Question

In a one-way ANOVA, what is the minimum difference between means (for each group/level/condition/sample) required to conclude that there is a significant difference between a pair of groups/levels/conditions/samples?

Answer 1

In a one-way ANOVA, directly we can't determine thje minimum difference between means (for each group / level / condition / sample) but we can do it by comparing respective p - values. If we want to know the minimum differences, we need to estimate comfidence intervals. Confidence Intervals gives us better idea on minimum differences.

In comparing the significant effect, we need to compare p value with 0.05 (at 95% confidence level). For a hypothesis, of p value is greater than 0.05 then the groups are not significant. Similarly, we can do the comparison among various levels too.