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fastmath.stats

Statistics functions.

  • Descriptive statistics.
  • Correlation / covariance
  • Outliers
  • Confidence intervals
  • Extents
  • Effect size
  • Tests
  • Histogram
  • ACF/PACF
  • Bootstrap (see fastmath.stats.bootstrap)
  • Binary measures

Functions are backed by Apache Commons Math or SMILE libraries. All work with Clojure sequences.

Descriptive statistics

All in one function stats-map contains:

  • :Size - size of the samples, (count ...)
  • :Min - minimum value
  • :Max - maximum value
  • :Range - range of values
  • :Mean - mean/average
  • :Median - median, see also: median-3
  • :Mode - mode, see also: modes
  • :Q1 - first quartile, use: percentile, quartile
  • :Q3 - third quartile, use: percentile, quartile
  • :Total - sum of all samples
  • :SD - sample standard deviation
  • :Variance - variance
  • :MAD - median-absolute-deviation
  • :SEM - standard error of mean
  • :LAV - lower adjacent value, use: adjacent-values
  • :UAV - upper adjacent value, use: adjacent-values
  • :IQR - interquartile range, (- q3 q1)
  • :LOF - lower outer fence, (- q1 (* 3.0 iqr))
  • :UOF - upper outer fence, (+ q3 (* 3.0 iqr))
  • :LIF - lower inner fence, (- q1 (* 1.5 iqr))
  • :UIF - upper inner fence, (+ q3 (* 1.5 iqr))
  • :Outliers - list of outliers, samples which are outside outer fences
  • :Kurtosis - kurtosis
  • :Skewness - skewness

Note: percentile and quartile can have 10 different interpolation strategies. See docs

Categories

    Other vars: ->confusion-matrix L0 L1 L2 L2sq LInf acf acf-ci ad-test-one-sample adjacent-values ameasure binary-measures binary-measures-all binomial-ci binomial-ci-methods binomial-test bootstrap bootstrap-ci brown-forsythe-test chisq-test ci cliffs-delta coefficient-matrix cohens-d cohens-d-corrected cohens-f cohens-f2 cohens-kappa cohens-q cohens-u2 cohens-u3 cohens-w contingency-2x2-measures contingency-2x2-measures-all contingency-table contingency-table->marginals correlation correlation-matrix count= covariance covariance-matrix cramers-c cramers-v cramers-v-corrected cressie-read-test demean dissimilarity epsilon-sq estimate-bins estimation-strategies-list eta-sq extent f-test fligner-killeen-test freeman-tukey-test geomean glass-delta harmean hedges-g hedges-g* hedges-g-corrected histogram hpdi-extent inner-fence-extent iqr jensen-shannon-divergence kendall-correlation kruskal-test ks-test-one-sample ks-test-two-samples kullback-leibler-divergence kurtosis levene-test mad mad-extent mae mape maximum mcc me mean mean-absolute-deviation means-ratio means-ratio-corrected median median-3 median-absolute-deviation minimum minimum-discrimination-information-test mode modes moment mse multinomial-likelihood-ratio-test neyman-modified-chisq-test omega-sq one-way-anova-test outer-fence-extent outliers p-overlap p-value pacf pacf-ci pearson-correlation pearson-r percentile percentile-bc-extent percentile-bca-extent percentile-extent percentiles pi pi-extent pooled-stddev pooled-variance population-stddev population-variance power-divergence-test powmean psnr quantile quantile-extent quantiles r2 r2-determination rank-epsilon-sq rank-eta-sq rescale rmse robust-standardize rows->contingency-table rss second-moment sem sem-extent similarity skewness span spearman-correlation standardize stats-map stddev stddev-extent sum t-test-one-sample t-test-two-samples trim tschuprows-t ttest-one-sample ttest-two-samples variance variation weighted-kappa winsor wmean wmedian wmw-odds wquantile wquantiles z-test-one-sample z-test-two-samples

    ->confusion-matrix

    (->confusion-matrix tp fn fp tn)(->confusion-matrix confusion-matrix)(->confusion-matrix actual prediction)(->confusion-matrix actual prediction encode-true)

    Convert input to confusion matrix

    view source

    acf

    (acf data)(acf data lags)

    Calculate acf (autocorrelation function) for given number of lags or a list of lags.

    If lags is omitted function returns maximum possible number of lags.

    See also acf-ci, pacf, pacf-ci

    Examples

    Usage

    (acf (repeatedly 1000 r/grand) 5)
;;=> (1.0
;;=>  0.024818272833702658
;;=>  -0.016643111047625263
;;=>  -0.04387141411591324
;;=>  -0.017525857903339097
;;=>  -0.02298214632194487)
(acf (repeatedly 1000 r/grand) [10 20 100 500])
;;=> (-0.0376606395291497
;;=>  -0.034034408698036596
;;=>  -0.010242012560395726
;;=>  0.0045013783824463)
(acf [1 2 3 4 5 4 3 2 1])
;;=> (1.0
;;=>  0.5396825396825397
;;=>  -0.013492063492063475
;;=>  -0.4666666666666665
;;=>  -0.6269841269841269
;;=>  -0.3015873015873015
;;=>  -0.011904761904761935
;;=>  0.17777777777777773
;;=>  0.20317460317460315)
    view source

    acf-ci

    (acf-ci data)(acf-ci data lags)(acf-ci data lags alpha)

    acf with added confidence interval data.

    :cis contains list of calculated ci for every lag.

    Examples

    Usage

    (acf-ci (repeatedly 1000 r/grand) 3)
;;=> {:acf
;;=>  (1.0 8.400697641833316E-4 0.0448042665012578 0.009808923241870098),
;;=>  :ci 0.06197950323045615,
;;=>  :cis (0.06197950323045615
;;=>        0.06197954697044274
;;=>        0.062103841288912796
;;=>        0.062109792420910005)}
(acf-ci [1 2 3 4 5 4 3 2 1] 3)
;;=> {:acf
;;=>  (1.0 0.5396825396825397 -0.013492063492063475 -0.4666666666666665),
;;=>  :ci 0.653321328180018,
;;=>  :cis (0.653321328180018
;;=>        0.8218653739461048
;;=>        0.8219599072345126
;;=>        0.9281841012727746)}
    view source

    ad-test-one-sample

    (ad-test-one-sample xs)(ad-test-one-sample xs distribution-or-ys)(ad-test-one-sample xs distribution-or-ys {:keys [sides kernel bandwidth], :or {sides :one-sided-greater, kernel :gaussian}})

    Anderson-Darling test

    view source

    adjacent-values

    (adjacent-values vs)(adjacent-values vs estimation-strategy)(adjacent-values vs q1 q3 m)

    Lower and upper adjacent values (LAV and UAV).

    Let Q1 is 25-percentile and Q3 is 75-percentile. IQR is (- Q3 Q1).

    • LAV is smallest value which is greater or equal to the LIF = (- Q1 (* 1.5 IQR)).
    • UAV is largest value which is lower or equal to the UIF = (+ Q3 (* 1.5 IQR)).
    • third value is a median of samples

    Optional estimation-strategy argument can be set to change quantile calculations estimation type. See estimation-strategies.

    Examples

    LAV, UAV

    (adjacent-values [1 2 3 -1 -1 2 -1 11 111])
;;=> [-1.0 11.0 2.0]

    Gaussian distribution LAV, UAV

    (adjacent-values (repeatedly 1000000 r/grand))
;;=> [-2.7024365882934935 2.7023587415571386 5.342937622886728E-4]
    view source

    ameasure

    (ameasure [group1 group2])(ameasure group1 group2)

    Vargha-Delaney A measure for two populations a and b

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (ameasure t c))
;;=> 0.375
    view source

    binary-measures

    (binary-measures tp fn fp tn)(binary-measures confusion-matrix)(binary-measures actual prediction)(binary-measures actual prediction true-value)

    Subset of binary measures. See binary-measures-all.

    Following keys are returned: [:tp :tn :fp :fn :accuracy :fdr :f-measure :fall-out :precision :recall :sensitivity :specificity :prevalence]

    Examples

    Usage

    (binary-measures [true false true false true false true false]
                 [true false false true false false false true])
;;=> {:accuracy 0.375,
;;=>  :f-measure 0.28571428571428575,
;;=>  :fall-out 0.5,
;;=>  :fdr 0.6666666666666667,
;;=>  :fn 3,
;;=>  :fp 2,
;;=>  :precision 0.3333333333333333,
;;=>  :prevalence 0.5,
;;=>  :recall 0.25,
;;=>  :sensitivity 0.25,
;;=>  :specificity 0.5,
;;=>  :tn 2,
;;=>  :tp 1}

    Treat 1 as true value.

    (binary-measures [1 0 1 0 1 0 1 0] [1 0 0 1 0 0 0 1] [1])
;;=> {:accuracy 0.375,
;;=>  :f-measure 0.28571428571428575,
;;=>  :fall-out 0.5,
;;=>  :fdr 0.6666666666666667,
;;=>  :fn 3,
;;=>  :fp 2,
;;=>  :precision 0.3333333333333333,
;;=>  :prevalence 0.5,
;;=>  :recall 0.25,
;;=>  :sensitivity 0.25,
;;=>  :specificity 0.5,
;;=>  :tn 2,
;;=>  :tp 1}

    Treat :a and :b as true value.

    (binary-measures [:a :b :c :d :e :f :a :b]
                 [:a :b :a :b :a :f :d :b]
                 {:a true, :b true, :c false})
;;=> {:accuracy 0.5,
;;=>  :f-measure 0.6,
;;=>  :fall-out 0.75,
;;=>  :fdr 0.5,
;;=>  :fn 1,
;;=>  :fp 3,
;;=>  :precision 0.5,
;;=>  :prevalence 0.5,
;;=>  :recall 0.75,
;;=>  :sensitivity 0.75,
;;=>  :specificity 0.25,
;;=>  :tn 1,
;;=>  :tp 3}
    view source

    binary-measures-all

    (binary-measures-all tp fn fp tn)(binary-measures-all confusion-matrix)(binary-measures-all actual prediction)(binary-measures-all actual prediction true-value)

    Collection of binary measures.

