Unit 2 Normal Distribution and Z Scores

Normal distribution shape

–Bell shape

–Most of area under the curve falls in the middle

–The tails of the distribution (ends) approach the X-axis but never touch

Normal Distribution Symmetry

All are bilaterally symmetrical (can fold it in half)

–Half scores fall on either side of mean

Normal Distribution Total area under the curve:

1.00 or 100% (Remember: the y-axis of all distributions represents frequency, so when we’re talking about particular sections under the curve, we’re talking about a number or proportion of the total number of observations

Normal Distribution Assumptions

1)The majority of scores (roughly 2/3) will fall within in one standard deviation of the mean

2)A minority of scores fall more than two standard deviations from the mean (about 5%)

Standard Deviation and Spread

•Area under the curve always = 1.00 or 100%

•Distribution can be narrow or wide—depending on SD (note: this   does not change our assumptions about area under the curve at   specific numbers of standard deviations from the mean – it just   becomes tall instead of wide)

Z score definition

•A unit-free standardized score that indicates how many standard deviations a score is above or below the mean of the distribution.

•Z-scores give the exact location of a score in a distribution

•Transforms raw scores into relative scores

•Use when appropriate data is interval or ratio and symmetric and normal

Allows you to compare scores across different distributions

Z score magnitude

•Magnitude tells how far in standard deviation units away from the mean (usually magnitude rarely going to be larger than |4|)

Z score direction

Direction: (+) or (-) sign tells whether the z-score is above or below the mean—remember, the Z-score of the mean is always 0