SOLUTION: 1. In a study comparing individual performance with group performance, Laughlin, Zander, Knievel, and Tan (2003) found that groups consistently outperformed the best of the individ

Question 1191312: 1. In a study comparing individual performance with group performance, Laughlin, Zander, Knievel, and Tan (2003) found that groups consistently outperformed the best of the individuals. The task was a letters-to-numbers problem in which an arithmetic problem was presented substituting a letter in place of each digit. Participants had to determine which letters corresponded to each number. Three-person groups competed with individuals and scores were compared for the groups and the best of the individuals. The dependent variable was the number of trials needed to solve each problem.
1.1 what is used to present the average score
1.2 what is used to present the dispersion of scores
1.3 testing the significant differences of the groups
1.4 what degrees of freedom to be used by the researcher
1.5 if the result proved to be significant, what method to be used to get the effect size?

Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Let's break down these questions related to the Laughlin et al. (2003) study:
**1.1 What is used to present the average score?**
The average score is typically presented using the **mean**. In this context, it would be the mean number of trials needed to solve the problems for both the individual "best" performers and the three-person groups.
**1.2 What is used to present the dispersion of scores?**
Dispersion, or variability, is usually presented using the **standard deviation**. This would show how spread out the scores are around the mean for both groups. Other measures of dispersion include variance, range, and interquartile range, but standard deviation is the most common.
**1.3 Testing the significant differences of the groups:**
To test for statistically significant differences between the group means (groups vs. best individuals), the researchers would likely use a **t-test**. Since they are comparing two independent groups, it would be an *independent samples t-test* (also known as a *between-subjects t-test* or *two-sample t-test*).
**1.4 What degrees of freedom to be used by the researcher?**
The degrees of freedom (df) for an independent samples t-test is calculated as:
df = (n₁ - 1) + (n₂ - 1)
Where n₁ is the number of participants in group 1 (e.g., the number of three-person groups) and n₂ is the number of participants in group 2 (e.g., the number of individual "best" performers).
**1.5 If the result proved to be significant, what method to be used to get the effect size?**
If the t-test reveals a statistically significant difference, the researchers would then calculate an effect size to determine the practical significance of the difference. A common effect size measure for t-tests is **Cohen's d**.
Cohen's d is calculated as:
d = (M₁ - M₂) / Spooled
Where:
* M₁ and M₂ are the means of the two groups.
* Spooled is the pooled standard deviation, a weighted average of the standard deviations of the two groups. There are slightly different formulas for calculating Spooled, depending on whether the variances of the two groups are assumed to be equal.

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