    Arguments: * confusion-matrix - either map or sequence with [:tp :fn :fp :tn] values

    or

    • actual - list of ground truth values
    • prediction - list of predicted values
    • true-value - optional, true/false encoding, what is true in truth and prediction

    true-value can be one of:

    • nil - values are treating as booleans
    • any sequence - values from sequence will be treated as true
    • map - conversion will be done according to provided map (if there is no correspondin key, value is treated as false)
    • any predicate

    https://en.wikipedia.org/wiki/Precision_and_recall

    Examples

    Usage

    (binary-measures-all [true false true false true false true false]
                     [true false false true false false false true])
;;=> {:accuracy 0.375,
;;=>  :ba 0.375,
;;=>  :bm -0.25,
;;=>  :cn 4.0,
;;=>  :cp 4.0,
;;=>  :dor 0.3333333333333333,
;;=>  :f-beta #,
;;=>  :f-measure 0.28571428571428575,
;;=>  :f1-score 0.28571428571428575,
;;=>  :fall-out 0.5,
;;=>  :fdr 0.6666666666666667,
;;=>  :fm 0.28867513459481287,
;;=>  :fn 3,
;;=>  :fnr 0.75,
;;=>  :for 0.6,
;;=>  :fp 2,
;;=>  :fpr 0.5,
;;=>  :hit-rate 0.25,
;;=>  :jaccard 0.16666666666666666,
;;=>  :kappa -0.25,
;;=>  :lr+ 0.5,
;;=>  :lr- 1.5,
;;=>  :mcc -0.2581988897471611,
;;=>  :miss-rate 0.75,
;;=>  :mk -0.2666666666666666,
;;=>  :n 4.0,
;;=>  :npv 0.4,
;;=>  :p 4.0,
;;=>  :pcn 5.0,
;;=>  :pcp 3.0,
;;=>  :phi -0.2581988897471611,
;;=>  :pn 5.0,
;;=>  :pp 3.0,
;;=>  :ppv 0.3333333333333333,
;;=>  :precision 0.3333333333333333,
;;=>  :prevalence 0.5,
;;=>  :pt 0.5857864376269049,
;;=>  :recall 0.25,
;;=>  :selectivity 0.5,
;;=>  :sensitivity 0.25,
;;=>  :specificity 0.5,
;;=>  :tn 2,
;;=>  :tnr 0.5,
;;=>  :total 8.0,
;;=>  :tp 1,
;;=>  :tpr 0.25,
;;=>  :ts 0.16666666666666666}

    Treat 1 as true value.

    (binary-measures-all [1 0 1 0 1 0 1 0] [1 0 0 1 0 0 0 1] [1])
;;=> {:accuracy 0.375,
;;=>  :ba 0.375,
;;=>  :bm -0.25,
;;=>  :cn 4.0,
;;=>  :cp 4.0,
;;=>  :dor 0.3333333333333333,
;;=>  :f-beta #,
;;=>  :f-measure 0.28571428571428575,
;;=>  :f1-score 0.28571428571428575,
;;=>  :fall-out 0.5,
;;=>  :fdr 0.6666666666666667,
;;=>  :fm 0.28867513459481287,
;;=>  :fn 3,
;;=>  :fnr 0.75,
;;=>  :for 0.6,
;;=>  :fp 2,
;;=>  :fpr 0.5,
;;=>  :hit-rate 0.25,
;;=>  :jaccard 0.16666666666666666,
;;=>  :kappa -0.25,
;;=>  :lr+ 0.5,
;;=>  :lr- 1.5,
;;=>  :mcc -0.2581988897471611,
;;=>  :miss-rate 0.75,
;;=>  :mk -0.2666666666666666,
;;=>  :n 4.0,
;;=>  :npv 0.4,
;;=>  :p 4.0,
;;=>  :pcn 5.0,
;;=>  :pcp 3.0,
;;=>  :phi -0.2581988897471611,
;;=>  :pn 5.0,
;;=>  :pp 3.0,
;;=>  :ppv 0.3333333333333333,
;;=>  :precision 0.3333333333333333,
;;=>  :prevalence 0.5,
;;=>  :pt 0.5857864376269049,
;;=>  :recall 0.25,
;;=>  :selectivity 0.5,
;;=>  :sensitivity 0.25,
;;=>  :specificity 0.5,
;;=>  :tn 2,
;;=>  :tnr 0.5,
;;=>  :total 8.0,
;;=>  :tp 1,
;;=>  :tpr 0.25,
;;=>  :ts 0.16666666666666666}

    Treat :a and :b as true value.

    (binary-measures-all [:a :b :c :d :e :f :a :b]
                     [:a :b :a :b :a :f :d :b]
                     {:a true, :b true, :c false})
;;=> {:accuracy 0.5,
;;=>  :ba 0.5,
;;=>  :bm 0.0,
;;=>  :cn 4.0,
;;=>  :cp 4.0,
;;=>  :dor 1.0,
;;=>  :f-beta #,
;;=>  :f-measure 0.6,
;;=>  :f1-score 0.6,
;;=>  :fall-out 0.75,
;;=>  :fdr 0.5,
;;=>  :fm 0.6123724356957945,
;;=>  :fn 1,
;;=>  :fnr 0.25,
;;=>  :for 0.5,
;;=>  :fp 3,
;;=>  :fpr 0.75,
;;=>  :hit-rate 0.75,
;;=>  :jaccard 0.42857142857142855,
;;=>  :kappa 0.0,
;;=>  :lr+ 1.0,
;;=>  :lr- 1.0,
;;=>  :mcc 0.0,
;;=>  :miss-rate 0.25,
;;=>  :mk 0.0,
;;=>  :n 4.0,
;;=>  :npv 0.5,
;;=>  :p 4.0,
;;=>  :pcn 2.0,
;;=>  :pcp 6.0,
;;=>  :phi 0.0,
;;=>  :pn 2.0,
;;=>  :pp 6.0,
;;=>  :ppv 0.5,
;;=>  :precision 0.5,
;;=>  :prevalence 0.5,
;;=>  :pt ##NaN,
;;=>  :recall 0.75,
;;=>  :selectivity 0.25,
;;=>  :sensitivity 0.75,
;;=>  :specificity 0.25,
;;=>  :tn 1,
;;=>  :tnr 0.25,
;;=>  :total 8.0,
;;=>  :tp 3,
;;=>  :tpr 0.75,
;;=>  :ts 0.42857142857142855}

    F-beta is a function. When beta is equal 1.0, you get f1-score.

    (let [fbeta (:f-beta (binary-measures-all
                      [true false true false true false true false]
                      [true false false true false false false true]))]
  [(fbeta 1.0) (fbeta 2.0) (fbeta 0.5)])
;;=> [0.28571428571428575 0.2631578947368421 0.3125]
    view source

    binomial-ci

    (binomial-ci number-of-successes number-of-trials)(binomial-ci number-of-successes number-of-trials method)(binomial-ci number-of-successes number-of-trials method alpha)

    Return confidence interval for a binomial distribution.

    Possible methods are: * :asymptotic (normal aproximation, based on central limit theorem), default * :agresti-coull * :clopper-pearson * :wilson * :prop.test - one sample proportion test * :cloglog * :logit * :probit * :arcsine * :all - apply all methods and return a map of triplets

    Default alpha is 0.05

    Returns a triple lower ci, upper ci, p=successes/trials

    view source

    binomial-ci-methods

    view source

    binomial-test

    (binomial-test xs)(binomial-test xs maybe-params)(binomial-test number-of-successes number-of-trials {:keys [alpha p ci-method sides], :or {alpha 0.05, p 0.5, ci-method :asymptotic, sides :two-sided}})

    Binomial test

    • alpha - significance level (default: 0.05)
    • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
    • ci-method - see binomial-ci-methods
    • p - tested probability
    view source

    bootstrap

    deprecated in Please use fastmath.stats.bootstrap/bootstrap instead

    (bootstrap vs)(bootstrap vs samples)(bootstrap vs samples size)

    Generate set of samples of given size from provided data.

    Default samples is 200, number of size defaults to sample size.

    Examples

    Usage

    (bootstrap [1 2 3 4 1 2 3 1 2 1] 2 20)
;;=> ((2.0
;;=>   3.0
;;=>   1.0
;;=>   2.0
;;=>   3.0
;;=>   2.0
;;=>   3.0
;;=>   2.0
;;=>   2.0
;;=>   2.0
;;=>   2.0
;;=>   2.0
;;=>   2.0
;;=>   1.0
;;=>   2.0
;;=>   2.0
;;=>   3.0
;;=>   2.0
;;=>   1.0
;;=>   2.0)
;;=>  (2.0
;;=>   2.0
;;=>   1.0
;;=>   2.0
;;=>   2.0
;;=>   1.0
;;=>   2.0
;;=>   2.0
;;=>   3.0
;;=>   4.0
;;=>   1.0
;;=>   1.0
;;=>   4.0
;;=>   3.0
;;=>   3.0
;;=>   2.0
;;=>   4.0
;;=>   2.0
;;=>   1.0
;;=>   1.0))
(let [data [1 2 3 4 1 2 3 1 2 1]
      fdata (frequencies data)
      bdata (bootstrap data 5 1000)]
  {:source fdata, :bootstrapped (map frequencies bdata)})
;;=> {:bootstrapped ({1.0 392, 2.0 295, 3.0 216, 4.0 97}
;;=>                 {1.0 388, 2.0 286, 3.0 228, 4.0 98}
;;=>                 {1.0 378, 2.0 305, 3.0 223, 4.0 94}
;;=>                 {1.0 423, 2.0 298, 3.0 190, 4.0 89}
;;=>                 {1.0 406, 2.0 294, 3.0 202, 4.0 98}),
;;=>  :source {1 4, 2 3, 3 2, 4 1}}
    view source

    bootstrap-ci

    deprecated in Please use fastmath.stats.boostrap/ci-basic instead

    (bootstrap-ci vs)(bootstrap-ci vs alpha)(bootstrap-ci vs alpha samples)(bootstrap-ci vs alpha samples stat-fn)

    Bootstrap method to calculate confidence interval.

