Lecture 8 – Comparing more than two means (Between-Groups)

 One-Way Between-Subjects ANOVA

-              Used to compare the means of more than two independent groups

-              To determine if there are statistically significant difference group means

Independent Variable (IV)

-              Categorical

-              3 or more levels

Dependent Variable (DV)

-              Continuous

o   Interval or ratio scale

Sum of Squares (SS)

Group SS

-              Measures the variance between group means and the overall mean

Residuals SS

-              Measures the variance within each group

o   Individual scores from their group mean

Degrees of Freedom (df)

Between-groups

-              k – 1

o   k = number of groups

Within-groups

-              N – k

o   N = total number of observations

Assumptions of ANOVA

Normality

-              Residuals should be normally distributed

Homogeneity of Variance

-              Variances among the groups should be

-              approximately equal

o   Tested using Levene’s test

Independence

-              Observations must be independent of one another

Statistical Analysis

ANOVA results

-              Example: caffeine levels significantly affected attention performance

o   

-     Effect size:  indicates a large effect size

Post-Hoc Test

-              Conducted to determine which specific groups differ

Post-Hoc Comparison

-              Control for Type 1 error when making multiple comparisons

o   Tukey

o   Bonferroni

Methods

-              Adjust p-values using techniques like Tukeys HSD or Bonferroni correlation

Results Interpretation

Attention Scores

-              No caffeine: M = 71.56, SD = 5.32

-              Low Caffeine: M = 74.56, SD = 5.32

-              High Caffeine: M = 81.00, SD = 5.34

Conclusion

-              Higher caffeine levels correlate with better attention performance

Practical Applications

-              Understanding the impact of substances (like caffeine) on cognitive functions

-              Designing experiments that require comparison of multiple groups