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The Mann–Whitney test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.
The version to be described here is commonly identified as the Mann–Whitney U test while the version developed by Wilcoxon (1949) is usually referred to as the Wilcoxon–Mann–Whitney test. Although they employ different equations and different tables, the two versions of the test yield comparable results.
It extends the Mann–Whitney U test, which is used for comparing only two groups. The parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least one sample stochastically dominates one other sample. The test does not identify where this stochastic ...
Excel for the web is a free lightweight version of Microsoft Excel available as part of Office on the web, which also includes web versions of Microsoft Word and Microsoft PowerPoint. Excel for the web can display most of the features available in the desktop versions of Excel, although it may not be able to insert or edit them.
Excel 4.0 was the first application to support new AppleScript. [177] Microsoft Office 4.2 for Mac was released in 1994. (Version 4.0 was skipped to synchronize version numbers with Office for Windows) Version 4.2 included Word 6.0, Excel 5.0, PowerPoint 4.0 and Mail 3.2. [185] It was the first Office suite for Power Macintosh. [177]
.xlt – Legacy Excel templates; officially designated "Microsoft Excel 97–2003 Template".xlm – Legacy Excel macro; OOXML Office Open XML (OOXML) format was introduced with Microsoft Office 2007 and became the default format of Microsoft Excel ever since. Excel-related file extensions of this format include:.xlsx – Excel workbook
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In probability theory, the continuous mapping theorem states that continuous functions preserve limits even if their arguments are sequences of random variables. A continuous function, in Heine's definition, is such a function that maps convergent sequences into convergent sequences: if x n → x then g(x n) → g(x).