    Alpha defaults to 0.98, samples to 1000. Last parameter is statistical function used to measure, default: mean.

    Returns ci and statistical function value.

    Examples

    Usage

    (bootstrap-ci [-5 1 1 1 1 2 2 5 11 71])
;;=> [-5.498000000000001 17.700000000000003 9.0]
(bootstrap-ci [-5 1 1 1 1 2 2 5 11 71] 0.8)
;;=> [2.5999999999999996 15.7 9.0]
(bootstrap-ci [-5 1 1 1 1 2 2 5 11 71] 0.8 100000)
;;=> [2.5999999999999996 15.7 9.0]
(bootstrap-ci [-5 1 1 1 1 2 2 5 11 71] 0.98 1000 median)
;;=> [-20.5 3.0 1.5]
    view source

    brown-forsythe-test

    (brown-forsythe-test xss)(brown-forsythe-test xss params)
    view source

    chisq-test

    (chisq-test contingency-table-or-xs)(chisq-test contingency-table-or-xs params)

    Chi square test, a power divergence test for lambda 1.0

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    ci

    (ci vs)(ci vs alpha)

    T-student based confidence interval for given data. Alpha value defaults to 0.05.

    Last value is mean.

    Examples

    Usage

    (ci [-5 1 1 1 1 2 2 5 11 71])
;;=> [-6.842279963189242 24.84227996318924 9.0]
(ci [-5 1 1 1 1 2 2 5 11 71] 0.8)
;;=> [7.172484402810223 10.827515597189777 9.0]
    view source

    cliffs-delta

    (cliffs-delta [group1 group2])(cliffs-delta group1 group2)

    Cliff’s delta effect size for ordinal data.

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (cliffs-delta t c))
;;=> -0.25
(let [t [:a :b :c :D :e :f] c [:a :z :X :y :x :y]] (cliffs-delta t c))
;;=> -0.4722222222222222
    view source

    coefficient-matrix

    (coefficient-matrix vss)(coefficient-matrix vss measure-fn)(coefficient-matrix vss measure-fn symmetric?)

    Generate coefficient (correlation, covariance, any two arg function) matrix from seq of seqs. Row order.

    Default method: pearson-correlation

    view source

    cohens-d

    (cohens-d [group1 group2])(cohens-d group1 group2)(cohens-d group1 group2 method)

    Cohen’s d effect size for two groups

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (cohens-d t c))
;;=> -0.42208932839491475
    view source

    cohens-d-corrected

    (cohens-d-corrected [group1 group2])(cohens-d-corrected group1 group2)(cohens-d-corrected group1 group2 method)

    Cohen’s d corrected for small group size

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (cohens-d-corrected t c))
;;=> -0.3990662741188285
    view source

    cohens-f

    (cohens-f [group1 group2])(cohens-f group1 group2)(cohens-f group1 group2 type)

    Cohens f, sqrt of Cohens f2.

    Possible type values are: :eta (default), :omega and :epsilon.

    view source

    cohens-f2

    (cohens-f2 [group1 group2])(cohens-f2 group1 group2)(cohens-f2 group1 group2 type)

    Cohens f2, by default based on eta-sq.

    Possible type values are: :eta (default), :omega and :epsilon.

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]]
  {:default (cohens-f2 t c),
   :eta (cohens-f2 t c :eta),
   :omega (cohens-f2 t c :omega),
   :epsilon (cohens-f2 t c :epsilon)})
;;=> {:default 0.06779661016949151,
;;=>  :epsilon -0.050847457627118633,
;;=>  :eta 0.06779661016949151,
;;=>  :omega -0.04576271186440677}
    view source

    cohens-kappa

    (cohens-kappa group1 group2)(cohens-kappa contingency-table)

    Cohens kappa

    view source

    cohens-q

    (cohens-q r1 r2)(cohens-q group1 group2a group2b)(cohens-q group1a group2a group1b group2b)

    Comparison of two correlations.

    Arity:

    • 2 - compare two correlation values
    • 3 - compare correlation of group1 and group2a with correlation of group1 and group2b
    • 4 - compare correlation of first two arguments with correlation of last two arguments

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]
      d [5 2 3 4 4 5 4 2 3 -1]
      e (range 10)]
  {:arity-2 (cohens-q 0.5 -0.25),
   :arity-3 (cohens-q t c d),
   :arity-4 (cohens-q t c d e)})
;;=> {:arity-2 0.8047189562170503,
;;=>  :arity-3 0.9030140869391835,
;;=>  :arity-4 0.8369271764963739}
    view source

    cohens-u2

    (cohens-u2 [group1 group2])(cohens-u2 group1 group2)(cohens-u2 group1 group2 estimation-strategy)

    Cohen’s U2, the proportion of one of the groups that exceeds the same proportion in the other group.

    view source

    cohens-u3

    (cohens-u3 [group1 group2])(cohens-u3 group1 group2)(cohens-u3 group1 group2 estimation-strategy)

    Cohen’s U3, the proportion of the second group that is smaller than the median of the first group.

    view source

    cohens-w

    (cohens-w group1 group2)(cohens-w contingency-table)

    Cohen’s W effect size for discrete data.

    Examples

    Usage

    (let [a [:a :a :b :b :f :a :a :b :b :c :a :a :b :b :c :a :a :b :b :c]
      b [:b :f :a :a :b :b :y :z :c :b :b :c :a :a :b :b :c :a :a :b]]
  (cohens-w a b))
;;=> 1.0408329997330665
    view source

    contingency-2x2-measures

    (contingency-2x2-measures & args)
    view source

    contingency-2x2-measures-all

    (contingency-2x2-measures-all a b c d)(contingency-2x2-measures-all map-or-seq)(contingency-2x2-measures-all [a b] [c d])
    view source

    contingency-table

    (contingency-table & seqs)

    Returns frequencies map of tuples built from seqs.

    view source

    contingency-table->marginals

    (contingency-table->marginals ct)
    view source

    correlation

    (correlation [vs1 vs2])(correlation vs1 vs2)

    Correlation of two sequences.

    Examples

    Correlation of uniform and gaussian distribution samples.

    (correlation (repeatedly 100000 (partial r/grand 1.0 10.0))
             (repeatedly 100000 (partial r/drand -10.0 -5.0)))
;;=> -0.003303068749082862
    view source

    correlation-matrix

    (correlation-matrix vss)(correlation-matrix vss measure)

    Generate correlation matrix from seq of seqs. Row order.

    Possible measures: :pearson (default), :kendall, :spearman.

    view source

    count=

    (count= [vs1 vs2-or-val])(count= vs1 vs2-or-val)

    Count equal values in both seqs. Same as L0

    view source

    covariance

    (covariance [vs1 vs2])(covariance vs1 vs2)

    Covariance of two sequences.

    Examples

    Covariance of uniform and gaussian distribution samples.

    (covariance (repeatedly 100000 (partial r/grand 1.0 10.0))
            (repeatedly 100000 (partial r/drand -10.0 -5.0)))
;;=> 0.04673681719722958
    view source

    covariance-matrix

    (covariance-matrix vss)

    Generate covariance matrix from seq of seqs. Row order.

    Examples

    Usage

    (covariance-matrix [[1 2 3 4 5 11] [3 2 3 2 3 4]])
;;=> ([12.666666666666668 1.8666666666666667]
;;=>  [1.8666666666666667 0.5666666666666667])
    view source

    cramers-c

    (cramers-c group1 group2)(cramers-c contingency-table)

    Cramer’s C effect size for discrete data.

    view source

    cramers-v

    (cramers-v group1 group2)(cramers-v contingency-table)

    Cramer’s V effect size for discrete data.

    Examples

    Usage

    (let [a [:a :a :b :b :f :a :a :b :b :c :a :a :b :b :c :a :a :b :b :c]
      b [:b :f :a :a :b :b :y :z :c :b :b :c :a :a :b :b :c :a :a :b]]
  (cramers-v a b))
;;=> 0.6009252125773316
    view source

    cramers-v-corrected

    (cramers-v-corrected group1 group2)(cramers-v-corrected contingency-table)

    Corrected Cramer’s V

    Examples

    Usage

    (let [a [:a :a :b :b :f :a :a :b :b :c :a :a :b :b :c :a :a :b :b :c]
      b [:b :f :a :a :b :b :y :z :c :b :b :c :a :a :b :b :c :a :a :b]]
  (cramers-v-corrected a b))
;;=> 0.3410563654946855
    view source

    cressie-read-test

    (cressie-read-test contingency-table-or-xs)(cressie-read-test contingency-table-or-xs params)

    Cressie-Read test, a power divergence test for lambda 2/3

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    demean

    (demean vs)

    Subtract mean from sequence

    Examples

    Usage

    (demean [-5 1 1 1 1 2 2 5 11 71])
;;=> (-14.0 -8.0 -8.0 -8.0 -8.0 -7.0 -7.0 -4.0 2.0 62.0)
    view source

    dissimilarity

    (dissimilarity method P-observed Q-expected)(dissimilarity method P-observed Q-expected {:keys [bins probabilities? epsilon log-base power], :or {probabilities? true, epsilon 1.0E-6, log-base m/E, power 2.0}})

    Various PDF distance between two histograms (frequencies) or probabilities.

    Q can be a distribution object. Then, histogram will be created out of P.

