Features/univariate anova

SigmaSwiftStatistics/GeometricMean.swift

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+//
+//  GeometricMean.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 30/12/2016.
+//  Copyright © 2016 Evgenii Neumerzhitckii. All rights reserved.
+//
+import Foundation
+
+public extension Sigma {
+
+  public static func geometricMean(data: [Double]) -> Double? {
+    let count = data.count
+    if count == 0 {
+      return nil
+    }
+    var data_log: [Double] = []
+    var log_val: Double
+    for item in data {
+      log_val = log(item)
+      data_log.append(log_val)
+    }
+    let return_val = exp(average(data_log)!)
+    return return_val
+  }
+}

SigmaSwiftStatistics/HarmonicMean.swift

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+
+//
+//  HarmonicMean.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 30/12/2016.
+//  Copyright © 2016 Evgenii Neumerzhitckii. All rights reserved.
+//
+import Foundation
+
+public extension Sigma {
+
+  public static func harmonicMean(data: [Double]) -> Double? {
+    let count = data.count
+    if count == 0 {
+      return nil
+    }
+    var data_inv: [Double] = []
+    var inv_val: Double
+    for item in data {
+      inv_val = 1.0 / item
+      data_inv.append(inv_val)
+    }
+    let m1 = average(data_inv)
+    let hm = 1.0 / m1!
+    return hm
+  }
+}

SigmaSwiftStatistics/Mode.swift

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+//
+//  Mode.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 19/01/2017.
+//  Copyright © 2017 Evgenii Neumerzhitckii. All rights reserved.
+//
+
+import Foundation
+
+public extension Sigma {
+  /**
+
+   Returns the mode(s) from the array after it is sorted and the indices where it occurs
+
+   https://en.wikipedia.org/wiki/Mode_(statistics)
+
+   - parameter values: Array of decimal numbers.
+   - returns: The mode value itself and an array of the indices where the mode occurs
+
+   Example:
+
+   Sigma.mode([1, 12, 9.5, 3, -5, 12]) // (12, [1,5])
+
+   */
+  public static func mode(_ values: [Double]) -> (Double, [Int])? {
+    let count = values.count
+    if count == 0 { return nil }
+    else if count == 1 {
+      return (values[0], [0])
+    }
+    var mode_value = values[0]
+    var mode_indices: [Int] = [0]
+
+    for index in 1...(count - 1) {
+      if values[index] > mode_value {
+        mode_value = values[index]
+        mode_indices = [index]
+      }
+      else if values[index] == mode_value {
+        mode_indices.append(index)
+      }
+    }
+    return (mode_value, mode_indices)
+  }
+}
+
+

SigmaSwiftStatistics/Probabilities.swift

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+import Foundation
+
+public extension Sigma {
+
+    public static func gammln(xx: Double) -> Double? {
+        let coeffs = [76.18009173, -86.50532033, 24.01409822, -1.231739516, 0.120858003e-2, -0.536382e-5]
+        var x = xx - 1.0
+        var tmp = x + 5.5
+        tmp = tmp - (x + 0.5) * log(tmp)
+        var ser = 1.0
+        for coeff in coeffs {
+            x = x + 1.0
+            ser = ser + (coeff / x)
+        }
+        return -tmp + log(2.50662827465*ser)
+    }
+
+
+
+}
+

