Compare t-test of difference in means of 3 samples I am comparing the statistical significance of the difference in means (say average age) using three samples (say classes) a, b, and c.
The results of t-test show that there is no significant difference between the mean of samples a and b, and  sample b and c (average age of students in class a is not different than in class b, similarly classes b and c). However, there a significant difference between samples a and c.
a - b = 0
b - c =0 
a - c =! 0
From the first two results, we can conclude that a=b and b=c, which means that a=c. However, this contradicts with the third result.  
What is the best way of analyzing this?
 A: I would make a recommendation that, rather than conducting three $t$-tests, you conduct an ANOVA test. This is a test designed to assess equality of means of three or more groups and, if memory serves correctly, requires the same assumptions as the $t$-test but for three or more groups.
In addition, your statement had a subtle flaw. The idea that two parameters are equal really means that we cannot detect a statistically significant difference between the means. Consider an example where you are evaluating the cost of a gallon of gasoline in three different cities.
City A has a cost of \$1.99 per gallon.
City B has a cost of \$2.19 per gallon.
City C has a cost of \$2.39 per gallon.
Assume the standard deviation for each city is 11 cents (.11 dollars).
Thus A and B do not have statistically different means. B and C do not have statistically different means. However, A and C do have statistically different means. You could generate confidence intervals or execute three $t$-tests to confirm this.
Does this make sense?
A: Let $a$, $b$, and $c$ denote the estimated means of group A, B, and C respectively. Let:
$$V = \left[\begin{array}{ccc} v_{aa} & v_{ab}&v_{ac} \\v_{ba} & v_{bb}&v_{bc} \\v_{ca} & v_{cb}&v_{cc} \end{array} \right] $$ be the estimated covariance matrix of your estimates $[a, b, c]'$. The standard error for the estimate $b-a$ would be:
$$SE_{b-a} = \sqrt{v_{bb} - 2 v_{ab} + v_{aa}}$$
The t-stat would be:
$$ \frac{b - a}{\sqrt{v_{bb} - 2 v_{ab} + v_{aa}}}$$
T-stat $<$ 2 roughly corresponds to significance at the 5 percent level.
$ \frac{c - b}{\sqrt{v_{cc} - 2 v_{bc} + v_{bb}}} < 2 \quad$ and $ \frac{b - a}{\sqrt{v_{bb} - 2 v_{ab} + v_{aa}}} < 2 \quad$ does not imply that $ \frac{c - a}{\sqrt{v_{cc} - 2 v_{ac} + v_{aa}}} < 2 \quad$ 
Hence it is possible that: $c-b$ is not significant at the 5 percent level, $b-a$ is not significant at the 5 percent level, but that $c-a$ is significant at the 5 percent level.