    Arguments:

    • method - distance method
    • P-observed - frequencies, probabilities or actual data (when Q is a distribution)
    • Q-expected - frequencies, probabilities or distribution object (when P is a data)

    Options:

    • :probabilities? - should P/Q be converted to a probabilities, default: true.
    • :epsilon - small number which replaces 0.0 when division or logarithm is used`
    • :log-base - base for logarithms, default: e
    • :power - exponent for :minkowski distance, default: 2.0
    • :bins - number of bins or bins estimation method, see histogram.

    The list of methods: :euclidean, :city-block, :manhattan, :chebyshev, :minkowski, :sorensen, :gower, :soergel, :kulczynski, :canberra, :lorentzian, :non-intersection, :wave-hedges, :czekanowski, :motyka, :tanimoto, :jaccard, :dice, :bhattacharyya, :hellinger, :matusita, :squared-chord, :euclidean-sq, :squared-euclidean, :pearson-chisq, :chisq, :neyman-chisq, :squared-chisq, :symmetric-chisq, :divergence, :clark, :additive-symmetric-chisq, :kullback-leibler, :jeffreys, :k-divergence, :topsoe, :jensen-shannon, :jensen-difference, :taneja, :kumar-johnson, :avg

    See more: Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions by Sung-Hyuk Cha

    view source

    epsilon-sq

    (epsilon-sq [group1 group2])(epsilon-sq group1 group2)

    Less biased R2

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]]
  (epsilon-sq t c))
;;=> -0.05357142857142856
    view source

    estimate-bins

    (estimate-bins vs)(estimate-bins vs bins-or-estimate-method)

    Estimate number of bins for histogram.

    Possible methods are: :sqrt :sturges :rice :doane :scott :freedman-diaconis (default).

    The number returned is not higher than number of samples.

    Examples

    Estimate number of bins for various methods. vs contains 1000 random samples from Log-Normal distribution.

    (estimate-bins vs :sqrt)
;;=> 31
(estimate-bins vs :sturges)
;;=> 11
(estimate-bins vs :rice)
;;=> 20
(estimate-bins vs :doane)
;;=> 18
(estimate-bins vs :scott)
;;=> 66
(estimate-bins vs :freedman-diaconis)
;;=> 201
    view source

    estimation-strategies-list

    List of estimation strategies for percentile/quantile functions.

    Examples

    List of estimation strategies for percentile

    (sort (keys estimation-strategies-list))
;;=> (:legacy :r1 :r2 :r3 :r4 :r5 :r6 :r7 :r8 :r9)
    view source

    eta-sq

    (eta-sq [group1 group2])(eta-sq group1 group2)

    R2, coefficient of determination

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]]
  (eta-sq t c))
;;=> 0.06349206349206347
    view source

    extent

    (extent vs)

    Return extent (min, max, mean) values from sequence

    Examples

    min/max and mean of gaussian distribution

    (extent (repeatedly 100000 r/grand))
;;=> [-4.754024082311232 4.226469292832746 0.0036117613630082942]
    view source

    f-test

    (f-test xs ys)(f-test xs ys {:keys [sides alpha], :or {sides :two-sided, alpha 0.05}})

    Variance F-test of two samples.

    • alpha - significance level (default: 0.05)
    • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
    view source

    fligner-killeen-test

    (fligner-killeen-test xss)(fligner-killeen-test xss {:keys [sides], :or {sides :one-sided-greater}})
    view source

    freeman-tukey-test

    (freeman-tukey-test contingency-table-or-xs)(freeman-tukey-test contingency-table-or-xs params)

    Freeman-Tukey test, a power divergence test for lambda -0.5

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    geomean

    (geomean vs)

    Geometric mean for positive values only

    Examples

    Geometric mean

    (geomean [1 2 3 1 1 2 1 11 111])
;;=> 2.903203203730772
    view source

    glass-delta

    (glass-delta [group1 group2])(glass-delta group1 group2)

    Glass’s delta effect size for two groups

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (glass-delta t c))
;;=> -0.3849741916091626
    view source

    harmean

    (harmean vs)

    Harmonic mean

    Examples

    Harmonic mean

    (harmean [1 2 3 -1 -1 2 -1 11 111])
;;=> -15.880057803468203
    view source

    hedges-g

    (hedges-g [group1 group2])(hedges-g group1 group2)

    Hedges’s g effect size for two groups

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (hedges-g t c))
;;=> -0.42208932839491475
    view source

    hedges-g*

    (hedges-g* [group1 group2])(hedges-g* group1 group2)

    Less biased Hedges’s g effect size for two groups, J term correction.

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (hedges-g* t c))
;;=> -0.3989958628030656
    view source

    hedges-g-corrected

    (hedges-g-corrected [group1 group2])(hedges-g-corrected group1 group2)

    Cohen’s d corrected for small group size

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [10 20 30 40 40 50]]
  (hedges-g-corrected t c))
;;=> -0.3990662741188285
    view source

    histogram

    (histogram vs)(histogram vs bins-or-estimate-method)(histogram vs bins-or-estimate-method [mn mx])

    Calculate histogram.

    Returns map with keys:

    • :size - number of bins
    • :step - distance between bins
    • :bins - list of pairs of range lower value and number of hits
    • :min - min value
    • :max - max value
    • :samples - number of used samples

    For estimation methods check estimate-bins.

    If difference between min and max values is 0, number of bins is set to 1.

    Examples

    3 bins from uniform distribution.

    (histogram (repeatedly 1000 rand) 3)
;;=> {:bins ([0.0011357582159668977 340]
;;=>         [0.3340889989822621 341]
;;=>         [0.6670422397485573 319]),
;;=>  :max 0.9999954805148524,
;;=>  :min 0.0011357582159668977,
;;=>  :samples 1000,
;;=>  :size 3,
;;=>  :step 0.3329532407662952}

    3 bins from uniform distribution for given range.

    (histogram (repeatedly 10000 rand) 3 [0.1 0.5])
;;=> {:bins
;;=>  ([0.1 1336] [0.23333333333333334 1370] [0.3666666666666667 1333]),
;;=>  :max 0.5,
;;=>  :min 0.1,
;;=>  :samples 4039,
;;=>  :size 3,
;;=>  :step 0.13333333333333333}

    5 bins from normal distribution.

    (histogram (repeatedly 10000 r/grand) 5)
;;=> {:bins ([-3.4805958085123243 188]
;;=>         [-2.0755018370184155 2289]
;;=>         [-0.6704078655245067 5299]
;;=>         [0.7346861059694016 2069]
;;=>         [2.139780077463311 155]),
;;=>  :max 3.544874048957219,
;;=>  :min -3.4805958085123243,
;;=>  :samples 10000,
;;=>  :size 5,
;;=>  :step 1.4050939714939088}

    Estimate number of bins

    (:size (histogram (repeatedly 10000 r/grand)))
;;=> 64

    Estimate number of bins, Rice rule

    (:size (histogram (repeatedly 10000 r/grand) :rice))
;;=> 44
    view source

    hpdi-extent

    (hpdi-extent vs)(hpdi-extent vs size)

    Higher Posterior Density interval + median.

    size parameter is the target probability content of the interval.

    view source

    inner-fence-extent

    (inner-fence-extent vs)(inner-fence-extent vs estimation-strategy)

    Returns LIF, UIF and median

    view source

    iqr

    (iqr vs)(iqr vs estimation-strategy)

    Interquartile range.

    Examples

    IQR

    (iqr (repeatedly 100000 r/grand))
;;=> 1.3535813918712551
    view source

    jensen-shannon-divergence

    deprecated in Use [[dissimilarity]].

    (jensen-shannon-divergence [vs1 vs2])(jensen-shannon-divergence vs1 vs2)

    Jensen-Shannon divergence of two sequences.

    Examples

    Jensen-Shannon divergence

    (jensen-shannon-divergence (repeatedly 100 (fn* [] (r/irand 100)))
                           (repeatedly 100 (fn* [] (r/irand 100))))
;;=> 439.86198157468397
    view source

    kendall-correlation

    (kendall-correlation [vs1 vs2])(kendall-correlation vs1 vs2)

    Kendall’s correlation of two sequences.

    Examples

    Kendall’s correlation of uniform and gaussian distribution samples.

    (kendall-correlation (repeatedly 100000 (partial r/grand 1.0 10.0))
                     (repeatedly 100000 (partial r/drand -10.0 -5.0)))
;;=> -6.012940129401294E-4
    view source

    kruskal-test

    (kruskal-test xss)(kruskal-test xss {:keys [sides], :or {sides :right}})

    Kruskal-Wallis rank sum test.

    view source

    ks-test-one-sample

    (ks-test-one-sample xs)(ks-test-one-sample xs distribution-or-ys)(ks-test-one-sample xs distribution-or-ys {:keys [sides kernel bandwidth distinct?], :or {sides :two-sided, kernel :gaussian, distinct? true}})

    One sample Kolmogorov-Smirnov test

    view source

    ks-test-two-samples

    (ks-test-two-samples xs ys)(ks-test-two-samples xs ys {:keys [sides distinct?], :or {sides :two-sided, distinct? true}})

    Two samples Kolmogorov-Smirnov test

    view source

    kullback-leibler-divergence

    deprecated in Use [[dissimilarity]].

    (kullback-leibler-divergence [vs1 vs2])(kullback-leibler-divergence vs1 vs2)

    Kullback-Leibler divergence of two sequences.

    Examples

    Kullback-Leibler divergence.

    (kullback-leibler-divergence (repeatedly 100 (fn* [] (r/irand 100)))
                             (repeatedly 100 (fn* [] (r/irand 100))))
;;=> 1511.2029846076014
    view source

    kurtosis

    (kurtosis vs)(kurtosis vs typ)

    Calculate kurtosis from sequence.

    Possible typs: :G2 (default), :g2 (or :excess), :geary or :kurt.

