paired_t_test

std.stats.paired_t_test · Level L5

Paired t-test of two matched samples: the one-sample t-test of their differences against 0, giving [t, ν, p]. Calls t_test_1samp.

d = x − y; t = d̄/(s_d/√n), ν = n − 1

Signature

paired_t_test(x: f64[n], y: f64[n]) → f64[3]

Requires: 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 n ≥ 2.
Agrees with the reference t_test_1samp(x − y, 0) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 120 float64 results inside the running error bound; the closest uses 15% 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 11% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 54%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 15

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

t_test_1samp

Called by

—

sha256:9f3f50d0a8382c575906dcc50c1827a4b2852bf1782e53c5ee90ae185ad444a1

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.paired_t_test · Ω:paired_t_test
Pins: sha256:9ea4ab3e492fe7fb9de2f95db0f287379c79c1d6a17d34fb0d3c39552136d5bethis graph and the 3 it reaches through calls
Evidence: sha256:44d71fea344419d47e74d077fa9c68c96ead283e3a075c083f321b0131a3497athe 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.