Everyone mentions why small sample sizes should be viewed with caution. But most of us ignore it in practice, because it's more fun to celebrate a player who has gotten off to a good start or criticize a player who has gotten off to a rotten start. We shouldn't, but we do.
So let's look at the example of Clint Barmes to see the dangers of giving in to the temptation. I'm going to use some technical language here: Clint is not a very good hitter. During the period 2008-2011 he hit for an average of 0.249 with a wOBA of 0.308. Among the 22 NL shortstops who had 1,000 AB during that period, Clint was 20th in average and 14th in wOBA. But, Clint was a good fielder, so he ranked 9th in FWAR, and I thought it was a good signing. Not Jose Reyes, but a good signing.
So what are we to make of his dreadful performance so far this year? He's not walking; he's striking out a lot; his average is 0.165; and his wOBA is 0.223. Obviously he's toast, and this was a dreadful signing. Right?
Wrong. It means very little. The average means 14 hits in 85 AB. You expect Clint to hit 0.230-0.250 with a wOBA of 0.275-300. That means you expected him to have had 20 or 21 hits. Six or seven more than he has now. Did I mention that his BABIP is 0.194 (about 80 points below his career average)? Might be some luck involved there.
To sum up, Clint is not a good hitter. What we've seen thus far does not tell us much, other than he hit 0.089 in his first 14 games and 0.250 in the next 12. His signing might turn out to have been good, bad, or indifferent.