Psychology Statistics Exam Two

Empirical distribution

A distribution based on actual observations or collected data.

Theoretical distribution

A predicted distribution based on mathematical formulas and probability.

Empirical vs. theoretical relation

As sample size N increases, an empirical distribution gets closer to the theoretical distribution.

Normal distribution

A theoretical, bell-shaped distribution predicting how frequently chance events occur.

Characteristics of the normal distribution

Symmetrical, mean equals median and mode, and total area under curve equals 1.00.

68-95-99.7 rule

Percentages of scores within 1 (68.28%), 2 (95.44%), and 3 (99.74%) standard deviations.

Z-score formula for individual score

z = (X - μ) / σ

Z-score meaning of z=0

Score is exactly at the mean.

Column C of normal table

Area between a z-score and the tail at infinity.

Column D of normal table

Area between the mean and a z-score.

Finding area above a positive z-score

Subtract the area between the mean and z from 0.5000.

Finding area below a negative z-score

Use symmetry; area below negative z equals area above positive z.

Raw score formula

X = μ + zσ

Expected number of cases formula

Expected number = N × p

Descriptive statistics

Describes data you have already collected.

Inferential statistics

Uses sample data to draw conclusions about a population with inherent uncertainty.

Parameter vs. Statistic

Parameter describes a population; statistic describes a sample.

Sampling error

The difference between a sample statistic and its population parameter.

Sampling distribution of means

The theoretical distribution of means from all possible samples of size N.

Central Limit Theorem (CLT)

Sampling distribution approaches a normal curve as sample size increases, normal when N > 30.

Standard deviation vs. Standard error

SD describes individual score variability; SE describes sample mean variability.

Standard error formula

SE = σ / √N

Z-score formula for a sample mean

z = (X̄ - μ) / SE

Statistical significance

Very improbable results fall in the region of rejection, indicating a real pattern.