Statistics

Over One Variable

Elements that calculate different statistics with the self-descriptive names:

• average calculates the arithmetic mean.
• standard_deviation square root of dispersion for a set of values
• dispersion dispersion for a set of values (Σ((x - x̅)^2) / n), , where n is the sample size and x̅ is the average value of x
• median median of a numeric data sample
• entropy calculates Shannon entropy of a set of values
• skew skewness of a set of values
• kurtosis kurtosis of a set of values
• quantileapproximate quantile of a numeric data sequence (have level argument from 0 to 1, 0.5 is median)

For example to calculate average reward:

average(of: Reward_Total)

Over Two Variables

Some statistics require 2 variables. One variable is specified in of attribute, the other in with attribute, for example:

correlation(of: Reward_Total with: Block_GasUsed)

Elements that calculate different statistics with the self-descriptive names:

• covariance value of Σ((x - x̅)(y - y̅)) / n
• correlation pearson correlation coefficient: Σ((x - x̅)(y - y̅)) / sqrt(Σ((x - x̅)^2) * Σ((y - y̅)^2))
• contingency calculates the contingency coefficient, a value that measures the association between two columns in a table. The computation is similar to the cramersV function but with a different denominator in the square root. Note that this coefficient does not reach 1 even for a near-deterministic relationship — its maximum depends on the dimensions of the underlying table. On data where cramers approaches 1, this coefficient sits well below it. Do not read it on a 0–1 scale or compare it directly with Cramér's V; for association strength prefer cramers_bias_corrected
• rank_correlation rank correlation coefficient of the ranks of x and y. The value of the correlation coefficient ranges from -1 to +1. The value close to +1 denotes a high linear relationship, and with an increase of one random variable, the second random variable also increases. The value close to -1 denotes a high linear relationship, and with an increase of one random variable, the second random variable decreases. The value close or equal to 0 denotes no relationship between the two random variables.
• cramers Cramér's V (sometimes referred to as Cramér's phi) is a measure of association between two columns in a table. The result of the cramers function ranges from 0 (corresponding to no association between the variables) to 1 and can reach 1 only when each value is completely determined by the other. It may be viewed as the association between two variables as a percentage of their maximum possible variation.
• cramers_bias_corrected Cramér's V is a measure of association between two columns in a table. The result of the cramersV function ranges from 0 (corresponding to no association between the variables) to 1 and can reach 1 only when each value is completely determined by the other. The function can be heavily biased, so this version of Cramér's V uses the bias correction.
• theils_corrected calculates the Theil's U uncertainty coefficient, a value that measures the association between two columns in a table. A value of 0.0 indicates the absence of association, and the magnitude grows towards 1.0 as association strengthens.
  The metric is named theils_corrected, not theils

  Querying theils fails with Cannot query field "theils". Note also that a strong association returns a value near −1, not +1 — interpret magnitude, not sign.

The following are also available and are not listed above:

• gini Gini coefficient of the values — 0 is perfectly even, 1 is fully concentrated
• theil_index Theil index, an entropy-based concentration measure
• entropy Shannon entropy of the value distribution, in bits
• nakamoto the number of rows that together account for ratio of the total of of (takes ratio, not if)
• skew, kurtosis, dispersion, median, quantile distribution shape and position

tip

You can use a condition on any of these metrics except gini, nakamoto and theil_index, which do not accept an if argument.