoring boost group performance but not individual performance? The answer involves the floor/ceiling of motivation. Individual participants were already near their maximum effort.
⚠️ The manipulation check results matter. They confirm internal validity. If participants had not recalled their condition correctly, the study's conclusions would be weaker. Know that chi-square was used for this and why (two categorical variables).
⚠️ The "better than average" finding is null across both studies. A question testing your ability to explain a non-significant result is very likely. The explanation: self-serving bias operates independently of actual performance and is resistant to experimental manipulation.
Q: In Study One, what were the three experimental conditions and what was the independent variable?
A: The three conditions were Individual Total, Group Total, and Group Average. The independent variable was the type of scoring condition participants were assigned to.
Q: What was the mean Total Math Score for the Individual condition in Study One, and how did it compare to the group conditions?
A: The Individual condition mean was 28.68 (SD = 11.18). Both group conditions scored lower: Group Total M = 22.32, Group Average M = 22.98. The difference was significant, F(2, 192) = 6.50, p < .001.
Q: Why was a Tukey post hoc test needed after the Study One ANOVA?
A: Because the ANOVA only tells you that at least one group differs. The Tukey test identifies which specific pairs of groups are significantly different from each other.
Q: In Study Two, describe the 2x2 factorial design. What are the two IVs and their levels?
A: IV1: Loafing condition (Individual vs Group). IV2: Anchor level (High, told prior participants completed 40 problems, vs Low, told they completed 20). This produces four cells: Individual/High, Individual/Low, Group/High, Group/Low.
Q: Explain the significant interaction found in Study Two for Total Math Score. What does it mean?
A: The interaction (F(1, 454) = 10.91, p = .001) means the effect of anchoring depended on the loafing condition. Specifically, anchoring had a large effect in the group condition (high anchor M = 27.56 vs low anchor M = 19.62, p < .001) but no significant effect in the individual condition (M = 30.48 vs 29.28, p = .427).
Q: Did anchoring affect participants' self-rated belief that they completed more problems than average? Explain.
A: No. Neither the loafing condition, the anchor, nor their interaction produced significant effects on this measure. All cell means were around 4.3 to 4.4 out of 7. Self-perception of relative effort was stable across all conditions.
Q: What was the purpose of the manipulation check, and what statistical test was used to analyse it?
A: The manipulation check verified that participants understood which scoring condition they were in. A chi-square test was used because both variables (assigned condition and recalled condition) are categorical. In both studies the chi-square was significant (p < .001), confirming participants noticed the manipulation.
Q: Name one confounding variable the researchers identified and explain how it could affect results.
A: Participants' pre-existing moral and social cognitive stance. Even though participants were randomly assigned, their personal beliefs about effort and fairness in groups were not measured. Someone who strongly values pulling their weight might resist loafing regardless of condition, which could reduce the observed effect size.
Social loafing, anchoring heuristic, anchoring and adjustment, one-way ANOVA, factorial ANOVA, 2x2 design, Tukey HSD, chi-square test, Cramer's V, manipulation check, attention check, between-subjects design, independent variable, dependent variable, main effect, interaction effect, simple effects, self-serving bias, better-than-average effect, identifiability, group dynamics, motivation, PSY II, Florida International University, Perez study, Epley and Gilovich, Griffith et al., Guerin, Hilkenmeier, Mihelic and Culiberg