Question

9. Effect size and ANOVA

Amit Almor, a psychology researcher at the University of South Carolina, conducted a series of experiments on conversation and attention level. He found that subjects were four times more distracted while preparing to speak or speaking than when they were listening. This research has many implications, including those for the issue of using cell phones while driving.
You decide to explore this issue by having three different groups try tracking a fast-moving target on a computer screen. The first group is preparing to speak, the second group is speaking, and the third group is listening to a conversation.
After collecting the data, you analyze the data using an ANOVA. The results of your analysis are presented in the following ANOVA table.
ANOVA Table
Source of Variation
SS
df
MS
F
Between groups 5,403.35 2 2,701.68 9.48
Within groups 426,575.14 1,497 284.95
Total 431,978.49 1,499
These findings are significant at α = 0.01, which tells you that the difference is very unlikely to have occurred just by chance, but it does not tell you the size of the effect. A simple measure of the effect size is given by .
Based on the data given, the effect size is . (Round your answer to two decimal places)
The percentage of variability in the scores accounted for by the effect due to groups is .
ω2
is a less biased measure of the magnitude of effect. Both of these measures are considered r-family measures because they .
Calculate ω2
. ω2
is .
Using ω2
, the percentage of variability in the scores accounted for by the effect due to groups is .
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Answer 1

Effect size small (η²=0.01, ω²=0.011). Groups differ but effect is minimal. Only 1.25-1.37% of variability explained by group differences.

Effect Size Analysis:-

Effect Size:

• Eta squared (η²) = 0.01 (small effect)

Percentage of Variability Explained:

• Using η², only 1.25% of the total variability in scores can be attributed to the group differences.

ω²:

• A less biased measure, omega-squared (ω²) = 0.011, suggests a slightly larger effect.

Percentage of Variability Explained (using ω²):

• Based on ω², 1.37% of the variability can be attributed to the group differences.

r-Family Measures:

• Both η² and ω² are considered r-family measures because they quantify the relationship between the groups and the dependent variable.

Interpretation:

• While statistically significant, the effect size is small. This suggests that the differences in tracking performance between the groups are not substantial.

• ω² provides a slightly more accurate estimate of the effect size compared to η².

• The percentage of variability explained indicates that group differences account for only a small portion of the overall variability in tracking performance.

This information provides valuable insights into the magnitude and practical significance of the observed differences in tracking performance between the three groups.