    Examples

    Kurtosis

    (kurtosis [1 2 3 -1 -1 2 -1 11 111])
;;=> 8.732515263272099
(kurtosis [1 2 3 -1 -1 2 -1 11 111] :G2)
;;=> 8.732515263272099
(kurtosis [1 2 3 -1 -1 2 -1 11 111] :g2)
;;=> 3.9845705132178515
(kurtosis [1 2 3 -1 -1 2 -1 11 111] :excess)
;;=> 3.9845705132178515
(kurtosis [1 2 3 -1 -1 2 -1 11 111] :kurt)
;;=> 6.984570513217852
    view source

    L0

    Count equal values in both seqs. Same as count==

    view source

    L1

    (L1 [vs1 vs2-or-val])(L1 vs1 vs2-or-val)

    Manhattan distance

    view source

    L2

    (L2 [vs1 vs2-or-val])(L2 vs1 vs2-or-val)

    Euclidean distance

    view source

    L2sq

    (L2sq [vs1 vs2-or-val])(L2sq vs1 vs2-or-val)

    Squared euclidean distance

    view source

    levene-test

    (levene-test xss)(levene-test xss {:keys [sides statistic scorediff], :or {sides :one-sided-greater, statistic mean, scorediff abs}})
    view source

    LInf

    (LInf [vs1 vs2-or-val])(LInf vs1 vs2-or-val)

    Chebyshev distance

    view source

    mad

    Alias for median-absolute-deviation

    view source

    mad-extent

    (mad-extent vs)

    -/+ median-absolute-deviation and median

    Examples

    median absolute deviation from median for gaussian distribution

    (mad-extent (repeatedly 100000 r/grand))
;;=> [-0.6730878283010525 0.6797538719277473 0.003333021813347429]
    view source

    mae

    (mae [vs1 vs2-or-val])(mae vs1 vs2-or-val)

    Mean absolute error

    view source

    mape

    (mape [vs1 vs2-or-val])(mape vs1 vs2-or-val)

    Mean absolute percentage error

    view source

    maximum

    (maximum vs)

    Maximum value from sequence.

    Examples

    Maximum value

    (maximum [1 2 3 -1 -1 2 -1 11 111])
;;=> 111.0
    view source

    mcc

    (mcc group1 group2)(mcc ct)

    Matthews correlation coefficient also known as phi coefficient.

    view source

    me

    (me [vs1 vs2-or-val])(me vs1 vs2-or-val)

    Mean error

    view source

    mean

    (mean vs)

    Calculate mean of vs

    Examples

    Mean (average value)

    (mean [1 2 3 -1 -1 2 -1 11 111])
;;=> 14.111111111111109
    view source

    mean-absolute-deviation

    (mean-absolute-deviation vs)(mean-absolute-deviation vs center)

    Calculate mean absolute deviation

    view source

    means-ratio

    (means-ratio [group1 group2])(means-ratio group1 group2)(means-ratio group1 group2 adjusted?)

    Means ratio

    view source

    means-ratio-corrected

    (means-ratio-corrected [group1 group2])(means-ratio-corrected group1 group2)

    Bias correced means ratio

    view source

    median

    (median vs estimation-strategy)(median vs)

    Calculate median of vs. See median-3.

    Examples

    Median (percentile 50%).

    (median [1 2 3 -1 -1 2 -1 11 111])
;;=> 2.0

    For three elements use faster median-3.

    (median [7 1 4])
;;=> 4.0
    view source

    median-3

    (median-3 a b c)

    Median of three values. See median.

    Examples

    Median of 7 1 4

    (median-3 7 1 4)
;;=> 4.0
    view source

    median-absolute-deviation

    (median-absolute-deviation vs)(median-absolute-deviation vs center)(median-absolute-deviation vs center estimation-strategy)

    Calculate MAD

    Examples

    MAD

    (median-absolute-deviation [1 2 3 -1 -1 2 -1 11 111])
;;=> 3.0
    view source

    minimum

    (minimum vs)

    Minimum value from sequence.

    Examples

    Minimum value

    (minimum [1 2 3 -1 -1 2 -1 11 111])
;;=> -1.0
    view source

    minimum-discrimination-information-test

    (minimum-discrimination-information-test contingency-table-or-xs)(minimum-discrimination-information-test contingency-table-or-xs params)

    Minimum discrimination information test, a power divergence test for lambda -1.0

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    mode

    (mode vs method)(mode vs method opts)(mode vs)

    Find the value that appears most often in a dataset vs.

    For sample from continuous distribution, three algorithms are possible: * :histogram - calculated from histogram * :kde - calculated from KDE * :pearson - mode = mean-3(median-mean) * :default - discrete mode

    Histogram accepts optional :bins (see histogram). KDE method accepts :kde for kernel name (default :gaussian) and :bandwidth (auto). Pearson can accept :estimation-strategy for median.

    See also modes.

    Examples

    Example

    (mode [1 2 3 -1 -1 2 -1 11 111])
;;=> -1.0

    Returns lowest value when every element appears equally.

    (mode [5 1 2 3 4])
;;=> 1.0
    view source

    modes

    (modes vs method)(modes vs method opts)(modes vs)

    Find the values that appears most often in a dataset vs.

    Returns sequence with all most appearing values in increasing order.

    See also mode.

    Examples

    Example

    (modes [1 2 3 -1 -1 2 -1 11 111])
;;=> (-1.0)

    Returns lowest value when every element appears equally.

    (modes [5 5 1 1 2 3 4 4])
;;=> (1.0 4.0 5.0)
    view source

    moment

    (moment vs)(moment vs order)(moment vs order {:keys [absolute? center mean? normalize?], :or {mean? true}})

    Calculate moment (central or/and absolute) of given order (default: 2).

    Additional parameters as a map:

    • :absolute? - calculate sum as absolute values (default: false)
    • :mean? - returns mean (proper moment) or just sum of differences (default: true)
    • :center - value of center (default: nil = mean)
    • :normalize? - apply normalization by standard deviation to the order power

    Examples

    Usage

    (moment [3 7 5 9 -8])
;;=> 35.36
(moment [3 7 5 9 -8] 1.0)
;;=> 0.0
(moment [3 7 5 9 -8] 4.0)
;;=> 3417.171199999999
(moment [3 7 5 9 -8] 3.0)
;;=> -229.82399999999993
(moment [3 7 5 9 -8] 3.0 {:center 0.0})
;;=> 142.4
(moment [3 7 5 9 -8] 3.0 {:mean? false})
;;=> -1149.1199999999997
(moment [3 7 5 9 -8] 3.0 {:absolute? true})
;;=> 332.15039999999993
(moment [3 7 5 9 -8] 3.0 {:center -3.0})
;;=> 666.2
(moment [3 7 5 9 -8] 0.5 {:absolute? true})
;;=> 1.8986344545712772
    view source

    mse

    (mse [vs1 vs2-or-val])(mse vs1 vs2-or-val)

    Mean squared error

    view source

    multinomial-likelihood-ratio-test

    (multinomial-likelihood-ratio-test contingency-table-or-xs)(multinomial-likelihood-ratio-test contingency-table-or-xs params)

    Multinomial likelihood ratio test, a power divergence test for lambda 0.0

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    neyman-modified-chisq-test

    (neyman-modified-chisq-test contingency-table-or-xs)(neyman-modified-chisq-test contingency-table-or-xs params)

    Neyman modifield chi square test, a power divergence test for lambda -2.0

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    omega-sq

    (omega-sq [group1 group2])(omega-sq group1 group2)

    Adjusted R2

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]]
  (omega-sq t c))
;;=> -0.04795737122557726
    view source

    one-way-anova-test

    (one-way-anova-test xss)(one-way-anova-test xss {:keys [sides], :or {sides :one-sided-greater}})
    view source

    outer-fence-extent

    (outer-fence-extent vs)(outer-fence-extent vs estimation-strategy)

    Returns LOF, UOF and median

    view source

    outliers

    (outliers vs)(outliers vs estimation-strategy)(outliers vs q1 q3)

    Find outliers defined as values outside inner fences.

    Let Q1 is 25-percentile and Q3 is 75-percentile. IQR is (- Q3 Q1).

    • LIF (Lower Inner Fence) equals (- Q1 (* 1.5 IQR)).
    • UIF (Upper Inner Fence) equals (+ Q3 (* 1.5 IQR)).

    Returns sequence.

    Optional estimation-strategy argument can be set to change quantile calculations estimation type. See estimation-strategies.

    Examples

    Outliers

    (outliers [1 2 3 -1 -1 2 -1 11 111])
;;=> (111.0)

    Gaussian distribution outliers

    (count (outliers (repeatedly 3000000 r/grand)))
;;=> 20801
    view source

    p-overlap

    (p-overlap [group1 group2])(p-overlap group1 group2)(p-overlap group1 group2 {:keys [kde bandwidth min-iterations steps], :or {kde :gaussian, min-iterations 3, steps 500}})

    Overlapping index, kernel density approximation

    view source

    p-value

    (p-value stat)(p-value distribution stat)(p-value distribution stat sides)

    Calculate p-value for given distribution (default: N(0,1)), stat and sides (one of :two-sided, :one-sided-greater or :one-sided-less/:one-sided).

    view source

    pacf

    (pacf data)(pacf data lags)

    Caluclate pacf (partial autocorrelation function) for given number of lags.

    If lags is omitted function returns maximum possible number of lags.

    pacf returns also lag 0 (which is 0.0).

