Standardization and Normal Distribution in Behavioral Sciences: Lecture Notes, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

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Ch. 5. Standardization and Normal Distribution

I. Standardization A. Definition; transforming raw scores to meaningful and standardized scores so that the relative positions of scores can be obtained. B. z-transformation

X - μ X - M z= ───────── or ────────── σ s

1. results in a new scale, z-scale, with the mean zero and SD one.
2. does not change the shape of the original distribution.

II. The normal distribution A. Definition; a theoretical, bell-shaped, symmetric, unimodal, and probability distribution. B. Mathematical function

y = f(x) =

2

2 2

( )

(^1) σ

μ

− x − e

where, y = height on the ordinate (Y-axis), x = point on the abscissa (X-axis), π ≈ 3.14....., e ≈ 2.72....., μ = population mean, and σ = population standard deviation.

C. Properties of the normal distribution

1. has two parameters, μ and σ.
2. a probability distribution from which we can obtain the probability associated with some values.
3. In fact, there are infinitely many normal distributions, one for each value of μ and σ.

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