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Khan academy - stats. Summarizing Your Data. Please ensure you have JavaScript enabled in your browser.

Summarizing Your Data

If you leave JavaScript disabled, you will only access a portion of the content we are providing. <a href="/science-fair-projects/javascript_help.php">Here's how. </a> Key Info So now you have collected your raw data, and you have results from multiple trials of your experiment. Fortunately, there are mathematical summaries of your data that can convey a lot of information with just a few numbers. Statistics Notation. This web page describes how symbols are used on the Stat Trek web site to represent numbers, variables, parameters, statistics, etc.

Statistics Notation

Capitalization In general, capital letters refer to population attributes (i.e., parameters); and lower-case letters refer to sample attributes (i.e., statistics). For example, P refers to a population proportion; and p, to a sample proportion. X refers to a set of population elements; and x, to a set of sample elements. Greek vs. Like capital letters, Greek letters refer to population attributes. Μ refers to a population mean; and x, to a sample mean. σ refers to the standard deviation of a population; and s, to the standard deviation of a sample. Population Parameters By convention, specific symbols represent certain population parameters. Μ refers to a population mean. σ refers to the standard deviation of a population. σ2 refers to the variance of a population.

Sample Statistics By convention, specific symbols represent certain sample statistics. Mann-Whitney U-Test. Non-parametric tests are basically used in order to overcome the underlying assumption of normality in parametric tests.

Mann-Whitney U-Test

Quite general assumptions regarding the population are used in these tests. A case in point is the Mann-Whitney U-test (Also known as the Mann-Whitney-Wilcoxon (MWW) or Wilcoxon Rank-Sum Test). Unlike its parametric counterpart, the t-test for two samples, this test does not assume that the difference between the samples is normally distributed, or that the variances of the two populations are equal.

Thus when the validity of the assumptions of t-test are questionable, the Mann-Whitney U-Test comes into play and hence has wider applicability. The Method The Mann-Whitney U-test is used to test whether two independent samples of observations are drawn from the same or identical distributions. The Mann-Whitney test criterion is based on the magnitude of the Y's in relation to the X's, i.e. the position of Y's in the combined ordered sequence.

Assumptions.