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Parametric methods (t-tests, ANOVA, Pearson correlation) assume specific properties of the data. This guide covers the three most common assumptions and the kstats functions for each.
Normality Available tests Test Function Best for Shapiro-Wilk shapiroWilkTest(sample)General-purpose default, samples up to ~5000 Anderson-Darling andersonDarlingTest(sample)Sensitive to tail deviations D’Agostino-Pearson dagostinoPearsonTest(sample)Omnibus check via skewness and kurtosis, n > 20 Jarque-Bera jarqueBeraTest(sample)Large samples, checks skewness and kurtosis jointly
Run all four on the same dataset val sensorReadings = doubleArrayOf ( 150.2 , 151.8 , 149.6 , 152.1 , 150.9 , 151.3 , 149.8 , 152.5 , 150.4 , 151.1 , 150.7 , 149.5 , 151.6 , 150.0 , 152.3 , 151.0 , 149.9 , 150.8 , 151.5 , 150.3 , 151.2 , 149.7 , 150.6 , 152.0 , 150.1 , 151.4 , 149.4 , 151.9 , 150.5 , 151.7 ) val shapiro = shapiroWilkTest (sensorReadings) val anderson = andersonDarlingTest (sensorReadings) val dagostino = dagostinoPearsonTest (sensorReadings) val jarqueBera = jarqueBeraTest (sensorReadings) shapiro.pValue // Shapiro-Wilk anderson.pValue // Anderson-Darling dagostino.pValue // D'Agostino-Pearson jarqueBera.pValue // Jarque-Bera
When tests disagree, prefer Shapiro-Wilk for small to medium samples and Anderson-Darling when tail behavior matters.
Combine with descriptive statistics val summary = sensorReadings. describe () summary.skewness // close to 0 for symmetric data summary.kurtosis // close to 0 (excess) for Normal-like tails
Variance Homogeneity When comparing groups (t-test, ANOVA), equal variances are often assumed.
Test Function Assumes normality? Levene leveneTest(group1, group2, ...)No — robust to non-normality Bartlett bartlettTest(group1, group2, ...)Yes — more powerful when data is normal Fligner-Killeen flignerKilleenTest(group1, group2, ...)No — non-parametric, median-based
Check variances before ANOVA val batchA = doubleArrayOf ( 48.2 , 47.8 , 49.1 , 48.5 , 47.9 , 48.7 , 48.3 , 49.0 , 48.1 , 48.6 ) val batchB = doubleArrayOf ( 51.3 , 50.8 , 52.1 , 51.0 , 51.7 , 50.5 , 51.9 , 51.2 , 50.9 , 51.5 ) val batchC = doubleArrayOf ( 49.5 , 50.2 , 49.8 , 50.0 , 49.3 , 50.4 , 49.7 , 50.1 , 49.6 , 50.3 ) val levene = leveneTest (batchA, batchB, batchC) val bartlett = bartlettTest (batchA, batchB, batchC) val fligner = flignerKilleenTest (batchA, batchB, batchC) levene.pValue // Levene bartlett.pValue // Bartlett fligner.pValue // Fligner-Killeen
A high p-value from all three tests supports proceeding with ANOVA or equal-variance t-test.
Then run ANOVA val anova = oneWayAnova (batchA, batchB, batchC) anova.fStatistic anova.pValue
Goodness-of-Fit Kolmogorov-Smirnov test Compare observed data against a theoretical distribution.
val temperatureReadings = doubleArrayOf ( 155.2 , 154.8 , 156.1 , 155.5 , 154.3 , 155.9 , 155.0 , 156.3 , 154.7 , 155.4 , 155.8 , 154.5 , 156.0 , 155.3 , 154.9 , 155.7 , 155.1 , 156.2 , 154.6 , 155.6 ) // Fit Normal from sample val fitted = NormalDistribution ( mu = temperatureReadings. mean (), sigma = temperatureReadings. standardDeviation () ) val ks = kolmogorovSmirnovTest (temperatureReadings, fitted) ks.statistic // smaller means better fit ks.pValue
Chi-squared goodness-of-fit Test whether observed category counts match expected proportions.
// Defect counts across 5 product categories val observedDefects = intArrayOf ( 12 , 18 , 25 , 15 , 30 ) // Test against uniform expectation (null = equal probability per category) val uniform = chiSquaredTest (observedDefects) uniform.pValue // Test against specific expected counts val expectedCounts = doubleArrayOf ( 20.0 , 20.0 , 20.0 , 20.0 , 20.0 ) val specific = chiSquaredTest (observedDefects, expectedCounts) specific.pValue
Two-sample KS test Compare two samples without assuming a specific distribution.
val morningReadings = doubleArrayOf ( 155.2 , 154.8 , 156.1 , 155.5 , 154.3 , 155.9 , 155.0 , 156.3 , 154.7 , 155.4 ) val nightReadings = doubleArrayOf ( 156.1 , 155.3 , 157.0 , 156.5 , 155.8 , 156.8 , 155.5 , 157.2 , 155.9 , 156.3 ) val twoSampleKs = kolmogorovSmirnovTest (morningReadings, nightReadings) twoSampleKs.pValue // low p-value suggests different underlying distributions
