- The ratio of two independent chi-square variables divided by their respective degrees of
freedom. If the population variances are equal, this simplifies to be the ratio of the
- Analysis of Variance (ANOVA)
- A technique used to test a hypothesis concerning the means of three or mor populations.
- One-Way Analysis of Variance
- Analysis of Variance when there is only one independent variable. The null hypothesis
will be that all population means are equal, the alternative hypothesis is that at least one
mean is different.
- Between Group Variation
- The variation due to the interaction between the samples, denoted SS(B) for Sum of
Squares Between groups. If the sample means are close to each other (and therefore
the Grand Mean) this will be small. There are k samples involved with one data value
for each sample (the sample mean), so there are k-1 degrees of freedom.
- Between Group Variance
- The variance due to the interaction between the samples, denoted MS(B) for Mean
Square Between groups. This is the between group variation divided by its degrees of
- Within Group Variation
- The variation due to differences within individual samples, denoted SS(W) for Sum of
Squares Within groups. Each sample is considered independently, no interaction
between samples is involved. The degrees of freedom is equal to the sum of the
individual degrees of freedom for each sample. Since each sample has degrees of
freedom equal to one less than their sample sizes, and there are k samples, the total
degrees of freedom is k less than the total sample size: df = N - k.
- Within Group Variance
- The variance due to the differences within individual samples, denoted MS(W) for Mean
Square Within groups. This is the within group variation divided by its degrees of
- Scheffe' Test
- A test used to find where the differences between means lie when the Analysis of
Variance indicates the means are not all equal. The Scheffe' test is generally used when
the sample sizes are different.
- Tukey Test
- A test used to find where the differences between the means lie when the Analysis of
Variance indicates the means are not all equal. The Tukey test is generally used when
the sample sizes are all the same.
- Two-Way Analysis of Variance
- An extension to the one-way analysis of variance. There are two independent variables.
There are three sets of hypothesis with the two-way ANOVA. The first null hypothesis
is that there is no interaction between the two factors. The second null hypothesis is
that the population means of the first factor are equal. The third null hypothesis is that
the population means of the second factor are equal.
- The two independent variables in a two-way ANOVA.
- Treatment Groups
- Groups formed by making all possible combinations of the two factors. For example, if
the first factor has 3 levels and the second factor has 2 levels, then there will be 3x2=6
different treatment groups.
- Interaction Effect
- The effect one factor has on the other factor
- Main Effect
- The effects of the independent variables.
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