Module 8 – The Standard Normal Distribution

The normal distribution is a crucial concept, especially in psychology.
- It's unimodal, symmetrical, and bell-shaped.
- Many dependent variables in psychology are assumed to be normally distributed within the population.
- Most statistical procedures rely on the assumption that the population of observations is normally distributed.
- Assuming a variable is approximately normally distributed allows us to make inferences about its values.

Density of Scores: The curve of a normal distribution represents the density of scores.
- The higher the curve, the higher the density of scores.
- Analogous to a histogram where the tops of the bars are connected, and the bars are erased.
Mean: The center score represents the mean.
- Most scores cluster around the mean, indicated by the highest point of the curve.
- Fewer scores are found as you move away from the mean, represented by the curve's lower points.
Curve Characteristics:
- The lines on each side of the curve extend indefinitely without touching the x-axis.

Real-world distributions may not perfectly match the idealized normal distribution.
Distributions might resemble slightly skewed or imperfectly symmetrical shapes.
Unless a distribution is obviously not unimodal or symmetrical, it can generally be assumed to be normally distributed for statistical tests.

Intelligence is normally distributed, allowing representation on a normal curve.
The mean IQ score is 100.
Standard deviation (SD) of IQ scores is 15.
Z-scores are used to label the curve, indicating how unusual scores are.
- Most people score within the -1 to +1 Z-score range (85 to 115 IQ).
- Scores beyond 2.5 SDs from the mean are often considered outliers.
- Z-scores < -2.5 or > +2.5 represent a very small proportion of the population.

Labeling with Z-scores shows the proportion/percentage of subjects achieving a particular score.
Example: Knowing most people score in the -1 to +1 Z-score range defines