Hi all!
Suppose that we have got a response y and an unbalanced treatment x with three
levels or groups.
The treatment is unbalanced by design. Indeed, the first group has 3
replications and the other two have two replications each.
For instance, in R the data might look like this:
y = c(66.18, 66.69, 50.31, 51.99, 52.07, 52.87, 54.03)
group = as.factor(c(rep("a", 3), rep("b", 2), rep("c",2)))
The group means are:
a b c
61.06 52.03 53.45
and the overall mean is 56.31.
Using Helmert contrasts in lm I get the following
> my.mod = lm(y~group, contrasts = list(group = "contr.helmert"))
> summary(my.mod)
Call:
lm(formula = y ~ group, contrasts = list(group = "contr.helmert"))
Residuals:
1 2 3 4 5 6 7
5.12 5.63 -10.75 -0.04 0.04 -0.58 0.58
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 55.513 2.540 21.858 2.59e-05 ***
group1 -4.515 3.012 -1.499 0.208
group2 -1.032 1.851 -0.557 0.607
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6.598 on 4 degrees of freedom
Multiple R-squared: 0.4093, Adjusted R-squared: 0.114
F-statistic: 1.386 on 2 and 4 DF, p-value: 0.3489
Here comes the questions. Is it possible to modify Helmert contrasts in order
to use weighted means instead of means of means?
Thanks
Erlis
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