Comparing two or more proportions from the same sample I have a sample of 167 subjects divided in A, B and C groups with proportions pA = #A/167, pB = #B/167 and pC = #C/167. Which test (or tests) can I use to know if, say, pA > pB and get the statistics to support the comparison?
Any help will be much appreciated. 
 A: If you have #A = 77, #B = 40, and #C = 50, then you could use an
exact binomial test of $H_0: p_A = p_B$ against $H_a: p_A > p_B.$
In R:
binom.test(c(77,40), alte="g")

    Exact binomial test

data:  c(77, 40)
number of successes = 77, number of trials = 117, p-value = 0.0003998
alternative hypothesis: true probability of success is greater than 0.5
95 percent confidence interval:
 0.5792561 1.0000000
sample estimates:
probability of success 
             0.6581197 

Th null hypothesis is rejected at any reasonable level of significance
because of the very small P-value.
The computation of the P-value is equivalent to finding $P(X \ge 77) = 0.0004,$
for $X \sim \mathsf{Binom}(117, \,.5).$
1 - pbinom(76, 117, 1/2)
[1] 0.0003997922

Omitting the parameter alte="g" of binom.test, you could test $H_0: p_A = p_B$ against $H_a: p_A \ne p_B,$  rejecting $H_0$ with a larger P-value.
If you want to test whether levels A, B, and C of a categorical variable have equal probabilities (or some other
specified distribution of probabilities), you could use
a chi-squared test.
