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Z-Score is a statistical term showing the number of standard deviations above or below the mean a data point sits. This encompasses the distribution of the data set being measured and technically is for population data, whereas the t-statistic is reserved for samples.
Synonyms: standard score, standardize, z-value, normal score, standardized value
Mathematically Z-Score is the raw data point (observation) minus the mean, then divided by the standard devation.
The Z-score is typically used when the population mean and standard deviations are known. Because this isn't usually practical, sample measures are used when sample sizes are large.
In cases where sample sizes are small then the Student's t-statistic is preferred.
For context, in the investment space, because the full population of investments is too difficult or costly to survey, samples are used and, in practice the Z-Score provides estimates that are very close to those from the t-distribution, so many practioners use the Z-Score for its simplicity and availability in statistical analysis software packages.
=STANDARDIZE() function in Excel is
used to find a normalized value from a distribution characterized by a
mean and standard deviation. It takes three inputs, the raw score, the mean
and the standard deviation.
For example, a stock with an observed return value (raw score) of 10% when its mean was 7% and standard deviation was 15%, would translate to a Z-Score of 0.20. This could then be translated into a probability assessment or aid in hypothesis testing.
Sam: If the Zed-score requires a known
population, why is it so common in Finance?
Leo: To translate. I think our friend from Canada meant Z-Score.
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