Identifying and interpreting a P-value for linear correlation

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to identify and interpret a p-value for a linear correlation.  Here's our problem statement: For a data set of brain volumes and IQ scores of 10 males, the linear correlation coefficient is found, and the p-value is 0.761.  Write a statement that interprets the p-value and includes a conclusion about linear correlation.

Part 1

OK, here we have a statement that we're going to write.  There's three different blanks that we need to fill in the statement.  Let's take a look at the first one.

So here it says, “The p-value indicates that the probability of a linear correlation coefficient that is at least as extreme is blank percent.”  Well, this statement right here — probability of a linear correlation coefficient that is at least as extreme — this is a definition of the p-value.  Well, they give us the p-value here in the problem statement — 0.761.  Therefore, these two must be the same.  If this is the definition (which it is) and this is a numerical value for the same thing, then these must be the same thing.  So I'm going to take this p-value here and convert from decimal to percent.  To do that, I just move the decimal place two points to the right — 76.1%.

Part 2

Let's look at the second blank here.  We're asked to say whether this p-value is high or low.  Well, this means we need to have a standard by which to judge.  And typically the standard or threshold that's used to judge is the level of confidence, represented with the lowercase Greek letter alpha.  We're not given anything like that in the problem statement, and therefore it's pretty safe to assume that we should just adopt the most commonly used threshold value.  And that is by far and away 5%.  So 76% is much much greater than 5%, so this is going to be high.

Part 3

And then, with a high p-value, we're looking to see is there or is there not sufficient evidence to make our conclusion.  Well, a high p-value typically means you're over that threshold.  And if you're over the threshold, then there is not sufficient evidence to make your conclusion.  If you were under the threshold — in other words, the p-value is low, so you're below that threshold — then you would have sufficient evidence to make your conclusion.  But that's not the case here.  Our p-value is really high, and so there is not sufficient evidence to make our conclusion.  I check the answer.  Well done!

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