TTEST

What it does

TTEST(array1, array2, tails, type)

TTEST(array1,array2,tails,type) returns a t-test probability for two samples. Type one is paired, two assumes equal variances, and three uses the unequal-variance model. Tails is one or two. This is the compatibility name.

Try it

=TTEST({1,2,3},{0,2,4},2,3) returns 1 under the current route: both means are two, giving t=0 with a positive standard error. One tail returns one half.

Quirks

Type and tail selectors are truncated. Invalid selectors give #NUM!; nonnumeric selectors give #VALUE!. A paired test needs matched data-point counts or gives #N/A. Two independent-sample tests may use different counts.

TTEST forms a nonnegative statistic. Its one-tail result is the upper probability for that magnitude, so it is half the two-tail result; swapping the samples does not select a different directional hypothesis in this function. The output is not the probability that the population means are equal.

The current numerical helpers return #DIV/0! for too few admitted observations or zero standard error. Type three retains its fractional Welch degree count internally; passing that count through the public TDIST wrapper would truncate it and change the calculation.

How to implement

Collect numeric observations, retaining aligned pairs for type one. Let mean, s² and n denote each sample’s arithmetic mean, sample variance and count. The current test helpers use forward binary64 means and centered squared-deviation sums; they do not call the separately recovered VAR.S computation tree.

For paired data set t=abs(mean(d)/SE); otherwise set t=abs((mean1-mean2)/SE). Reject zero SE. Retain fractional v for type three.

The current inner tail forms t2=t*t, den=v+t2, then separately stores z=v/den and w=t2/den. Evaluate bratio(v/2,0.5,z,w).first. This is the two-tail probability; divide it by two for one tail. Its paired beta arguments are not formed by computing w=1-z.

For a worked unequal-variance case, samples {1,2,3} and {2,4,6} have means two and four, variances one and four, and counts three each. Then a=1/3,b=4/3, SE is about 1.2909944487, t about 1.5491933385, and v is 50/17, about 2.9411764706. This shows why rounding v to an integer is a different test. In the starter example the means are equal, so t is zero and the two-tail probability one.

These formulas specify the current composition and operation order. The beta-ratio approximation and remaining numerical discrepancies remain open; a mathematical t-test implementation alone does not identify Excel’s private program.

Rust code

105 ttest "TTEST" (4, 4) [R "array1", R "array2", V "tails", V "type"] |s, a, sv| {
    t_test_of(s, a, sv)
}

No implementation has been published with a Handbook test suite for this function.

Version differences

No same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.

Alternatives

T.TEST is the modern spelling; TDIST accepts a supplied t statistic; F.TEST compares variances.

Named variants

No named variants are recorded yet.