Read the following points for a general idea on interpreting statistics.
A) Biased data
Things to think about include:
i) Are the data that the relationship is based upon a representative (i.e., unbiased) selection of all the possible individuals that could have been sampled? E.g., think about the paradox of the falling cats.
ii) Could the researchers have been verified the accuracy of their data by some independent means? E.g., survey respondents might give false information.
B) Lying with averages and the effects of extreme data points
i) When “averages” are reported do you always know what is being discussed?
ii) Note that there are three different types of “average”: the mean (arithmetic average), median (middle value in a distribution), and mode (most commonly occurring value).
iii) These three numbers can be very different, and so the “average” value of something may not be typical. E.g., the average size of tax breaks that politicians talk about don’t necessarily tell you anything about what most people will actually get.
C) Spurious correlations
i) Just because two things are correlated with each other (i.e., as one changes, so does the other in some systematic way), does not mean that one is actually affecting the other.
ii) Lots of examples of this. Here is one: people who have an annual physical live for longer than those that don’t, yet most tests performed in physicals have no detectable health benefits.
D) Inappropriate comparisons
i) It is easy to mislead people by using different types of statistics in a comparison.
ii) E.g., this quote is supposed to make you believe that dolphins living in captivity die at a higher rate than they would in the wild: "Calculations taken from the study showed that on average the expected life span of a bottle-nosed dolphin in captivity could be as little as 14 years, while in the wild the dolphin could live twenty to twenty-nine years."
iii) Did you spot the problem? Read it again. Now, did you notice that the statement compares an average to a maximum? This statement tells us absolutely nothing useful and is clearly intended to mislead you.
E) Extrapolation beyond the data
i) When you look at graphs, pay attention to whether the line through points goes beyond the range of values spanned by the points. If any assertions are made about values outside of the data range, you probably shouldn’t put too much faith in them.
Hope it helps!