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In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. For example, the ranks of the numerical data 3.4, 5.1, 2.6, 7.3 are 2, 3, 1, 4. As another example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.
A rating scale is a set of categories designed to obtain information about a quantitative or a qualitative attribute. In the social sciences, particularly psychology, common examples are the Likert response scale and 0-10 rating scales, where a person selects the number that reflecting the perceived quality of a product.
If F(r) is the Fisher transformation of r, the sample Spearman rank correlation coefficient, and n is the sample size, then z = n − 3 1.06 F ( r ) {\displaystyle z={\sqrt {\frac {n-3}{1.06}}}F(r)} is a z -score for r , which approximately follows a standard normal distribution under the null hypothesis of statistical independence ( ρ = 0 ).
In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to the concept of an ancillary statistic. While an ancillary statistic contains no information about the model parameters, a complete statistic contains only information about the parameters, and ...
In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power among all possible tests of a given size α.For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
A similar important statistic in exploratory data analysis that is simply related to the order statistics is the sample interquartile range. The sample median may or may not be an order statistic, since there is a single middle value only when the number n of observations is odd.
For example, suppose that scale scores are found to have a mean of 23.5, a standard deviation of 4.2, and to be approximately normally distributed. Then sten scores for this scale can be calculated using the formula, () +. It is also usually necessary to truncate such scores, particularly if the scores are skewed.
In statistical theory, a U-statistic is a class of statistics defined as the average over the application of a given function applied to all tuples of a fixed size. The letter "U" stands for unbiased. [citation needed] In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased estimators.