Building a Statistics Pipeline

data class AssumptionCheck(
    val normalityPValue: Double,
    val isNormal: Boolean,
    val varianceEqualityPValue: Double,
    val isVarianceEqual: Boolean
)

data class GroupComparison(
    val testName: String,
    val pValue: Double,
    val isSignificant: Boolean,
    val confidenceInterval: ConfidenceInterval?
)

data class AnalysisReport(
    val controlSummary: DescriptiveStatistics,
    val treatmentSummary: DescriptiveStatistics,
    val assumptions: AssumptionCheck,
    val comparison: GroupComparison
)

fun checkAssumptions(
    control: DoubleArray,
    treatment: DoubleArray,
    alpha: Double = 0.05
): AssumptionCheck {
    val controlNormality = shapiroWilkTest(control)
    val treatmentNormality = shapiroWilkTest(treatment)
    val normality = minOf(controlNormality.pValue, treatmentNormality.pValue)

    val variance = leveneTest(control, treatment)

    return AssumptionCheck(
        normalityPValue = normality,
        isNormal = normality >= alpha,
        varianceEqualityPValue = variance.pValue,
        isVarianceEqual = variance.pValue >= alpha
    )
}

fun compareGroups(
    control: DoubleArray,
    treatment: DoubleArray,
    assumptions: AssumptionCheck,
    alpha: Double = 0.05
): GroupComparison {
    val result = if (assumptions.isNormal) {
        tTest(control, treatment, equalVariances = assumptions.isVarianceEqual)
    } else {
        mannWhitneyUTest(control, treatment)
    }

    return GroupComparison(
        testName = result.testName,
        pValue = result.pValue,
        isSignificant = result.isSignificant(alpha),
        confidenceInterval = result.confidenceInterval
    )
}

fun analyze(
    control: DoubleArray,
    treatment: DoubleArray,
    alpha: Double = 0.05
): AnalysisReport {
    val assumptions = checkAssumptions(control, treatment, alpha)
    val comparison = compareGroups(control, treatment, assumptions, alpha)

    return AnalysisReport(
        controlSummary = control.describe(),
        treatmentSummary = treatment.describe(),
        assumptions = assumptions,
        comparison = comparison
    )
}

val pageLoadControl = doubleArrayOf(
    1.23, 1.45, 1.31, 1.52, 1.38, 1.41, 1.29, 1.47, 1.35, 1.44,
    1.33, 1.50, 1.27, 1.42, 1.36, 1.48, 1.30, 1.46, 1.39, 1.43
)
val pageLoadTreatment = doubleArrayOf(
    1.10, 1.25, 1.18, 1.32, 1.15, 1.22, 1.12, 1.28, 1.19, 1.26,
    1.14, 1.30, 1.11, 1.24, 1.17, 1.29, 1.13, 1.27, 1.20, 1.23
)

val report = analyze(pageLoadControl, pageLoadTreatment)

report.controlSummary.mean
report.treatmentSummary.mean
report.assumptions.isNormal
report.assumptions.isVarianceEqual
report.comparison.testName
report.comparison.pValue
report.comparison.isSignificant
report.comparison.confidenceInterval

data class ExtendedReport(
    val base: AnalysisReport,
    val correlationCoefficient: Double,
    val correlationPValue: Double,
    val regressionSlope: Double,
    val regressionRSquared: Double
)

fun analyzeWithCorrelation(
    control: DoubleArray,
    treatment: DoubleArray,
    metricX: DoubleArray,
    metricY: DoubleArray
): ExtendedReport {
    val base = analyze(control, treatment)
    val correlation = pearsonCorrelation(metricX, metricY)
    val regression = simpleLinearRegression(metricX, metricY)

    return ExtendedReport(
        base = base,
        correlationCoefficient = correlation.coefficient,
        correlationPValue = correlation.pValue,
        regressionSlope = regression.slope,
        regressionRSquared = regression.rSquared
    )
}