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gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z ≤ 0.69) = 0.2549. Cumulative gives a probability that a statistic is less than Z. This equates to the area of the distribution below Z. Example: Prob(Z ≤ 0.69) = 0.7549. Complementary cumulative gives a probability that a statistic is greater than Z.
Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.
Because of the central limit theorem, many test statistics are approximately normally distributed for large samples.Therefore, many statistical tests can be conveniently performed as approximate Z-tests if the sample size is large or the population variance is known.
In educational statistics, a normal curve equivalent (NCE), developed for the United States Department of Education by the RMC Research Corporation, [1] is a way of normalizing scores received on a test into a 0-100 scale similar to a percentile rank, but preserving the valuable equal-interval properties of a z-score.
Most test statistics have the form t = Z/s, where Z and s are functions of the data. Z may be sensitive to the alternative hypothesis (i.e., its magnitude tends to be larger when the alternative hypothesis is true), whereas s is a scaling parameter that allows the distribution of t to be determined. As an example, in the one-sample t-test
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics. However, a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily interpretable.
The term normal score is used with two different meanings in statistics. One of them relates to creating a single value which can be treated as if it had arisen from a standard normal distribution (zero mean, unit variance). The second one relates to assigning alternative values to data points within a dataset, with the broad intention of ...