Name Rascal/Libraries/analysis/statistics

Synopsis Statistical functions.

Details Frequency Descriptive Correlation Inference SimpleRegression

Description A collection of statistical functions based on the Apache statistics library.

We do not provide a course on (or even an introduction to) statistics. Useful background information can be found here:

• Statistics on Wikipedia.
• An Introduction to Statistics by Keone Hon.
• Think Stats: Probability and Statistics for Programmers by Allan B. Downey gives a very readable overview of statistic techniques.
• Statistics Calculator allows entering data and get an overview of the values of various statistical indicators.
• Online Calculation on STATISTICS gives calculators for individual measures.

The following functionality is offered:

• Frequency: Frequency distributions.
• cumFreq: Cumulative frequency of values less than or equal to a given value.
• cumPct: Cumulative percentage of values less than or equal to a given value.
• distribution: Compute a distribution: count how many times events are mapped to which bucket.
• pct: Percentage of values that are equal to a given value.
• Descriptive: Descriptive Statistics.
• geometricMean: Geometric mean of data values.
• kurtosis: Kurtosis of data values.
• max: Largest data value.
• mean: Arithmetic mean of data values.
• median: Median of data values.
• min: Smallest data value.
• percentile: Percentile of data values.
• skewness: Skewness of data values.
• standardDeviation: Standard deviation of data values.
• sum: Sum of data values.
• sumsq: Sum of the squares of data values.
• variance: Variance of data values.
• Correlation: Correlation between data values.
• covariance: Covariance of data values.
• PearsonsCorrelation: Pearson product-moment correlation coefficient.
• PearsonsCorrelationPValues: P-values (significance) associated with Pearson correlation.
• PearsonsCorrelationStandardErrors: Standard errors associated with Pearson correlation.
• SpearmansCorrelation: Spearman's rank correlation coefficient.
• Inference: Statistical inference methods.
• anovaFValue: Analysis of Variance (ANOVA) f-value.
• anovaPValue: Analysis of Variance (ANOVA) p-value.
• anovaTest: Analysis of Variance (ANOVA) test.
• chiSquare: Chi-square coefficient of data values.
• chiSquareTest: Chi-square test on data values.
• gini: Gini coefficient.
• tTest: T-test on sample data.
• SimpleRegression:
• intercept: Intercept of regression line.
• interceptStdErr: Standard error of intercept estimate.
• meanSquareError: Sum of squared errors divided by the degrees of freedom.
• predict: Predict a value.
• R: Pearson's product-moment correlation coefficient.
• regressionSumSquares: Sum of squared deviations of the predicted y values about their mean.
• RSquare: Coefficient of determination.
• significance: Significance of the slope correlation.
• slope: Slope of regression line.
• slopeConfidenceInterval: The 95% slope confidence interval.
• slopeStdErr: Standard error of slope estimate.
• sumOfCrossProducts: Sum of cross products of observations.
• sumSquaredErrors: Sum of squared errors.
• totalSumSquares: Sum of squared deviations.
• XSumSquares: Sum of squared deviations of x values about their mean.

Pitfalls

• Be aware that in creating data for statistical analysis, repeated values may occur. This implies that you should avoid creating sets of observations. This also explains why the functions provided here take lists (with elements of various types) as argument.
• The validity of several of the statistics depend on the assumption that the observations included in the model are drawn from a Bivariate Normal Distribution. This is explicitly stated for functions this is the case.
• The stat library is still highly experimental. Interfaces may change and functions maybe added or deleted without notice.

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