Please enable JavaScript.
Coggle requires JavaScript to display documents.
Z-Scores or Standard Score: - Coggle Diagram
Z-Scores or Standard Score:
Used to identify and describe the exact location of each score in a distribution.
Allows for a standardized distribution in order to compare scores to other distributions.
Establishes a relationship between the score, the mean, and the standard deviation.
Provides a (+ or -) to indicate whether the score is above or below the mean.
This is known as the sign: (+ or -)
Scores below the mean are positive and scores below the mean are negative.
Z-score translates into a number that indicates the distance between the mean and the score by number of standard deviations.
This is known as the magnitude.
Formula to transform scores into z-scores for population:
Numerator is a deviation score divided by the standard deviation.
Process can be reversed in order to turn a z-score into a raw score using the formula:
Computing z-scores for samples:
Identical to population equation but uses sample statistics.
Process can be reversed using the formula:
Population Distributions: entire distribution transformed into a z-score.
Shape: the distribution of z-scores should have exactly the same shape as the original distribution of scores.
Mean: The score distribution will always have a mean of zero.
The distribution of z-scores will always have a standard deviation of 1.
X to Z:
Sample Distribution: entire distribution transformed into z-score.
Shape: The distribution will have the same shape as the original sample of scores.
Mean: the sample will have a mean of zero.
Standard Deviation: the sample will have a standard deviation of 1.
Standardized distributions are used to make dissimilar distributions comparable.
Can be used for comparing populations or samples.
Two Step Process: 1. Original scores are transformed into z-scores.
The scores are then transformed into new X values so that the specific mean and standard deviation are attained.
