[R] runs.test question

[Ista Zahn]

Hi everyone,
I have data from an experiment in which human participants were
instructed to generate a random sequence of yes/no answers under 4
different conditions. I want to test how successful they were in doing
this. More specifically, I want to test the null hypothesis that the 4
conditions come from a single population with a given level of
randomness. Some searching turned up the runs.test() function in the
tseries package. This looks promising, but I'm not sure how to
proceed.

A simplified version of the data structure is

> Data <- data.frame(participant=c(rep(1,4),rep(2,4), rep(3,4), rep(4,4)), question = factor(rep(c("one", "two", "three", "four"), 4)), condition = factor(c(rep(1,8), rep(2,8))), answer=(factor(sign(rnorm(16)), labels=c("yes", "no"))))
> Data
   participant question condition answer
1            1      one         1     no
2            1      two         1    yes
3            1    three         1    yes
4            1     four         1     no
5            2      one         1    yes
6            2      two         1    yes
7            2    three         1     no
8            2     four         1    yes
9            3      one         2    yes
10           3      two         2     no
11           3    three         2    yes
12           3     four         2    yes
13           4      one         2     no
14           4      two         2     no
15           4    three         2     no
16           4     four         2     no


My questions are: 1) Can I test my hypothesis using the runs.test()
function? If no, is there a better approach? 2) Does it make sense to
do a runs.test() for each condition, ignoring the participant
variable? Or do I need to do a runs.test() separately for each
participant? If the latter, how can I combine the information to test
for differences across conditions?

Thanks,
Ista