## Psychology 320: Psychological Statistics

Professor: Howard B. Lee

Lecture Notes

Week 3 : Chapters 5 and 6

Lecture 6

Ex. A student obtained a test score of 56. The test scores were normally distributed with a mean of 50 and a standard deviation of 8. What proportion of the scores were below 56?

1. Draw a normal distribution.

What is the percentile for X = 56?

* The normal curve table will be provided with the quiz.

Normal curve table---> Z score

Ex. A person gets a score of 615 on the verbal section of the SAT. What is the percentile rank for 615? ( verbal section is normally distributed ).

Mean = 500
Standard deviation = 100
( The above figures are known because it is a CEEB scale ).

.8749 x 100 = 87.49
87.5 = 88 ( expressed in integer form ).

```Z = (score - mean)/standard deviation
```
```Z = 115/100 = 1.15
```

Ex. Wilma received a score of 29 on an exam where the mean = 25 and the standard deviation = 3. The scores were normally distributed. There were 200 people taking this exam. How many people scored below Wilma?

`Z =  (29 - 25)/3 = 4/3 = 1.33`

Use the Z table and find 1.33. Use column B.
.9082 of the people ( or the proportion ).

.9082 x 200 = 181.64 =>182.

Therefore, 182 of the people scored below Wilma.

Lecture 7

Correlation and Regression :

Correlation
The degree of linear relationship between bivariate data or a bivariate population.

Bivariate data
Data that occur in ordered pairs, such as height and weight: two-variable data.

Correlations are the most often used statistics in psychology.

Ex. Is sex related to coffee consumption? The word "related" indicates a relationship.
In contrast to this, causality ( cause and effect ) involves 2 variables, one of which causes ( or changes in one variable ) causes changes in the other variable.

With causality you must have a strict and carefully designed experiment.
With correlations they are only considered with relationships and no causality is implied.

Ex. Height and weight are correlated approximately at r = .68, where -1 is less than or equal to r and r is less than or equal to 1. r = .68 is a positive correlation.
Therefore, taller people tend to be heavier than shorter people, however this is not a perfect correlation.

Does height cause weight or weight cause height? No, there is no causality.
Is there a variable that would cause weight or height? Yes, genetics,diet.
Examples of correlational studies in psychology.