binomial glm with null-hypothesis = 0.33 I have a dataset and need to test if the values are statistical different to 0.33 (=1/3). Flies have the choice between 3 types of berries. So, if they do not care about the type they would lay 1/3 of their eggs in each typ of berry and that would be the null-hypothesis. I want to know, if they layed signifikcant more than 1/3 of their eggs in one specific type of berry.
With this model I would test if the values are different from 0.5:
fail<-(Summe-SummeF)
c1<-cbind(SummeF,fail)
m1<-glm(c1 ~ 1, family=quasibinomial(link= "logit"), data = data1)

But I need a test against 0.33. As far as I understand the answers to other questions regarding this topic I can change the test by including an offset command, but I quit do not understand what exactly to include to test against 0.33.
Many thanks for any help you can provide.
 A: Edit: This answer addresses the simple case in which there are three counts and the distribution of these counts are tested against a null hypothesis of equal distribution. Comments by the OP suggest the set-up of the experiment is more complicated than this.
Aside from the multinomial test mentioned by @a_statistician , you could also use a chi-square goodness-of-fit test.  This test is probably more common, but also may be inappropriate when there are low expected counts.
observed    = c(10, 20, 30)
theoretical = c(1/3, 1/3, 1/3)

chisq.test(x = observed,
           p = theoretical)

   ### Chi-squared test for given probabilities
   ### 
   ### X-squared = 10, df = 2, p-value = 0.006738

Probably more beneficial would be looking at the multinomial confidence intervals for the proportions.
if(!require(DescTools)){install.packages("DescTools")}

library(DescTools)

observed    = c(10, 20, 30)

MultinomCI(observed,
           conf.level=0.95,
           method="sisonglaz")


   ###            est    lwr.ci    upr.ci
   ### [1,] 0.1666667 0.0500000 0.3079439
   ### [2,] 0.3333333 0.2166667 0.4746106
   ### [3,] 0.5000000 0.3833333 0.6412772

Plotting these gives us a basis for comparison.
if(!require(DescTools)){install.packages("DescTools")}
if(!require(ggplot2)){install.packages("ggplot2")}

library(DescTools)
library(ggplot2)

MCI = MultinomCI(observed,
           conf.level=0.95,
           method="sisonglaz")

MCID = as.data.frame(MCI)

MCID$Berry = c("B1", "B2", "B3")

ggplot(MCID, aes(x = Berry, y = est)) +
    geom_bar(stat = "identity",
            color = "black",
             fill  = "gray50",
             width =  0.6) +
    geom_errorbar(aes(ymin  = lwr.ci, ymax  = upr.ci),
             width = 0.2) +
    theme_bw() +
    ylab("Proportion")


Sources:
(Caveat: I am the author of these pages.)
http://rcompanion.org/handbook/H_03.html
http://rcompanion.org/handbook/H_02.html
A: If the probability of the event was 0.33, then the log-odds of the event (the linear predictor for a binomial and quasibinomial model) is:
$$\mbox{logit} 0.33 = -0.7081851$$
To fit the model in R:
data1$os <- qlogis(0.33)
m1<-glm(c1 ~ offset(os) + 1, family=quasibinomial(link= "logit"), data = data1) 

The statistical significance of the intercept term will tell you whether the risk is different from that value.
The quasibinomial works in spite of the constraint of the model probabilities, because of the quasilikelihood. But the multinomial likelihood is preferred here.
To do a multinomial model is quite easy. It's just a special case of a log-linear model:
n <- c(10, 20, 30)
p <- c(0.33)
en <- p * c(60, 60, 60)
x <- factor(0:2)
fit <- glm(n ~ x + offset(log(en)), family=poisson)

test the statistical significance of the x group indicator term.
A: Need to install package EMT. 
library(EMT)

observed <- c(n1,n2,n3) ## n1, n2, n3 are observed numbers of eggs on each type of berry

prob <- c(0.33333, 0.33333, 0.33333) 

out <- multinomial.test(observed, prob)   

Example: 
multinomial.test(c(10,20,30),c(0.33333,.33333,0.33333))

 Exact Multinomial Test, distance measure: p

    Events    pObs    p.value
      1891   1e-04     0.0059

It is called as goodness of fit test for multinomial distribution.
