# Exploring the Impact of Consensus Conditions on Confidence Ratings: A Comprehensive Statistical Analysis

In this statistical exploration, we delve into the effects of consensus conditions on participants' accuracy scores and confidence ratings when evaluating supporting secondary sources. The analysis employs a one-sample t-test, Levene's test for variance equality, one-way ANOVA, and post-hoc tests, providing valuable insights into the nuanced relationship between consensus conditions and statistical outcomes in the context of information evaluation.

## Problem Description:

The statistical analysis assignment aimed to explore the impact of consensus conditions on participants' accuracy scores and confidence ratings in a scenario where individuals evaluate the number of secondary sources supporting a conclusion. The analysis involved a one-sample t-test, Levene's test for variance equality, one-way ANOVA, and post-hoc tests.

### 1. One Sample T-Test for Accuracy Score:

A one-sample t-test assessed whether participants' accuracy scores in the false consensus group differed significantly from the chance level of 50%. The results indicated a rejection of the null hypothesis (t(99)=13.62, p<.001, d=1.362), suggesting a substantial difference with a large effect size.

Table 1: One Sample T-Test Results

t df p Cohen's d
SourceAccuracy 13.620 99 < .001 1.362

One Sample T-Test

Note. For the Student t-test, effect size is given by Cohen's d.

### 2. Assumption Check - Levene's Test for Variance Equality:

Levene's test was applied to examine if there was a significant difference in the variance of participants' confidence across consensus condition groups. Results indicated no significant difference in variance (F(2, 297)=1.28, p=.28), confirming the assumption of equality of variance.

Table 2: Levene's Test for Variance Equality

Assumption Checks

F df1 df2 p
1.283 2.000 297.000 0.279

### 3. Confidence Rating Visualization:

Figure 1: Error Bar Displaying the Mean and 95% Confidence Interval of Confidence Rating across Consensus Condition Group

### 4. One-Way ANOVA for Confidence Ratings:

A one-way ANOVA investigated whether there was a significant difference in average confidence ratings across consensus condition groups. The null hypothesis was rejected (F(2, 297) = 52.1, p<.001), indicating a significant difference.

Table 3: ANOVA Results

ANOVA - Confidence

Sum of Squares df
10125.780 2
28861.940 297

Note. Type III Sum of Squares

### 5. Effect Size:

The effect size (η²) was 0.26, indicating a medium effect.

### 6. Post-Hoc Tests:

Post-hoc tests using Holm’s correction revealed significant differences in average confidence ratings between various consensus condition groups. Notably, the false consensus group had higher ratings than the no consensus group, while there was no significant difference between false and true consensus groups.

Table 4: Post Hoc Comparisons

Post Hoc Comparisons - Condition

Mean Difference SE
No 10.830 1.394
True -2.580 1.394
True -13.410 1.394

Note. P-value adjusted for comparing a family of 3

## 7. Conclusion:

The analysis revealed that participants prioritized the number of supporting secondary sources, as seen in the higher confidence ratings for the false consensus group compared to the no consensus group. While there was no significant difference between false and true consensus groups, the confidence ratings of the false consensus group closely matched those of the true consensus group.