anova_oneway

std.stats.anova_oneway · Level L5

One-way analysis of variance for g groups of n observations each, the rows of X: [F, d₁, d₂, p] with F the ratio of the between-group to the within-group mean square, d₁ = g − 1, d₂ = g(n − 1), and p = P(F_{d₁,d₂} > F). Calls f_sf.

F = (SSB/(g−1)) / (SSW/(g(n−1))), p = P(F_{g−1, g(n−1)} > F)

Signature

anova_oneway(X: f64[g, n]) → f64[4]

Requires: g, n ≥ 2

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size with g, n ≥ 2.
Agrees with the reference F from the between- and within-group sums of squares; p as the upper beta integral to 80 digits (100-digit arithmetic), on all 40 test cases.
All 160 float64 results inside the running error bound; the closest uses 5% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 5% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 66%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 124

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

f_sf

Called by

—

sha256:5704a4e961a547d9633a1eb3697c16f39e58aadca515dbe49e71723eaa64fdaa

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.anova_oneway · Ω:anova_oneway
Pins: sha256:fa3cce47e45e033c2c72c744f8189cdbea2cef2af5f717cd0ccc1f1684ac02cdthis graph and the 1 it reaches through calls
Evidence: sha256:2eee017e882bdb6a6a497fd937cc07a9e84c3cbd754c4ce408bb7e128f6bc5a2the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.