In some applications (such as weight-for-age in nutritional studies), the Z-scores are not based upon the known population mean and standard deviation, but on an external reference population. In other words converting data to Z-scores does not normalize the distribution of that data! If however, the original distribution is skewed, then the Z-score distribution willĪlso be skewed. You can then make assumptions about the proportion of observations below or above specific Z-values. If the original distribution is normal, then the Z-score distribution will be normal, and you will be dealing with a standard normal distribution. The shape of a Z-score distribution will be identical to the original distribution of the raw measurements. If your Z-score distribution is based on the population mean and population standard deviation, then the mean and the standard deviation of the Z-score distribution will only approximate to zero and one if the sample is random. If your Z-score distribution is based on the sample mean and sample standard deviation, then the mean and standard deviation of the Z-score distribution will equal zero and one respectively. Commonly a known reference population mean and standard deviation are used. A Z-score is calculated by subtracting the mean value from the value of the observation, and dividing by the standard deviation. The sign of the Z-score (+ or - ) indicates whether the score is above (+) or below ( - ) the mean. A Z-score serves to specify the precise location of each observation within a distribution. In other words it merely re-scales, or standardizes, your data. The resulting misuse is, shall we say, predictable.Ī Z-score (or standard score) represents how many standard deviations a given measurement deviates from the mean.
#WEIGHTED STANDARD DEVIATION REFERENCE HOW TO#
Statistics courses, especially for biologists, assume formulae = understanding and teach how to do statistics, but largely ignore what those procedures assume, and how their results mislead when those assumptions are unreasonable.