SigmaSwiftStatistics/Ttest.swift

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+//
+//  Ttest.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 19/01/2017.
+//  Copyright © 2017 Evgenii Neumerzhitckii. All rights reserved.
+//
+
+import Foundation
+
+public extension Sigma {
+    /**
+
+     Performs one of 3 t-tests: Single sample, unpaired samples, paired samples. 
+
+     Paired is also known as related, within or dependent
+     Unpaired is also known as unrelated, between or independent
+
+     https://en.wikipedia.org/wiki/Student's_t-test
+
+     */
+
+     /*
+
+     One sample t-test
+
+     This performs a one-sample t-test and returns the t-statistic, the degrees of freedom, the probability (p-value)
+     and the Cohen's d statistic
+
+     - parameter values: Array of double numbers.
+     - returns: t (the t statistic), df (degrees of freedom) and p (probability), d (Cohen's d)
+
+     Example:
+
+     Sigma.tTest_one(
+
+     */
+    public static func tTest_one(_ values: [Double], userMean: Double) -> Dictionary<String, Double>? {
+        let count = Double(values.count)
+        if count == 0 { return nil }
+        else if count == 1 {
+            return (nil)
+        }
+
+        let df = count - 1.0
+
+        let numerator = average(values)! - userMean
+        let denominator = standardDeviationSample(values)! / sqrt(Double(count))
+
+        if denominator != 0.0 {
+            let t = numerator / denominator
+
+            let probability = tProbability(DF: df, T: t)!
+
+            // compile results into dictionary
+            var results = [String: Double]()
+
+            // store sums of squares
+            results["t"] = t
+            results["df"] = df
+            results["probability"] = probability
+            results["D"] = 0.0
+
+            return results
+        }
+        else {
+            return nil
+        }
+    }
+
+    public static func tTest(_ values1: [Double], _ values2: [Double], testTails: Int = 2, testType: Int = 1) -> Dictionary<String, Double>? {
+        let count1 = Double(values1.count)
+        let count2 = Double(values2.count)
+        if count1 < 2 { return nil }
+        if count2 < 2 { return nil }
+        var df: Double
+        var t: Double // ignore warning about 't' not being used
+        var numerator: Double
+        var denominator: Double
+
+        if (testType < 1 || testType > 3) {
+            return nil
+        }
+        else if testType == 1 { // Paired t-test
+            if count1 != count2 { return nil }
+            df = Double(count1 - 1)
+
+            var deltaSum: Double = 0.0
+            var deltaSquared: Double = 0.0
+            var delta: Double = 0.0
+
+            for idx in 0...Int(count1 - 1.0) {
+                delta = values1[idx] - values2[idx]
+                deltaSum += delta
+                deltaSquared += (delta * delta)
+            }
+
+            numerator = deltaSum / count1
+            denominator = sqrt((deltaSquared - ((deltaSum * deltaSum) / count1)) / ((count1 - 1.0) * count1))
+
+        }
+        else { // Unpaired t-test
+            let m1 = average(values1)!
+            let m2 = average(values2)!
+            let s1 = varianceSample(values1)!
+            let s2 = varianceSample(values2)!
+            df = Double(count1 + count2 - 2.0)
+
+            let sd = ((s1 * (count1 - 1)) + (s2 * (count2 - 1))) / (count1 + count2 - 2.0)
+
+            // Alternative DF formula for unequal variances (heteroscedastic)
+            if testType == 3 {
+                let s12 = s1 / count1
+                let s22 = s2 / count2
+                let dfNumerator = (s12 + s22) * (s12 + s22)
+                let dfDenominator1 = (s12 * s12) / (count1 - 1.0)
+                let dfDenominator2 = (s22 * s22) / (count2 - 1.0)
+
+                print (dfNumerator, dfDenominator1, dfDenominator2)
+                let dfDenominator = dfDenominator1 + dfDenominator2
+                df = dfNumerator / dfDenominator
+            }
+
+            numerator = m1 - m2
+            denominator = sqrt((sd / count1) + (sd / count2))
+        }
+
+        if denominator == 0.0 {
+            print ("Divide by zero")
+            return nil
+        }
+        else {
+            let t = numerator / denominator
+
+            // Calculate the probability
+            let probability = tProbability(DF: df, T: t)!
+
+            // compile results into dictionary
+            var results = [String: Double]()
+
+            // store sums of squares
+            results["t"] = t
+            results["df"] = df
+            results["probability"] = probability
+
+            return results
+        }
+    }
+
+}
+
+

SigmaSwiftStatistics/multipleRegression.swift

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+//
+//  multipleRegression.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 22/02/2017.
+//  Copyright © 2017 Evgenii Neumerzhitckii. All rights reserved.
+//
+
+import Foundation