    See also acf, acf-ci, pacf-ci

    Examples

    Usage

    (pacf (repeatedly 1000 r/grand) 10)
;;=> (0.0
;;=>  -0.007493264913704033
;;=>  0.03950940288978749
;;=>  -0.027119682527161276
;;=>  -8.127647576342593E-4
;;=>  0.023184353076001057
;;=>  -0.07492493089581809
;;=>  -0.00415801721495847
;;=>  -0.029857518595778
;;=>  -0.025366182150073028
;;=>  0.02293649431732736)
(pacf [1 2 3 4 5 4 3 2 1])
;;=> (0.0
;;=>  0.5396825396825397
;;=>  -0.4299857803057234
;;=>  -0.388084834596935
;;=>  -0.2792571208141194
;;=>  0.17585056996358742
;;=>  -0.2652225487589841
;;=>  -0.17978918763554708
;;=>  -0.10771973872263883)
    view source

    pacf-ci

    (pacf-ci data)(pacf-ci data lags)(pacf-ci data lags alpha)

    pacf with added confidence interval data.

    Examples

    Usage

    (pacf-ci (repeatedly 1000 r/grand) 3)
;;=> {:ci 0.06197950323045615,
;;=>  :pacf
;;=>  (0.0 -0.04930794881410651 -0.005276481462760803 -0.03643226574541986)}
(pacf-ci [1 2 3 4 5 4 3 2 1] 3)
;;=> {:ci 0.653321328180018,
;;=>  :pacf (0.0 0.5396825396825397 -0.4299857803057234 -0.388084834596935)}
    view source

    pearson-correlation

    (pearson-correlation [vs1 vs2])(pearson-correlation vs1 vs2)

    Pearson’s correlation of two sequences.

    Examples

    Pearson’s correlation of uniform and gaussian distribution samples.

    (pearson-correlation (repeatedly 100000 (partial r/grand 1.0 10.0))
                     (repeatedly 100000 (partial r/drand -10.0 -5.0)))
;;=> -0.002465297102056219
    view source

    pearson-r

    (pearson-r [group1 group2])(pearson-r group1 group2)

    Pearson r correlation coefficient

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]]
  (pearson-r t c))
;;=> 0.2519763153394848
    view source

    percentile

    (percentile vs p)(percentile vs p estimation-strategy)

    Calculate percentile of a vs.

    Percentile p is from range 0-100.

    See docs.

    Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

    See also quantile.

    Examples

    Percentile 25%

    (percentile [1 2 3 -1 -1 2 -1 11 111] 25.0)
;;=> -1.0

    Percentile 50% (median)

    (percentile [1 2 3 -1 -1 2 -1 11 111] 50.0)
;;=> 2.0

    Percentile 75%

    (percentile [1 2 3 -1 -1 2 -1 11 111] 75.0)
;;=> 7.0

    Percentile 90%

    (percentile [1 2 3 -1 -1 2 -1 11 111] 90.0)
;;=> 111.0

    Various estimation strategies.

    (percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :legacy)
;;=> 61.0
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r1)
;;=> 11.0
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r2)
;;=> 11.0
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r3)
;;=> 11.0
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r4)
;;=> 8.199999999999996
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r5)
;;=> 25.999999999999858
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r6)
;;=> 61.0
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r7)
;;=> 9.399999999999999
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r8)
;;=> 37.66666666666675
(percentile [1 2 3 -1 -1 2 -1 11 111] 85.0 :r9)
;;=> 34.75000000000007
    view source

    percentile-bc-extent

    (percentile-bc-extent vs)(percentile-bc-extent vs p)(percentile-bc-extent vs p1 p2)(percentile-bc-extent vs p1 p2 estimation-strategy)

    Return bias corrected percentile range and mean for bootstrap samples. See https://projecteuclid.org/euclid.ss/1032280214

    p - calculates extent of bias corrected p and 100-p (default: p=2.5)

    Set estimation-strategy to :r7 to get the same result as in R coxed::bca.

    Examples

    for samples from gaussian distribution

    (percentile-bc-extent (repeatedly 100000 r/grand))
;;=> [-1.9686998976773415 1.9488455054357283 -0.001753000836894031]
(percentile-bc-extent (repeatedly 100000 r/grand) 10)
;;=> [-1.2644568505959903 1.2992608668913583 0.006974183450094526]
(percentile-bc-extent (repeatedly 100000 r/grand) 30 70)
;;=> [-0.5390348516759447 0.5110256349062376 7.918286580104579E-4]
    view source

    percentile-bca-extent

    (percentile-bca-extent vs)(percentile-bca-extent vs p)(percentile-bca-extent vs p1 p2)(percentile-bca-extent vs p1 p2 estimation-strategy)(percentile-bca-extent vs p1 p2 accel estimation-strategy)

    Return bias corrected percentile range and mean for bootstrap samples. Also accounts for variance variations throught the accelaration parameter. See https://projecteuclid.org/euclid.ss/1032280214

    p - calculates extent of bias corrected p and 100-p (default: p=2.5)

    Set estimation-strategy to :r7 to get the same result as in R coxed::bca.

    Examples

    for samples from gaussian distribution

    (percentile-bca-extent (repeatedly 100000 r/grand))
;;=> [-1.9611115428631776 1.9395600880977821 -0.0031832554346387315]
(percentile-bca-extent (repeatedly 100000 r/grand) 10)
;;=> [-1.2666928768037038 1.2838206326649084 0.0011417437187627867]
(percentile-bca-extent (repeatedly 100000 r/grand) 30 70)
;;=> [-0.5316035303243614 0.5241767534807082 0.001668106379069707]
    view source

    percentile-extent

    (percentile-extent vs)(percentile-extent vs p)(percentile-extent vs p1 p2)(percentile-extent vs p1 p2 estimation-strategy)

    Return percentile range and median.

    p - calculates extent of p and 100-p (default: p=25)

    Examples

    for samples from gaussian distribution

    (percentile-extent (repeatedly 100000 r/grand))
;;=> [-0.6811300265122471 0.67725176529625 0.002258912209196587]
(percentile-extent (repeatedly 100000 r/grand) 10)
;;=> [-1.2775454067052694 1.2710171173948166 7.651774916386039E-4]
(percentile-extent (repeatedly 100000 r/grand) 30 70)
;;=> [-0.5247561462693245 0.5243627229342358 -0.001450827530566729]
    view source

    percentiles

    (percentiles vs)(percentiles vs ps)(percentiles vs ps estimation-strategy)

    Calculate percentiles of a vs.

    Percentiles are sequence of values from range 0-100.

    See docs.

    Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

    See also quantile.

    Examples

    Usage

    (percentiles [1 2 3 -1 -1 2 -1 11 111] [25 50 75 90])
;;=> [-1.0 2.0 7.0 111.0]
    view source

    pi

    (pi vs)(pi vs size)(pi vs size estimation-strategy)

    Returns PI as a map, quantile intervals based on interval size.

    Quantiles are (1-size)/2 and 1-(1-size)/2

    view source

    pi-extent

    (pi-extent vs)(pi-extent vs size)(pi-extent vs size estimation-strategy)

    Returns PI extent, quantile intervals based on interval size + median.

    Quantiles are (1-size)/2 and 1-(1-size)/2

    view source

    pooled-stddev

    (pooled-stddev groups)(pooled-stddev groups method)

    Calculate pooled standard deviation for samples and method

    view source

    pooled-variance

    (pooled-variance groups)(pooled-variance groups method)

    Calculate pooled variance for samples and method.

    Methods: * :unbiased - sqrt of weighted average of variances (default) * :biased - biased version of :unbiased * :avg - sqrt of average of variances

    view source

    population-stddev

    (population-stddev vs)(population-stddev vs u)

    Calculate population standard deviation of vs.

    See stddev.

    Examples

    Population standard deviation.

    (population-stddev [1 2 3 -1 -1 2 -1 11 111])
;;=> 34.4333315406403
    view source

    population-variance

    (population-variance vs)(population-variance vs u)

    Calculate population variance of vs.

    See variance.

    Examples

    Population variance

    (population-variance [1 2 3 -1 -1 2 -1 11 111])
;;=> 1185.6543209876543
    view source

    power-divergence-test

    (power-divergence-test contingency-table-or-xs)(power-divergence-test contingency-table-or-xs {:keys [lambda ci-sides sides p alpha bootstrap-samples ddof bins], :or {lambda m/TWO_THIRD, sides :one-sided-greater, ci-sides :two-sided, alpha 0.05, bootstrap-samples 1000, ddof 0}})

    Power divergence test.

    First argument should be one of:

    • contingency table
    • sequence of counts (for goodness of fit)
    • sequence of data (for goodness of fit against distribution)

    For goodness of fit there are two options:

    • comparison of observed counts vs expected probabilities or weights (:p)
    • comparison of data against given distribution (:p), in this case histogram from data is created and compared to distribution PDF in bins ranges. Use :bins option to control histogram creation.

    Options are:

    view source

    powmean

    (powmean vs power)

    Generalized power mean

    Examples

    Power mean

    (powmean [1 2 3 1 1 2 1 11 111] 0.0)
;;=> 2.903203203730772
(powmean [1 2 3 1 1 2 1 11 111] 0.1)
;;=> 3.2703950036489737
(powmean [1 2 3 1 1 2 1 11 111] 0.5)
;;=> 6.201625343593919
(powmean [1 2 3 1 1 2 1 11 111] 1.0)
;;=> 14.777777777777782
(powmean [1 2 3 1 1 2 1 11 111] 2.0)
;;=> 37.21260240533814
(powmean [1 2 3 1 1 2 1 11 111] 3.0)
;;=> 53.381150691705734
(powmean [1 2 3 1 1 2 1 11 111] 5.5)
;;=> 74.44312203513597
    view source

    psnr

    (psnr [vs1 vs2-or-val])(psnr vs1 vs2-or-val)(psnr vs1 vs2-or-val max-value)

    Peak signal to noise, max-value is maximum possible value (default: max from vs1 and vs2)

    view source

    quantile

    (quantile vs q)(quantile vs q estimation-strategy)

    Calculate quantile of a vs.

    Quantile q is from range 0.0-1.0.

    See docs for interpolation strategy.

    Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

    See also percentile.

