Normal Distribution

frequency curve - smoothed histogram
 

normal curve - symmetric, unimodal/single peaked, and bell-shaped
 

• common in nature, including many psychological and sociological variables
• theoretical distribution that many empirical situations approximate

Empirical Rule - for normal distributions:
 

• 68% of observations w/in 1 sd of mean
• 95% of observations w/in 2 sd of mean
• 99.7% of observations w/in 3 sd of mean

z-scores -  standardized or standard scores
 

• z = (X - Xbar) / sd
• standardizing changes mean and sd, but not shape of distribution
• use to estimate percentile if distribution is approximately normal
• using z-scores to compare observations in different distributions
• e.g., comparing an individual woman's height relative to women vs. an individual man's height relative to men
• U.S. 1976-80 (HANES):
• adult women: mean = 63.5, sd = 2.5
• adult men: mean = 69.0, sd = 3.0

assessing normality

• look at graphical display of distribution; computer-drawn curve
• indirect, numerical approach
• examine percentage of observations within 1, 2, 3 sds of mean