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z-Scores - Coggle Diagram
z-Scores
Standardized distribution
It is possible to transform every X value in a population into a corresponding z-score, resulting in a distribution of z scores. A z-score transformation simply re-labels the values along the X-axis.
It's composed of scores that have been transformed to create predetermined values for μ and σ. It’s the z score distribution.
Using z-scores to make comparison
Standardizing distributions makes it possible to compare different scores or different individuals even though they come from completely different distributions (e.g. how did a z score of 25 in math compare to a score of 33 in science test z score?).
2 steps to creating a new standardized distribution:
(1) transform the original X values into z scores, then (2) turn those those z-scores into new X values.
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Standardized distribution is composed of scores that have been transformed to create predetermined values for μ and σ. It’s the z score distribution; will always have a mean of μ = 0 and a standard deviation of σ = 1
If all the scores in a sample are transformed into z-scores, the result is a sample distribution of z-scores. The distribution for the sample of z-scores will have the same shape as the original sample of scores.
You can standardize a distribution by transforming the scores into a new distribution with a predetermined mean and standard deviation that are positive whole numbers.
The new distribution has “simple” values for the mean and standard deviation but does not change any individual’s location within the distribution.
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What is a z-Score?
Also known as a standard score, a z-score provides more context to a raw score (X). It represents a placement across standard distributions.
It shows the relationship among the mean, the score, and the standard deviation. It uses the mean as a reference point and the standard deviation as a yard stick to determine how much a score strays from the average (+ for above, - for below).
How do z-scores help us with inferential statistics?
The interpretation of research results depends on whether the sample is noticeably different from the population--Z scores can offer a better idea of influence.
Two standard deviations from the mean is considered extreme, e.g. "The treatment is having an impact" vs. no notable effect (less than one standard deviation).