Z statistic: Difference between revisions
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The Z score is calculated as the difference between the data point (X) and the mean E[x], all divided by the standard deviation of the population (SD). | The Z score is calculated as the difference between the data point (X) and the mean E[x], all divided by the standard deviation of the population (SD). | ||
For example if: | For example if: | ||
the mean (E[x]) of a population = 100; | |||
the standard deviation (SD) = 10; and | |||
a given observation (or data point) = 83.6; | |||
then the Z score (Z) is calculated as: | |||
Z = (X - E[x])/SD | Z = (X - E[x])/SD | ||
= (83.6 - 100 = -16.4)/10 | |||
= - 1.64 standard deviations. | |||
In this case the Z score is negative, indicating that the data point (83.6) lies below the mean (of 100). | In this case the Z score is negative, indicating that the data point (83.6) lies below the mean (of 100). | ||
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== See also == | == See also == | ||
* [[Standardised normal distribution]] | * [[Standardised normal distribution]] | ||
Revision as of 14:55, 28 May 2013
A commonly used transformation of a standard normal distribution. The resulting distribution has a mean of 0 and a standard deviation of 1. Used extensively in hypothesis testing.
Also known as the Z score.
So for example if a data point has a Z score (or Z statistic) of -1.64, then it lies 1.64 standard deviations below the mean.
The Z score is calculated as the difference between the data point (X) and the mean E[x], all divided by the standard deviation of the population (SD). For example if:
the mean (E[x]) of a population = 100;
the standard deviation (SD) = 10; and
a given observation (or data point) = 83.6;
then the Z score (Z) is calculated as: Z = (X - E[x])/SD
= (83.6 - 100 = -16.4)/10
= - 1.64 standard deviations.
In this case the Z score is negative, indicating that the data point (83.6) lies below the mean (of 100).
