The Normal Curve

You've seen that diagram before, when we were studying standard deviations, although mine was something very crude on a blackboard.

We tend to think that most things fall out normally, that if we could count up a huge population, that all of the variables associated with that population would have a mean, median and mode at the very center. That vertical center line that passes through the top of the curve to the horizontal line at the bottom represents all three measures of central tendency. The other vertical lines represent one, two, and three deviations, standard deviations from the mean.

We can find probabilities using this curve. We assume that the sum of the area under the curve equals one. So any other area (other than all of the space under the line) will represent some proportion less than one.

The area between an SD of 1 and an SD of -1 represents .6826 of the area under the curve, or almost 68%. The area between an SD of 1.96 and an SD of -1.96 represents .9544, or 95% or the area. The area between an SD of 3 and an SD of -3 represents .9974 of the probability.



It is the very same type of curve, the normal curve, that helps you to see the rejection areas, the critical regions that we're looking for to be able to reject a null hypothesis.

Figure 10.6 (the top one)