# Minimum sample size in ANOVA

#### Miro

##### New Member
Dear all, my question is here: what is the minimum sample size in ANOVA?
I want to compare three groups consisting of 4-5 populations each. The individual populations are represented by arithmetic mean taken from 30+ individuals.
The results of ANOVA confirmed significant difference between these three groups of populations. Still, there is only 4, 4, and 5 data for the groups, so I want to be sure.

Thx for the help.

#### Karabiner

##### TS Contributor
I guess this is possible, but you cannot say much about (non-)violation of assumptions with just n(total)=12-15.
Kruskal-Wallis H-test would be a robust alternative, but with less statistical power.
You do not have the data from the individuals, I supppose?

With kind regards

Karabiner

#### Miro

##### New Member

No, I do have the data from the individuals of respective populations. Data corresponded to 80 loci. Values of population genetic index were averaged across loci for each of the populations and standard deviation was calculated. Then I wanted to compare these averages to see whether or not there is a difference between the population groups. According to one-way ANOVA, there was. But I think I should do some different ANOVA, with standard deviations ... because the mean values represent some variation. I am not sure in this. I do not know Kruskal-Wallis H-test.
I will consider.

Anyway, I am just asking, thx for trying : )

Last edited:

#### GretaGarbo

##### Human
my question is here: what is the minimum sample size in ANOVA?
The minimum sample size is 2 in one group and 1 in each of the other groups.

Here is an R coded example:

Code:
 aovdat <- data.frame(y = c(1.0, 1.1, 2, 3), group = c(1, 1, 2, 3))
> aovdat
y group
1 1.0     1
2 1.1     1
3 2.0     2
4 3.0     3
> anova(aov(y ~ group, data = aovdat ) )
Analysis of Variance Table

Response: y
Df  Sum Sq Mean Sq F value   Pr(>F)
group      1 2.60205 2.60205  954.08 0.001046 **
Residuals  2 0.00545 0.00273
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
As you can see it is statistically significant which is due to the large difference between the groups in comparison to the small difference within group (1.0 and 1.1)

#### statswork15

##### New Member
Minimum sample size in ANOVA
The sample size required for a one-way ANOVA with two groups, which tests for differences on one independent variable, is 128, which is the same as the independent samples t-test. The sample size depends on the number of groups in the independent variable, but for a three-group independent variable, you'll need 156 people or about 52 per group.