Question

Explain the difference between the between-treatment variability and the within-treatment variability when performing a one-way ANOVA. Provide the equivalent formula that we use for both of these entities and thereafter provide your rationale for why they would create a proper metric for one-way ANOVA.

Answer 1

Between group variation is used in ANOVA (analysis of variance) to measure variation between separate groups of interest. Unlike within group variation, where the focus is on the differences between a population and its mean, between group variation is concerned with finding how the means of groups differ from each other.

"between variance" the variance among treatments, that is, how much of the variation in the response variable(s) is explained by your explanatory variable(s) ; and the "within variance" is the variance left unexplained (how much variation there is within treatments after removing the differences among them).

1-way between groups ANOVA :--

between treatments variability

Treatment/group effects - the treatment caused the differences

Individual difference effects - differences due to differences in individuals

Random (experimental) error - just what it sounds like, random error

within treatment variability

Individual difference effects

Random (experimental) error1-way within groups ANOVA

1-way within groups ANOVA :--

between treatments variability

Treatment/group effects - the treatment caused the differences

Random (experimental) error - just what it sounds like, random error

within treatment variability

Random (experimental) error

Source of 8 Sum of squares segrees of Variation Kreed on Within KI LE df - K-1 SW = 22.-x, 880- ; -3." Betcomes df = n-K 0 The Variation between the classes is due to allignable causes which can be detected and controlled by human endeavour Chereas the Karnation coithin the classes is due to chance causes cottich are beyond the control of human hard. The main objective of Calysis of variance technique is to if examine there is ditt erence signiticant between the in means vieco class inherent of the variability within the reperate classes.