Comparing frequencies I'm trying to find the right test to use to compare 3 frequencies.
Basically, in my research, 3 separate user interface prototypes were given to the same sample (10 people) and particular tasks needed to be done using the interface. The following is the frequency table of how many of the sample actually managed to perform the task assigned:
DESIGN      SUCCESS/10   
Design 1    3  
Design 2    9   
Design 3    2

Is there any statistical test that I can use to show that the frequencies are significantly different? ie. Design 2 is significantly superior
 A: You have paired data, i.e. you have the same sample of (10) individuals that are tested on three interface prototypes. Hence you cannot use Fisher's exact test nor the binomial test for comparing proportions. 
What you can use, instead, is the McNemmar's test (see wikipedia and references therein); in R see ?mcnemar.test. You might consider a pairwise test for each Design type against the other, and then correct the resulting pvalues for multiplicity with the command p.adjust in R. 
If you are interested in testing jointly all the three Design types, then you can consider the Cochran's Q test (see again wikipedia and ref.s there in). In R you can perform this test using the command cochran.qtest from the RVAideMemoire package of R (there might be other packages doing the same thing, but this is the first result I found on google). Hope this helps!
A: You can use the Fisher's exact test, because your data has only two columns and the Chi-square test will yield inaccurate results.
The results for your data in R are like this (this compared all 3 designs):
Fisher's Exact Test for Count Data

data:  data
p-value = 0.3019
alternative hypothesis: two.sided

If you want to compare each design with the other two, you can use the proportion test (prop.test in R), where you have the counts of successes (Success) and the counts of trials (10).
