Final answer:
When conducting a one-way ANOVA, the larger the between-treatment variability is when compared to the within-treatment variability, the higher the value of FDATA will tend to be.
Step-by-step explanation:
In Analysis of Variance (ANOVA), FDATA (F-ratio) is calculated by dividing the variance between treatments (σ²_B) by the variance within treatments (σ²_W). A higher FDATA value signifies greater differences among group means compared to differences within individual groups. Mathematically, FDATA = σ²_B / σ²_W.
When the between-treatment variability (σ²_B) increases in relation to within-treatment variability (σ²_W), the FDATA value becomes larger. This occurs because a greater difference among the treatment means contributes to a larger numerator in the F-ratio formula, resulting in a higher FDATA value. Conversely, if the within-treatment variability dominates (i.e., larger than the between-treatment variability), the F-ratio becomes smaller.
Understanding this relationship is crucial in interpreting the F-ratio in ANOVA. A larger F-ratio suggests a higher likelihood that the treatment means are significantly different, indicating a more substantial effect of the independent variable. Conversely, a smaller F-ratio implies less evidence for treatment differences and suggests the independent variable may not have a significant effect.