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Lecture 5

PSYC 241 Lecture 5: Lecture 5: Z-scores
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Department
Psychology
Course Code
PSYC 241
Professor
Kristen Leighton

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Lecture 5: z-scores
Distributions
How do we describe distribution?
Shape (symmetrical, +/- skewed, bimodal, etc.)
Central tendency: one number that describes typical score (mean, median,
mode)
Variability: quantitative measure of the degree to which scores in a distribution
are spread out or clustered together
Normal distributions
Normal distributions are precisely defined and always the same shape
If you randomly choose a score from a normal distribution, it is most likely to be the
mean
If you rephrase the question in terms of 'how close would the score be to the mean,' it is
most likely to be within one standard deviation of the mean
Z-scores
Our goal is to identify exactly where any score lies in this distribution
Raw score (X value) provides little information about comparison to other scores in
distribution
Score may be relatively low, average, or high
If raw score is transformed into z-score, the z-score tells us exactly where the score is
located relative to all the other scores
Changing and X value into a z-score creates a signed number
The sign (+/-) = whether X value is above or below the mean
The numerical value of the z-score = the number of standard deviations
between X and the mean of the distribution
z-scores are not statistics
z-scores are transformed scores
Same mathematical operation on every score
Transform each individual score to a z-score to see where each score lies in the
distribution
z-scores tell us the same things a SD does:
Distance from mean
Direction from mean
Z-scores and location
A score that is two standard deviations above the mean. . .
A score that is one standard deviation below the mean. . .
Transforming X to Z
Two-step process:
Compare each score to the mean (deviation scores = distance and direction
score from mean)
Divide by one standard deviation
Z = (X-μ)/σ
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Description
Lecture 5: zscores Distributions How do we describe distribution? Shape (symmetrical, + skewed, bimodal, etc.) Central tendency: one number that describes typical score (mean, median, mode) Variability: quantitative measure of the degree to which scores in a distribution are spread out or clustered together Normal distributions Normal distributions are precisely defined and always the same shape If you randomly choose a score from a normal distribution, it is most likely to be the mean If you rephrase the question in terms of how close would the score be to the mean, it is most likely to be within one standard deviation of the mean Zscores Our goal is to identify exactly where any score lies in this distribution Raw score (X value) provides little information about comparison to other scores in distribution Score may be relatively low, average, or high If raw score is transformed into zscore, the zscore tells us exactly whe
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