Statistics and combinatorics

examples/09-statistics.axis

"Statistics"

data = [2, 4, 4, 4, 5, 5, 7, 9] @ hidden

folder "Summaries" {
    "Each of these reduces the list to a single number."
    n = length(data) @ hidden
    tot = total(data) @ hidden
    avg = mean(data) @ hidden
    mid = median(data) @ hidden
    low = min(data) @ hidden
    high = max(data) @ hidden
}

folder "Spread" {
    "Sample and population standard deviation, variance, mean absolute deviation."
    s = stdev(data) @ hidden
    sp = stdevp(data) @ hidden
    v = var(data) @ hidden
    vp = varp(data) @ hidden
    dev = mad(data) @ hidden
}

folder "Where a value falls" {
    "The quantile a fraction of the way through the list, and a quartile."
    q9 = quantile(data, 0.9) @ hidden
    q1 = quartile(data, 1) @ hidden
    "How far the mean is from 4, in standard errors."
    t = tscore(data, 4) @ hidden
    "Shown as the fraction it is."
    third = 1 / 3 @ displayEvaluationAsFraction
}

folder "Two lists" {
    "A second list, paired with the first."
    other = [1, 3, 2, 5, 4, 6, 8, 9] @ hidden
    r = corr(data, other) @ hidden
    rho = spearman(data, other) @ hidden
    c = cov(data, other) @ hidden
    cp = covp(data, other) @ hidden
}

folder "Distributions" {
    "A distribution is drawn as its density, and read with its members."
    N = normaldist(avg, s) @ color: ORANGE, hidden
    y = N.pdf(x) @ color: ORANGE, lineWidth: 3
    below = N.cdf(5) @ hidden
    within = N.cdf(avg - s, avg + s) @ hidden
    "Shaded between two bounds, a distribution shows the probability of landing there."
    normaldist(0, 1) @ color: PURPLE, cdf: -1..1
    B = binomialdist(8, 0.5) @ hidden
    heads = B.pdf(4) @ hidden
}

folder "Testing" {
    "Is the mean of data different from 4? A t-test says how surprising the sample is if it were."
    T = ttest(data).null(4) @ hidden
    tp = T.pright @ hidden
    "A 95% confidence interval for the mean."
    ci_low = ttest(data).conf(0.95).lower @ hidden
    ci_high = ttest(data).conf(0.95).upper @ hidden
}

folder "Seeing the data" {
    "The samples along a line."
    (data, 0) @ color: BLUE, pointSize: 14
    "The mean, and one standard deviation either side."
    x = avg @ color: RED, lineWidth: 3
    x = avg - s @ color: RED, lineStyle: DASHED, lineOpacity: 0.6
    x = avg + s @ color: RED, lineStyle: DASHED, lineOpacity: 0.6
    "A bell curve over the same centre and spread."
    y = exp(-0.5 * ((x - avg) / s) ^ 2) @ color: GREEN, lineWidth: 3
}

folder "Charts" {
    "A histogram of the data in bins of width 2, a dot plot over it, and a box plot above both."
    histogram(data, 2) @ color: BLUE, binAlignment: left
    dotplot(data) @ color: PURPLE
    boxplot(data) @ color: GREEN, axisOffset: 8, breadth: 1.5
    "The same numbers, as a row of summary statistics."
    stats(data)
}

folder "Combinatorics" {
    "Choose, permute, factorial."
    ways = nCr(5, 2) @ hidden
    orders = nPr(5, 2) @ hidden
    fact = factorial(5) @ hidden
    "Row 6 of Pascal's triangle, as points."
    K = [0, 1, 2, 3, 4, 5, 6] @ hidden
    (K, nCr(6, K)) @ color: PURPLE, pointSize: 14
}

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