Help is needed about "correlation puzzles"

• Mar 23rd 2009, 05:28 AM
sci
There were 2 research groups in the study.
The authors studied 2 variables A and B.
They announced that there was correlationship between A and B (P<0.05).
There was significant difference of variable A between these 2 groups (P<0.05).
But there was NOT difference of variable B between these 2 groups (P>0.05).
These resulsts seem a little ridiculous to us.
I am not expert in statistics and mathmatics.
So I would like to know whether there is anyone I can get some help.
Thanks.
• Mar 24th 2009, 08:28 AM
meymathis
So I assume you are questioning how can A and B be correlated when A shows a significant difference between the groups while B does not? Significant here refers to statistical significance as opposed to saying that they differ largely. The former refers to whether there is statistical justification to make a claim, and the latter refers to the size of the difference.

While the authors results seem paradoxical, from a mathematical standpoint it isn't because these are statistical tests (i.e. inferences about the population are made based on samples) and you may not have large enough sample sizes to elimanate errors in the conclusions. In fact, the 0.05 threshold says that there is a 5% chance that you say they are correlated (or that they differ on the two groups) when they are NOT.

Don't get me wrong. These are inconsistent statements. What it shows is that the sample size(s) was not sufficiently large to resolve the questions. In other words, the authors got mixed results.

For smaller sample sizes, you have larger error bars, i.e. your sample statistics have more variance. So it becomes harder to justify that A & B are different on the two groups or that they are correlated (the rejection region becomes smaller). So it is possible to have the results from 2 of the tests contradict the result from the other test. It must be that for at least one of the tests an error was made.

I don't mean to say the authors erred. It just means that the statistical methods established (hypothesis testing) point you to a conclusion for each test, but those methods cannot remove all errors (saying yes when the answer is no, or vice versa) because you are sampling the population.

If you were to redo the tests with larger sample sizes then you should be able to eliminate the contradiction.
• Mar 24th 2009, 10:18 PM
sci
Thank you, Mr. or Mrs. meymathis
We tried several place to seek for clues to the puzzles.
Thank you very much for your opinions.