    Examples

    Quantile 0.25

    (quantile [1 2 3 -1 -1 2 -1 11 111] 0.25)
;;=> -1.0

    Quantile 0.5 (median)

    (quantile [1 2 3 -1 -1 2 -1 11 111] 0.5)
;;=> 2.0

    Quantile 0.75

    (quantile [1 2 3 -1 -1 2 -1 11 111] 0.75)
;;=> 7.0

    Quantile 0.9

    (quantile [1 2 3 -1 -1 2 -1 11 111] 0.9)
;;=> 111.0

    Various estimation strategies.

    (quantile [1 11 111 1111] 0.7 :legacy)
;;=> 611.0
(quantile [1 11 111 1111] 0.7 :r1)
;;=> 111.0
(quantile [1 11 111 1111] 0.7 :r2)
;;=> 111.0
(quantile [1 11 111 1111] 0.7 :r3)
;;=> 111.0
(quantile [1 11 111 1111] 0.7 :r4)
;;=> 90.99999999999999
(quantile [1 11 111 1111] 0.7 :r5)
;;=> 410.99999999999983
(quantile [1 11 111 1111] 0.7 :r6)
;;=> 611.0
(quantile [1 11 111 1111] 0.7 :r7)
;;=> 210.99999999999966
(quantile [1 11 111 1111] 0.7 :r8)
;;=> 477.66666666666623
(quantile [1 11 111 1111] 0.7 :r9)
;;=> 460.99999999999966
    view source

    quantile-extent

    (quantile-extent vs)(quantile-extent vs q)(quantile-extent vs q1 q2)(quantile-extent vs q1 q2 estimation-strategy)

    Return quantile range and median.

    q - calculates extent of q and 1.0-q (default: q=0.25)

    view source

    quantiles

    (quantiles vs)(quantiles vs qs)(quantiles vs qs estimation-strategy)

    Calculate quantiles of a vs.

    Quantilizes is sequence with values from range 0.0-1.0.

    See docs for interpolation strategy.

    Optionally you can provide estimation-strategy to change interpolation methods for selecting values. Default is :legacy. See more here

    See also percentiles.

    Examples

    Usage

    (quantiles [1 2 3 -1 -1 2 -1 11 111] [0.25 0.5 0.75 0.9])
;;=> [-1.0 2.0 7.0 111.0]
    view source

    r2

    (r2 [vs1 vs2-or-val])(r2 vs1 vs2-or-val)

    R2

    view source

    r2-determination

    (r2-determination [group1 group2])(r2-determination group1 group2)

    Coefficient of determination

    Examples

    Usage

    (let [t [10 10 20 20 20 30 30 30 40 50]
      c [-50 20 30 40 40 50 10 20 30 10]]
  (r2-determination t c))
;;=> 0.06349206349206347
    view source

    rank-epsilon-sq

    (rank-epsilon-sq xs)

    Effect size for Kruskal-Wallis test

    view source

    rank-eta-sq

    (rank-eta-sq xs)

    Effect size for Kruskal-Wallis test

    view source

    rescale

    (rescale vs)(rescale vs low high)

    Lineary rascale data to desired range, 0,1 by default

    view source

    rmse

    (rmse [vs1 vs2-or-val])(rmse vs1 vs2-or-val)

    Root mean squared error

    view source

    robust-standardize

    (robust-standardize vs)(robust-standardize vs q)

    Normalize samples to have median = 0 and MAD = 1.

    If q argument is used, scaling is done by quantile difference (Q_q, Q_(1-q)). Set 0.25 for IQR.

    view source

    rows->contingency-table

    (rows->contingency-table xss)
    view source

    rss

    (rss [vs1 vs2-or-val])(rss vs1 vs2-or-val)

    Residual sum of squares

    view source

    second-moment

    deprecated in Use [[moment]] function

    view source

    sem

    (sem vs)

    Standard error of mean

    Examples

    SEM

    (sem [1 2 3 -1 -1 2 -1 11 111])
;;=> 12.174021115615695
    view source

    sem-extent

    (sem-extent vs)

    -/+ sem and mean

    Examples

    standard error of mean and mean for gaussian distribution

    (sem-extent (repeatedly 100000 r/grand))
;;=> [6.802850148960229E-4 0.007013149643892707 0.003846717329394365]
    view source

    similarity

    (similarity method P-observed Q-expected)(similarity method P-observed Q-expected {:keys [bins probabilities? epsilon], :or {probabilities? true, epsilon 1.0E-6}})

    Various PDF similarities between two histograms (frequencies) or probabilities.

    Q can be a distribution object. Then, histogram will be created out of P.

    Arguments:

    • method - distance method
    • P-observed - frequencies, probabilities or actual data (when Q is a distribution)
    • Q-expected - frequencies, probabilities or distribution object (when P is a data)

    Options:

    • :probabilities? - should P/Q be converted to a probabilities, default: true.
    • :epsilon - small number which replaces 0.0 when division or logarithm is used`
    • :bins - number of bins or bins estimation method, see histogram.

    The list of methods: :intersection, :czekanowski, :motyka, :kulczynski, :ruzicka, :inner-product, :harmonic-mean, :cosine, :jaccard, :dice, :fidelity, :squared-chord

    See more: Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions by Sung-Hyuk Cha

    view source

    skewness

    (skewness vs)(skewness vs typ)

    Calculate skewness from sequence.

    Possible types: :G1 (default), :g1 (:pearson), :b1, :B1 (:yule), :B3, :skew, :mode or :median.

    Examples

    Skewness

    (skewness [1 2 3 -1 -1 2 -1 11 111])
;;=> 2.94268445417954
(skewness [1 2 3 -1 -1 2 -1 11 111] :G1)
;;=> 2.94268445417954
(skewness [1 2 3 -1 -1 2 -1 11 111] :g1)
;;=> 2.4275908211830184
(skewness [1 2 3 -1 -1 2 -1 11 111] :pearson)
;;=> 2.4275908211830184
(skewness [1 2 3 -1 -1 2 -1 11 111] :b1)
;;=> 2.034448511531534
(skewness [1 2 3 -1 -1 2 -1 11 111] :B1)
;;=> 0.25
(skewness [1 2 3 -1 -1 2 -1 11 111] :yule)
;;=> 0.25
(skewness [1 2 3 -1 -1 2 -1 11 111] :B3)
;;=> 0.8449612403100772
(skewness [1 2 3 -1 -1 2 -1 11 111] :mode)
;;=> 0.4137529407252298
(skewness [1 2 3 -1 -1 2 -1 11 111] :median)
;;=> 0.9948324383613981
(skewness [1 2 3 -1 -1 2 -1 11 111] :skew)
;;=> 0.8091969403943394
    view source

    span

    (span vs)

    Width of the sample, maximum value minus minimum value

    view source

    spearman-correlation

    (spearman-correlation [vs1 vs2])(spearman-correlation vs1 vs2)

    Spearman’s correlation of two sequences.

    Examples

    Spearsman’s correlation of uniform and gaussian distribution samples.

    (spearman-correlation (repeatedly 100000 (partial r/grand 1.0 10.0))
                      (repeatedly 100000 (partial r/drand -10.0 -5.0)))
;;=> -0.0020795592460891798
    view source

    standardize

    (standardize vs)

    Normalize samples to have mean = 0 and stddev = 1.

    Examples

    Standardize

    (standardize [1 2 3 -1 -1 2 -1 11 111])
;;=> (-0.3589915220998317
;;=>  -0.33161081278713267
;;=>  -0.30423010347443363
;;=>  -0.4137529407252298
;;=>  -0.4137529407252298
;;=>  -0.33161081278713267
;;=>  -0.4137529407252298
;;=>  -0.08518442897284138
;;=>  2.652886502297062)
    view source

    stats-map

    (stats-map vs)(stats-map vs estimation-strategy)

    Calculate several statistics of vs and return as map.

    Optional estimation-strategy argument can be set to change quantile calculations estimation type. See estimation-strategies.

    Examples

    Stats

    (stats-map [1 2 3 -1 -1 2 -1 11 111])
;;=> {:IQR 8.0,
;;=>  :Kurtosis 8.732515263272099,
;;=>  :LAV -1.0,
;;=>  :LIF -13.0,
;;=>  :LOF -25.0,
;;=>  :MAD 3.0,
;;=>  :Max 111.0,
;;=>  :Mean 14.11111111111111,
;;=>  :Median 2.0,
;;=>  :Min -1.0,
;;=>  :Mode -1.0,
;;=>  :Outliers (111.0),
;;=>  :Q1 -1.0,
;;=>  :Q3 7.0,
;;=>  :Range 112.0,
;;=>  :SD 36.522063346847084,
;;=>  :SEM 12.174021115615695,
;;=>  :Size 9,
;;=>  :Skewness 2.94268445417954,
;;=>  :Total 127.0,
;;=>  :UAV 11.0,
;;=>  :UIF 19.0,
;;=>  :UOF 31.0,
;;=>  :Variance 1333.8611111111113}
    view source

    stddev

    (stddev vs)(stddev vs u)

    Calculate standard deviation of vs.

    See population-stddev.

    Examples

    Standard deviation.

    (stddev [1 2 3 -1 -1 2 -1 11 111])
;;=> 36.522063346847084
    view source

    stddev-extent

    (stddev-extent vs)

    -/+ stddev and mean

    Examples

    standard deviation from mean and mean for gaussian distribution

    (stddev-extent (repeatedly 100000 r/grand))
;;=> [-0.9996022983939234 0.9951962468655247 -0.0022030257641994337]
    view source

    sum

    (sum vs)

    Sum of all vs values.

