L33 Psych 300 Chapter Notes - Chapter 6: Normal Distribution, Central Limit Theorem, Standard Deviation


Department
Psychological & Brain Sci (Psychology)
Course Code
L33 Psych 300
Professor
Nestojko
Chapter
6

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Chapter 06: The Normal Curve, Standardization, and z

Scores
The Normal Curve - a specific bell-shaped curve that is unimodal, symmetric, and defined
mathematically
●The normal curve describes the distributions of many variables
●As the size of a sample approaches the size of the population, the distribution resembles
a normal curve (as long as the population is normally distributed)
Building Blocks of Inferential Statistics:
●The characteristics of the normal curve
●How to use the normal curve to standardize any variable by using a tool called the z

score
●The central limit theorem, which, coupled with a grasp of standardization, allows us to
make comparisons between means
Standardization, z

Scores, and the Normal Curve
●Standardization - a way to convert individual scores from different normal distributions
to a shared normal distribution with a known mean, standard deviation, and percentiles
●z

Score - the number of standard deviations a particular score is from the mean
β—‹Like all statistical symbols, the z

is italicized
β—‹If your score is 2 standard deviations above the mean, your z

score is 2.0, if your
score is 1.6 standard deviations below the mean, your z

score is -1.6
β– If the mean is 70, the standard deviation is 10, and your score is an 80,
your z

score is 1.0
β—‹The z

distribution always has a mean of zero (0) and a standard deviation of 1
●How do we calculate a z

score?
β—‹Determine the distance of a particular person’s score (X) from the population
mean (u

) as part of the calculation (X - u

)
β—‹Express this distance in terms of standard deviations by dividing by the
population standard deviation, o
●Transforming z

Scores into Raw Scores
β—‹Multiply the z

score by the population standard deviation (o

)
β—‹Add the population mean (u

) to this product to get the raw score
β—‹Make sure not to forget the negative sign if your z

score is negative
●The z

distribution is a normal distribution of standardized scores (z scores), and the
standard normal distribution is a normal distribution of z scores
●Using z

Scores to Make Comparisons:
β—‹You can compare how you did on one test with how your friend did on a different
test by finding your z

scores - how far above or below the mean you were. This
shows who did better with respect to their class’ scores.
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