The Machines · Runtime stack

seedstats

A reckoner seed: stats's descriptive layer (machines/seeds/seedstats.shoddy)

Summary

seedstats bridges the eleven statistics words a data session reaches for: MEAN MEDIAN STDDEV STDDEVP VAR SUM QUANTILE CORREL NORMCDF NORMINV TCDF. stats carries a much larger surface: skewness, the t/F/chi-squared tests, ANOVA, confidence intervals. Those are deliberately left for a future seed rather than bridged wholesale here. The promise is that a domain arrives with zero engine changes whenever it is wanted. That does not mean every word in a machine arrives on day one.

Why It's Useful

Guarded where stats.shoddy is not. Mean, Median, StdDev, Var and Quantile all divide, index or Error somewhere inside on an empty or too-short list. Every guard here runs before the call that would otherwise abort. CORREL refuses two lists of different lengths. It also refuses a list that does not vary (one whose standard deviation, the spread measure, is zero) before Correl's own division sees either.

User's Guide

Let st0 = RckSeedStats(RckNew())
RckEval(st0, "{ 12500 13100 11900 } MEAN")     ' x: 12500
RckEval(st0, "{ 12500 13100 11900 } STDDEV")    ' x: 606.9...
RckEval(st0, "{ 1 2 3 4 5 } 0.5 QUANTILE")     ' x: 3

Every list-taking word pops exactly one cell: the list as a single value, never one value per element. That is cuttle's single-cell contract. So a data column loaded from a file goes straight in.

Word Reference

Word	Description
MEAN ( xs -- m )	The arithmetic mean of a list of numbers; refuses an empty list.
MEDIAN ( xs -- m )	The middle value of a list of numbers; refuses an empty list.
STDDEV ( xs -- s )	Sample standard deviation (divides by n-1); refuses fewer than two values.
STDDEVP ( xs -- s )	Population standard deviation (divides by n); refuses an empty list.
VAR ( xs -- v )	Sample variance (divides by n-1); refuses fewer than two values.
SUM ( xs -- s )	The total of a list of numbers; 0 for an empty list.
QUANTILE ( xs p -- q )	The value at fraction p (0 to 1) into the sorted list; refuses an empty list or p outside 0..1.
CORREL ( xs ys -- r )	Pearson correlation between two lists of numbers of the same length; refuses mismatched lengths, fewer than two values, or a list that does not vary.
NORMCDF ( z -- p )	The standard normal cumulative distribution at z.
NORMINV ( p -- z )	The standard normal quantile for probability p; refuses p outside the open interval 0..1.
TCDF ( t df -- p )	The Student's t cumulative distribution at t with df degrees of freedom; refuses a non-positive df.

Who Uses It

	User	How
	halifax	A list to a statistic in one line: { 12500 13100 11900 } MEAN is the mill's headline example, and MEDIAN, STDDEV, QUANTILE and CORREL come with it.
	sparky	Sparky folds it too, so a model calling eval reaches the same words halifax puts at a prompt.

A mill (a complete Shoddy program) claims this seed by folding RckSeedStats over its reckoner state. That is all halifax does.

The Machines It Uses

	Machine	Why
	cuttle	The Cell type a LIST argument is read out of.
	reckoner	RckReg, RckSeeding and the argument readers every registered word is built from.
	seq	List plumbing under the LIST-of-NUMBER reader every word here shares.
	stats	The domain this seed bridges: Mean, StdDev, Quantile, Correl and the normal/t distributions.