1. Chapter 7 (Probability)
Probability and Statistics
A. Tells us likelihood of an outcome
B. Tells us degree of confidence in a finding or outcome (i.e., how sure are we that the observed outcome is due to X versus random chance? AND how likely is it that our research hypothesis is true?).
Normal Curve or Bell-Shaped Curve Properties
A. Mean, median and mode are same
NOT Skewed

3. B. Perfectly symmetrical about the mean (i. e
B. Perfectly symmetrical about the mean (i.e., two halves fit perfectly together).
C. Tails of the normal curve are asymptotic. Curves come close, but never touch the horizontal axis.
Are curves usually normal? Yes, especially with large sets of data (more than 30). Most scores are concentrated in the center and few are concentrated at the ends (height, intelligence, p. 137).

4. Divisions of the Normal Curve (fig. 8.4)
A. Mean is at the center
B. Scores along x-axis correspond to standard deviations.
C. Sections within the bell curve represent % of cases expected to fall therein. Geometrically true (these are percentages of entire normal distribution).
D. For normal distributions (most data sets), practically all scores fall in between +3 and -3 sd’s (99.74%). Look at the probabilities of falling in between.
-34.13% x 2 = 68.26% cases fall within 1 to -1 sd’s from mean.

6. Z-scores (standard scores; i. e
Z-scores (standard scores; i.e., # of standard deviations from the mean)
A. Allow us to compare distributions with one another because they are scores that are standardized in units of standard deviations (can’t compare scores if they are measured differently; nonsensical). Different variables or groups will have different means and cannot be compared. But z-scores between groups of data can be compared because they are equivalent (e.g., one unit above or below the mean, respectively).

7. Formula and interpretation (p. 142)
*Do table on p. 143
Comparing z-scores from different distributions
-The raw scores of 12.8 and 64.8 in our data are equal distances from their respective means (z=.4 for both)
What z-scores represent
A. Z-scores correspond to sections under the curve (percentages under the curve).

8. B. These percentages can be seen as probabilities of a certain score occurring given in Table B1 Appendix B.
Example of what we are saying:
“In a distribution with a mean of 100 and standard deviation of 10, what is the probability that any score will be 110 or above?”
The answer = _________.
C. What about a z-score of 1.38? What are the chances that a score will fall within the mean and a z-score of 1.38? _______
What about above a z-score of 1.38?____
What about at or below 1.38?______

9. What about between a z-score of 1 and 2. 5
What about between a z-score of 1 and 2.5? Answer:______ (look at picture p. 124)
Again, we are asking, what is the probability that a score will fall in between 1 and 2.5 standard deviations (z’s) of the mean? -1 and 2.5?
Computer help: probability computations on the web
Back to a research hypothesis
Z-scores help us determine the likelihood of an event or outcome.
Example:
1. Suppose we use a standard that if a coin lands on heads only 5% of the time, we can not have confidence in it (it is rigged). Not just chance.

10. 5% is the standard level for social science research
5% is the standard level for social science research. It means, that if the probability of an event (# of heads or differences between the averages of two groups, or so on) occurs in the extreme (i.e., defined as less than 5% of all cases), then it is unlikely (95% sure) that the outcome is due to random chance (options: it is random chance; it is due to something else: rigged, trickery).
2. Probability tells us how likely something is. It is highly unlikely that we would get 1 head out of ten flips of a coin. We might conclude that it is due to something else.

11. The null says that an outcome is likely (no differences between groups like heads or tails; any difference observed is due to random chance). But the research hypothesis says that the likelihood of an event is extreme and unlikely due to random chance alone. SO, if we find an extreme z-score (less than 5% chance of occurring), then we may say that observed differences are not due to chance but something else (independent variable). More to come!
Null: outcomes equally as likely (diff due to chance)
Research: Outcomes not equally as likely (diff due to something other than chance)

12. Z-scores and SPSS
A. Analyze, descriptive statistics, descriptives
B. Move variable to dialogue box
C. Click save standardized values as variables
D. Click ok
Homework: See Website