Z statistic: Difference between revisions
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A commonly used transformation of a | A commonly used transformation of a normal distribution. | ||
The resulting standardised normal distribution has a [[mean]] of 0 and a [[standard deviation]] of 1. | |||
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. | |||
It is used extensively in hypothesis testing. | |||
The Z statistic is 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). | 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). | ||
== See also == | == See also == | ||
* [[Hypothesis testing]] | |||
* [[Standardised normal distribution]] | * [[Standardised normal distribution]] | ||
* [[Transformation]] | |||
* [[t-statistic]] | |||
[[Category:Risk_frameworks]] | |||
Latest revision as of 09:08, 28 September 2022
A commonly used transformation of a normal distribution.
The resulting standardised normal distribution has a mean of 0 and a standard deviation of 1.
It is used extensively in hypothesis testing.
The Z statistic is 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).
