median
The median of a list, exact.
xs(array) --
Statistics
mode
The most frequent value(s) of a list, as an array.
xs(array) --
variance
Population variance (divide by n), exact.
xs(array) --
sampleVariance
Sample variance (divide by n - 1), exact.
xs(array) --
stdDev
Population standard deviation, exact (a surd when needed).
xs(array) --
sampleStdDev
Sample standard deviation (n - 1), exact.
xs(array) --
covariance
Population covariance of two equal-length lists, exact.
xs(array) --ys(array) --
correlation
Pearson correlation coefficient of two lists, exact.
xs(array) --ys(array) --
percentile
The p-th percentile of a list (p from 0 to 100).
xs(array) --p(number) -- 0 to 100
zScore
How many standard deviations x lies from the mean of the list.
xs(array) --x(number) --
dataRange
max - min of a list. (range() makes an array of whole numbers.)
xs(array) --
fiveNumberSummary
Minimum, first quartile, median, third quartile and maximum. The quartiles are by the halves method of school courses and the SAT/ACT: Q1 is the median of the lower half, Q3 of the upper half, the middle value left out of both when the count is odd ([1, 2, ..., 8]: 2.5 and 6.5). Exact for exact data.
xs(array) --
iqr
Interquartile range: third quartile minus first quartile, the quartiles by the halves method (as fiveNumberSummary).
xs(array) --
binCounts
Frequency counts of a list in equal-width bins from lower to upper. (histogram() draws one.)
xs(array) --lower(number) --upper(number) --bins(integer) --
chiSquareTest
The chi-square goodness-of-fit test as the AP Biology equations sheet gives it: observed counts against an expected ratio (9:3:3:1 as [9, 3, 3, 1]) or the expected counts themselves. Gives expected (the counts the ratio predicts), contributions ((o - e)^2/e for each outcome), chi_square (exact when the counts are), df (outcomes minus one), p_value (the upper tail), critical_05 and critical_01 (the sheet's table: the quantile to two places), and decision_05, decision_01: reject null hypothesis when chi_square is greater than the critical value, else fail to reject null hypothesis.
observed(array) -- the observed counts, two or moreratio(array) -- the expected ratio, or the expected counts, one for each observed count; every one above 0
tTest
One-sample t test of a mean from data. Gives t, df, p, estimate (the sample mean), se. Numerical. The alternative is "two_sided" (the default), "less" or "greater".
data(array) --mu0(number) -- the null valuealternative(string) -- optional
tTestSummary
tTest from the sample mean, standard deviation and size.
mean(number) --s(number) --n(number) --mu0(number) --alternative(string) -- optional
tInterval
t confidence interval for a mean from data. Gives lower, upper, estimate, margin, critical, se. The level is written 0.95, not 95.
data(array) --confidence(number) --
tIntervalSummary
tInterval from the sample mean, standard deviation and size.
mean(number) --s(number) --n(number) --confidence(number) --
tTest2
Two-sample t test of mean1 - mean2 from data: Welch's, no equal variances assumed, with Satterthwaite's df (not rounded). Gives t, df, p, estimate, se.
data1(array) --data2(array) --alternative(string) -- optional
tTest2Summary
tTest2 from each sample's mean, standard deviation and size.
mean1(number) --s1(number) --n1(number) --mean2(number) --s2(number) --n2(number) --alternative(string) -- optional
tInterval2
Welch's confidence interval for mean1 - mean2 from data.
data1(array) --data2(array) --confidence(number) --
tInterval2Summary
tInterval2 from each sample's mean, standard deviation and size.
mean1(number) --s1(number) --n1(number) --mean2(number) --s2(number) --n2(number) --confidence(number) --
tTestPaired
Paired t test: the one-sample test of the differences data1 - data2 against 0.
data1(array) --data2(array) -- the same lengthalternative(string) -- optional
tIntervalPaired
t confidence interval for the mean of the differences data1 - data2.
data1(array) --data2(array) -- the same lengthconfidence(number) --
zTestProportion
One-proportion z test, x successes in n against p0, the standard error from p0. Gives z, p, estimate, se. Numerical.
x(number) --n(number) --p0(number) --alternative(string) -- optional
zIntervalProportion
One-proportion z interval, the standard error from the sample proportion.
x(number) --n(number) --confidence(number) --
zTest2Proportions
Two-proportion z test of p1 - p2, the standard error from the pooled proportion.
x1(number) --n1(number) --x2(number) --n2(number) --alternative(string) -- optional
zInterval2Proportions
Two-proportion z interval for p1 - p2, the standard error from the two separate proportions (not pooled).
x1(number) --n1(number) --x2(number) --n2(number) --confidence(number) --
chiSquareTable
Chi-square test of a table of counts, the test of independence and of homogeneity being this one computation, with no continuity correction. Gives chi_square, df, p, expected (a matrix). For goodness of fit use chiSquareTest.
table(matrix) --
oneWayAnova
One-way analysis of variance of a list of groups. Gives f, p, df_between, df_within, ss_between, ss_within, ms_between, ms_within. Numerical.
groups(list) -- a list of arrays
slopeTest
The t test of a regression slope against 0. Gives t, df (n - 2), p, slope, intercept, se, s, r_squared, residuals. A perfect fit is refused: it has no standard error.
xs(array) --ys(array) --alternative(string) -- optional
slopeInterval
The t confidence interval for a regression slope.
xs(array) --ys(array) --confidence(number) --