Concept of ANOVA
F statistic
Named in honour of R A Fisher
The f statistic, also known as an f value, is a random variable that has an F distribution
The distribution of all possible values of the f statistic is called an F distribution, with v1 = n1 - 1 and v2 = n2 - 1 degrees of freedom
Analysis of variances (ANOVA)
One way ANOVA: A One-Way Analysis of Variance is a way to test the equality of three or more means at one time by using variances. Two way ANOVA: A Two-Way ANOVA is useful when we desire to compare the effect of multiple levels of two factors and we have multiple observations at each level.
Grand Mean
The grand mean of a set of samples is the total of all the data values divided by the sample size. It turns out that all that is necessary to find perform a one-way analysis of variance are the number of samples, the sample means, the sample variances, and the sample sizes.
Total Variation
The total variation is comprised the sum of the squares of the differences of each mean with the grand mean.
There is the between group variation and the within group variation. The whole idea behind the analysis of variance is to compare the ratio of between group variance to within group variance. Between Group Variation
The variation due to the interaction between the samples is denoted SS(B) for Sum of Squares Between groups. If the sample means are close to each other 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.
The variance due to the interaction between the samples is denoted MS(B) for Mean Square Between groups. This is the between group variation divided by its degrees of freedom.
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. Since each sample has degrees of
Named in honour of R A Fisher
The f statistic, also known as an f value, is a random variable that has an F distribution
The distribution of all possible values of the f statistic is called an F distribution, with v1 = n1 - 1 and v2 = n2 - 1 degrees of freedom
Analysis of variances (ANOVA)
One way ANOVA: A One-Way Analysis of Variance is a way to test the equality of three or more means at one time by using variances. Two way ANOVA: A Two-Way ANOVA is useful when we desire to compare the effect of multiple levels of two factors and we have multiple observations at each level.
Grand Mean
The grand mean of a set of samples is the total of all the data values divided by the sample size. It turns out that all that is necessary to find perform a one-way analysis of variance are the number of samples, the sample means, the sample variances, and the sample sizes.
Total Variation
The total variation is comprised the sum of the squares of the differences of each mean with the grand mean.
There is the between group variation and the within group variation. The whole idea behind the analysis of variance is to compare the ratio of between group variance to within group variance. Between Group Variation
The variation due to the interaction between the samples is denoted SS(B) for Sum of Squares Between groups. If the sample means are close to each other 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.
The variance due to the interaction between the samples is denoted MS(B) for Mean Square Between groups. This is the between group variation divided by its degrees of freedom.
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. Since each sample has degrees of