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In statistics, the standard score is the (signed) number of standard deviations an observation or datum is ''above'' the mean. Thus, a positive standard score indicates a datum above the mean, while a negative standard score indicates a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see normalization (statistics) for more). Standard scores are also called z-values, ''z''-scores, normal scores, and standardized variables; the use of "Z" is because the normal distribution is also known as the "Z distribution". They are most frequently used to compare a sample to a standard normal deviate, though they can be defined without assumptions of normality. The z-score is only defined if one knows the population parameters; if one only has a sample set, then the analogous computation with sample mean and sample standard deviation yields the Student's t-statistic. == Calculation from raw score == The standard score of a raw score ''x'' 〔Kreyszig 1979, p880 eq(5)〕 is : where: : ''μ'' is the mean of the population; : ''σ'' is the standard deviation of the population. The absolute value of ''z'' represents the distance between the raw score and the population mean in units of the standard deviation. ''z'' is negative when the raw score is below the mean, positive when above. A key point is that calculating ''z'' requires the population mean and the population standard deviation, not the sample mean or sample deviation. It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest. But knowing the true standard deviation of a population is often unrealistic except in cases such as standardized testing, where the entire population is measured. In cases where it is impossible to measure every member of a population, the standard deviation may be estimated using a random sample. It measures the sigma distance of actual data from the average. The Z value provides an assessment of how off-target a process is operating. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Standard score」の詳細全文を読む スポンサード リンク
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