    Examples

    Sum

    (sum [1 2 3 -1 -1 2 -1 11 111])
;;=> 127.0
    view source

    t-test-one-sample

    (t-test-one-sample xs)(t-test-one-sample xs m)

    One sample Student’s t-test

    • alpha - significance level (default: 0.05)
    • sides - one of: :two-sided, :one-sided-less (short: :one-sided) or :one-sided-greater
    • mu - mean (default: 0.0)
    view source

    t-test-two-samples

    (t-test-two-samples xs ys)(t-test-two-samples xs ys {:keys [paired? equal-variances?], :or {paired? false, equal-variances? false}, :as params})

    Two samples Student’s t-test

    • alpha - significance level (default: 0.05)
    • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
    • mu - mean (default: 0.0)
    • paired? - unpaired or paired test, boolean (default: false)
    • equal-variances? - unequal or equal variances, boolean (default: false)
    view source

    trim

    (trim vs)(trim vs quantile)(trim vs quantile estimation-strategy)(trim vs low high nan)

    Return trimmed data. Trim is done by using quantiles, by default is set to 0.2.

    view source

    tschuprows-t

    (tschuprows-t group1 group2)(tschuprows-t contingency-table)

    Tschuprows T effect size for discrete data

    Examples

    Usage

    (let [a [:a :a :b :b :f :a :a :b :b :c :a :a :b :b :c :a :a :b :b :c]
      b [:b :f :a :a :b :b :y :z :c :b :b :c :a :a :b :b :c :a :a :b]]
  (tschuprows-t a b))
;;=> 0.5288813325243744
    view source

    ttest-one-sample

    deprecated in Use [[t-test-one-sample]]

    Examples

    Usage

    (ttest-one-sample [1 2 3 4 5 6 7 8 9 10])
;;=> {:alpha 0.05,
;;=>  :confidence-interval [3.3341494103317983 7.665850589668201],
;;=>  :df 9,
;;=>  :estimate 5.5,
;;=>  :level 0.95,
;;=>  :mu 0.0,
;;=>  :n 10,
;;=>  :p-value 2.7819601104828173E-4,
;;=>  :stat 5.744562646538029,
;;=>  :stderr 0.9574271077563381,
;;=>  :t 5.744562646538029,
;;=>  :test-type :two-sided}
(ttest-one-sample [1 2 3 4 5 6 7 8 9 10] {:alpha 0.2})
;;=> {:alpha 0.2,
;;=>  :confidence-interval [4.175850795053416 6.824149204946584],
;;=>  :df 9,
;;=>  :estimate 5.5,
;;=>  :level 0.8,
;;=>  :mu 0.0,
;;=>  :n 10,
;;=>  :p-value 2.7819601104828173E-4,
;;=>  :stat 5.744562646538029,
;;=>  :stderr 0.9574271077563381,
;;=>  :t 5.744562646538029,
;;=>  :test-type :two-sided}
(ttest-one-sample [1 2 3 4 5 6 7 8 9 10] {:sides :one-sided})
;;=> {:alpha 0.05,
;;=>  :confidence-interval [##-Inf 7.255072013309326],
;;=>  :df 9,
;;=>  :estimate 5.5,
;;=>  :level 0.95,
;;=>  :mu 0.0,
;;=>  :n 10,
;;=>  :p-value 0.9998609019944759,
;;=>  :stat 5.744562646538029,
;;=>  :stderr 0.9574271077563381,
;;=>  :t 5.744562646538029,
;;=>  :test-type :one-sided}
(ttest-one-sample [1 2 3 4 5 6 7 8 9 10] {:mu 5.0})
;;=> {:alpha 0.05,
;;=>  :confidence-interval [3.334149410331798 7.665850589668201],
;;=>  :df 9,
;;=>  :estimate 5.5,
;;=>  :level 0.95,
;;=>  :mu 5.0,
;;=>  :n 10,
;;=>  :p-value 0.6141172548083933,
;;=>  :stat 0.5222329678670935,
;;=>  :stderr 0.9574271077563381,
;;=>  :t 0.5222329678670935,
;;=>  :test-type :two-sided}
    view source

    ttest-two-samples

    deprecated in Use [[t-test-two-samples]]

    Examples

    Usage

    (ttest-two-samples [1 2 3 4 5 6 7 8 9 10]
                   [7 8 9 10 11 12 13 14 15 16 17 18 19 20])
;;=> {:alpha 0.05,
;;=>  :confidence-interval [-11.052801725158163 -4.9471982748418375],
;;=>  :df 21.982212340188994,
;;=>  :equal-variances? false,
;;=>  :estimate -8.0,
;;=>  :estimated-mu [5.5 13.5],
;;=>  :level 0.95,
;;=>  :mu 0.0,
;;=>  :n [10 14],
;;=>  :nx 10,
;;=>  :ny 14,
;;=>  :p-value 1.8552818325118146E-5,
;;=>  :paired? false,
;;=>  :sides :two-sided,
;;=>  :stat -5.4349297638940595,
;;=>  :stderr 1.4719601443879746,
;;=>  :t -5.4349297638940595,
;;=>  :test-type :two-sided}
(ttest-two-samples [1 2 3 4 5 6 7 8 9 10]
                   [7 8 9 10 11 12 13 14 15 16 17 18 19 20 200])
;;=> {:alpha 0.05,
;;=>  :confidence-interval [-47.242899887102105 6.376233220435439],
;;=>  :df 14.164598953012467,
;;=>  :equal-variances? false,
;;=>  :estimate -20.43333333333333,
;;=>  :estimated-mu [5.5 25.93333333333333],
;;=>  :level 0.95,
;;=>  :mu 0.0,
;;=>  :n [10 15],
;;=>  :nx 10,
;;=>  :ny 15,
;;=>  :p-value 0.12451349808974498,
;;=>  :paired? false,
;;=>  :sides :two-sided,
;;=>  :stat -1.632902633201205,
;;=>  :stderr 12.51350381698818,
;;=>  :t -1.632902633201205,
;;=>  :test-type :two-sided}
(ttest-two-samples [1 2 3 4 5 6 7 8 9 10]
                   [7 8 9 10 11 12 13 14 15 16 17 18 19 20]
                   {:equal-variances? true})
;;=> {:alpha 0.05,
;;=>  :confidence-interval [-11.22324472988163 -4.77675527011837],
;;=>  :df 22.0,
;;=>  :equal-variances? true,
;;=>  :estimate -8.0,
;;=>  :estimated-mu [5.5 13.5],
;;=>  :level 0.95,
;;=>  :mu 0.0,
;;=>  :n [10 14],
;;=>  :nx 10,
;;=>  :ny 14,
;;=>  :p-value 3.690577215911943E-5,
;;=>  :paired? false,
;;=>  :sides :two-sided,
;;=>  :stat -5.147292847304685,
;;=>  :stderr 1.5542150480497916,
;;=>  :t -5.147292847304685,
;;=>  :test-type :two-sided}
(ttest-two-samples [1 2 3 4 5 6 7 8 9 10]
                   [200 11 200 11 200 11 200 11 200 11]
                   {:paired? true})
;;=> {:alpha 0.05,
;;=>  :confidence-interval [-171.66671936335894 -28.333280636641092],
;;=>  :df 9,
;;=>  :estimate -100.0,
;;=>  :level 0.95,
;;=>  :mu 0.0,
;;=>  :n 10,
;;=>  :p-value 0.011615504295919215,
;;=>  :paired? true,
;;=>  :stat -3.156496045715208,
;;=>  :stderr 31.680698645494967,
;;=>  :t -3.156496045715208,
;;=>  :test-type :two-sided}
    view source

    variance

    (variance vs)(variance vs u)

    Calculate variance of vs.

    See population-variance.

    Examples

    Variance.

    (variance [1 2 3 -1 -1 2 -1 11 111])
;;=> 1333.861111111111
    view source

    variation

    (variation vs)

    Coefficient of variation CV = stddev / mean

    view source

    weighted-kappa

    (weighted-kappa contingency-table)(weighted-kappa contingency-table weights)

    Cohen’s weighted kappa for indexed contingency table

    view source

    winsor

    (winsor vs)(winsor vs quantile)(winsor vs quantile estimation-strategy)(winsor vs low high nan)

    Return winsorized data. Trim is done by using quantiles, by default is set to 0.2.

    view source

    wmean

    (wmean vs)(wmean vs weights)

    Weighted mean

    view source

    wmedian

    (wmedian vs ws)(wmedian vs ws method)

    Weighted median.

    Calculation is done using interpolation. There are three methods: * :linear - linear interpolation, default * :step - step interpolation * :average - average of ties

    Based on spatstat.geom::weighted.quantile from R.

    view source

    wmw-odds

    (wmw-odds [group1 group2])(wmw-odds group1 group2)

    Wilcoxon-Mann-Whitney odds

    view source

    wquantile

    (wquantile vs ws q)(wquantile vs ws q method)

    Weighted quantile.

    Calculation is done using interpolation. There are three methods: * :linear - linear interpolation, default * :step - step interpolation * :average - average of ties

    Based on spatstat.geom::weighted.quantile from R.

    view source

    wquantiles

    (wquantiles vs ws)(wquantiles vs ws qs)(wquantiles vs ws qs method)

    Weighted quantiles.

    Calculation is done using interpolation. There are three methods: * :linear - linear interpolation, default * :step - step interpolation * :average - average of ties

    Based on spatstat.geom::weighted.quantile from R.

    view source

    z-test-one-sample

    (z-test-one-sample xs)(z-test-one-sample xs m)

    One sample z-test

    • alpha - significance level (default: 0.05)
    • sides - one of: :two-sided, :one-sided-less (short: :one-sided) or :one-sided-greater
    • mu - mean (default: 0.0)
    view source

    z-test-two-samples

    (z-test-two-samples xs ys)(z-test-two-samples xs ys {:keys [paired? equal-variances?], :or {paired? false, equal-variances? false}, :as params})

    Two samples z-test

    • alpha - significance level (default: 0.05)
    • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
    • mu - mean (default: 0.0)
    • paired? - unpaired or paired test, boolean (default: false)
    • equal-variances? - unequal or equal variances, boolean (default: false)
    view source