Question

I'm new to statistics and I'm working on a project where I'm basically trying to rig a coin toss. I have three groups and n = 50 tosses for each group: Control (24/50 success) vs treatment 1 (28/50 success) vs treatment 2 (30/50 success). Success = 1 and is for Heads, failure = 0 and is for tails. My problem is that I don't know how to analyze this data. Can you analyze this data completely and show me how to do it? I want to see if my treatments actually worked so that one side is favored over the other. Also, how do you calculate for power in this example? Thank you

Answer 1

Answer:  I interpret it as asking how to test the hypothesis that the binomial p (probability of success) is the same in the three groups. This can be formulated as a logistic regression, but in this case there is simpler (approximate) ways. I can show how you can do it in R:

 yourtab <- as.table(cbind(succ=c(24, 28, 30), fail=c(26, 22, 20)))
  yourtab
  succ fail
A   24   26
B   28   22
C   30   20
  prop.test(yourtab)

3-sample test for equality of proportions without continuity correction

data:  yourtab
X-squared = 1.5065, df = 2, p-value = 0.4708
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3 
  0.48   0.56   0.60 

This uses an approximate chi-squared test. Using logistic regression we can do:

groups <- as.factor(1:3)
 mod0 <- glm(yourtab ~ 1,  family=binomial)
 mod1 <- glm(yourtab ~ groups,  family=binomial)
 anova(mod0,  mod1)
Analysis of Deviance Table

Model 1: yourtab ~ 1
Model 2: yourtab ~ groups
  Resid. Df Resid. Dev Df Deviance
1         2     1.5067            
2         0     0.0000  2   1.5067

Compare the deviance above with the chisquared (X-squared) from prop.test. This is effectively the same test.