These are used to
characteristic of a
group of people. For example, what is the
average ACT score of incoming ISU
freshman? How tall is the
average NBA center? How much do starting salaries of new
college graduates vary? Of high school seniors in rural Iowa, how many have never been
drunk? How many have been drunk once? How many have been drunk more than once?
statistics are what we
decisions… or to decide
what conclusion we should make about the results of a study. For example, do Iowa
elementary school students score more highly on reading tests than the rest of the nation?
Does increasing the room temperature make people behave more angrily toward each
other? Does GPA predict future salary?
Inferential statistics allow us to decide whether the relationship between two
variables (or the difference between two groups of people) is big enough that it is very
unlikely to have occurred just due to the chance differences that always affect results in
research. If we did not have statistics, then we could not make much progress because
researchers with different points of view would argue about whether a relationship or
difference was really meaningful, or whether it was just due to a random fluctuation.
Mean – the mean is the
average, and it is really easy to calculate. You just take all
the numbers, add them up, and then divide them by how many numbers there are. So, if
you measure 5 people on some variable called y, and the 5 values of y are 2, 7, 1, 12, and
2, then the mean is just (2 + 7 + 1 + 12 + 2)/5 = 24/5 = 4.8
Range – the range is kind of tricky, because people think of it in terms of the
actual numbers. For the five values of y given above, it would be WRONG
to say that the
range of y was 1 to 12. The CORRECT
answer is that the range is 11. The range is
greatest number. So, 12 – 1 = 11.
Be careful of negative numbers. If we had four numbers, 5, 1, 0, -4…. the range would be
9, which is the result of subtracting the smallest number (-4) from the biggest number (5).
Deviation score – this is another easy thing to calculate. For each value of y, you
how much it deviates from the mean of y. So, for y=2 with a mean of 4.8, the
deviation score is 2 – 4.8 = –2.8. For y=7 with the mean still being 4.8, the deviation
score would be +2.2. If you add up the deviation scores for all the numbers that went into
calculating a mean, the sum must be 0. That little fact is important to know.
Variance – The variance is a measure of