We are more confident in the difference between sets C and D. The smaller the p value the greater is our confidence in the diffference. Remember, the p value is the probability that the null hypothesis is true; it is the probability that none of the alternative hypotheses are true. You shouldn't be biased, but if you want to find a change, an effect, or a difference, then you will want to obtain a low p value. Now, how low is considered low?
Somewhat arbitrarily, we accept a p value of 0.05 as indicating that a difference between means is significant. If a p value is > 0.05 then we cannot reject the null hypothesis with confidence. If it is a little bit smaller than 0.05 then we cautiously reject it. We exercise caution because, after all, with p value of 0.05 there is a 1 in 20 chance that there is no difference after all. What is considered to be significant is really up to the investigator. Some investigators consider a difference to be marginally significant with p value between 0.02 and 0.05. A difference is considered significant when the a p value is between, say, 0.005 and 0.02. With a p value below 0.005 we consider the difference to be highly significant.
We will get to an actual t test shortly. First, let's work on this p value issue some more. A t test returned a p value of 0.008. With what level of confidence is our investigator likely to report the outcome?
marginally significant
significant
highly significant