Key Terms
One-way ANOVA
Tests whether the means of three or more groups are equal, using a single categorical factor to define the groups.
Written as
Mu1 = mu2 = mu3 = ... = muk
Ha
At least two group means are NOT equal. NOT "all means are different" — just one pair being different is enough.
Notation
F ~ F(df_numerator, df_denominator) Example: F ~ F(4, 10) means df_num = 4, df_denom = 10.
Note
Df_numerator = n1 - 1; df_denominator = n2 - 1. This is different from ANOVA where df uses k (number of groups).
Also called
Variation due to error, unexplained variation, pooled variance. This is the average of the sample variances across all g
Relationship
SS_within = SS_total - SS_between
When group sizes are equal (balanced design)
F = (n * s_xbar^2) / s_pooled^2
Conclusion
No sufficient evidence that mean grades differ among sororities.
Second major use of the F-distribution
Comparing two population variances directly; not means.
When to use it
You want to know if two groups have the same spread, not the same average. Examples: two instructors grading the same ex
Distribution
F ~ F(29, 29). p-value = P(F < 0.5818) = 0.0753.
F-statistic (ANOVA)
F = MS_between / MS_within
Mean of F-distribution
Mu = df_denom / (df_denom - 1)