Central Limit Theorem -- if we take a large number of random samples, all the same size, and measure each member of each sample on any dependent variable, calculate sample means, then randomly pair these means and subtract, these differences between means will tend to be zero (the larger the samples the stronger this tendency) and they will always be normally distributed (even though the raw scores may not be).

Percentage as probability -- if we find that a certain percentage of scores have a certain characteristic (e.g., are greater than a certain value) we can interpret this percentage as the probability of randomly choosing a score possessing that property from the set of scores.

z-score -- this is the number of standard deviation units a score lies from the mean of its distribution. If the distribution is normal, then there is a fixed relationship between z-score and frequencies (because the mean and standard deviation totally determine the distribution if it is normal).

Inferential question --

Is a result due to chance or is it a real effect?

That is, is the result nonsignificant or significant?

Hypothesis Testing:

H₀: the result is due to chance

H_A: the result is not due to chance -- it is real

Criterion or significance level -- this is the probability level at which you are willing to be wrong in rejecting H₀. If at the beginning of an experiment you set p = .05, and if this leads you to reject the H₀ at the end of the experiment, you have a 5% chance of being wrong (see "percentage as probability" above).

Areas of "fail to reject" and "reject" -- these terms refer to failing to reject the null hypothesis, and are areas of the normal curve defined by the criterion.

To test a hypothesis (z-test):

1. determine H_A and H₀

2. select a criterion (how willing are you to be wrong when you reject H₀?)

3. determine corresponding z values

4. define areas of "fail to reject" and "reject" on the normal curve

5. calculate a z-score for the data and determine whether it falls in the area of "fail to reject" or "reject"

6. accordingly, decide whether to reject H₀

Formula for z-test:

  _      _
(Y₁ - Y₂) - 0

________________

       _     _
  S_{Y1 - Y2}

Compare to the z-score formula:

       _
X - X

   Sx