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Lecture 4

PSY201H1 Lecture Notes - Lecture 4: Lightning, Statistical Inference, Standard Deviation

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Maria Iankilevitch

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What are z-scores?
Determining the location of a score
Transforming distributions into z-scores and other standardized distributions
Comparing scores of different distributions
Purpose of transforming X values into z-scores:
1. To determine the exact location of a score relative to the distribution
2. To form a standardized distribution that can be directly compared to other distributions
Ex. 78% in this class. Another section of the class had a different mu and different standard
deviation. If you wanted to compare both scores, you need a standardized way to do that. Z-
scores can convert our scores to their scores or vice versa, or we transform them all into z-
soes ad e a see ho they’e all elatie to eah othe.
1. Determining the location of a score in a distribution
Sign indicates whether the score is located above (+) or below (-) the mean
Number indicates the distance between the score and the mean
Indicates the number of standard deviations a score is from the mean
Z-soe distiutio alays has a ea of . It’s alays eual to the ea. Eah stadad
deviation is equal to 1. When you transform raw scores into z-scores, we transform them so the
mean is 0 and the SD is 1. If you had a skewed distribution, then your z-scores would also be
A z-soe of z = +. idiates a positio i a distiutio…
= above the mean by a distance equal to 1 standard deviation
A negative z-score always indicates a location below the mean. (true)
A score close to the mean has a z-score close to 1.00. (false)
Population: Z = (x μ/σ
Sample: Z = (x M)/s
What is Maus’s z-score? z = (x μ/σ =  – 7)/0.5 = 1/0.5 = +2
What is Kei’s z-score? z = (x μ/σ = . – 7)/0.5 = 0.5/0.5 = +1
What is Jaie’s z-score? z= (x- μ/σ = (6.5 7)/0.5 = -0.5/0.5 = -1
What is Ai’s z-score? z= (x- μ/σ = (8.2 7)0.5 = 1.2/0.5 = +2.4
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