{ "category": "Compatibility", "display_name": "TTEST", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.TTEST", "implementation_state": { "answer_bank": null, "detail": "Everything else matches (8 workbook cells). Last-bit means a finite number within 16 ULP of Excel's.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "close", "state_label": "Close: last-bit deviations remain", "summary": "Close: 2 of 8 recorded answers differ in the last bits, worst 2 ULP", "workbook_corpus": { "cells": 8, "last_bit": 2, "matched": 6, "worst_ulp": 2 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L345-L347" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::sample", "catalogue/distributions::whole", "catalogue/distributions::t_test_of", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_mul_add", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::add", "ported/special_math_common::bratio_ftoi", "ported/special_math_common::bratio_spmpar1", "ported/special_math_common::bratio_exparg", "ported/special_math_common::bratio_esum", "ported/special_math_common::bratio_esum20", "ported/special_math_common::bratio_alnrel", "ported/special_math_common::bratio_rlog1", "ported/special_math_common::bratio_gam1", "ported/special_math_common::bratio_gamln1", "ported/special_math_common::bratio_gamln", "ported/special_math_common::bratio_algdiv", "ported/special_math_common::bratio_bcorr", "ported/special_math_common::bratio_gsumln", "ported/special_math_common::bratio_betaln", "ported/special_math_common::bratio_betaln_60", "ported/special_math_common::bratio_erf_nswc", "ported/special_math_common::bratio_erfc1", "ported/special_math_common::bratio_rexp", "ported/special_math_common::bratio_psi", "ported/special_math_common::bratio_fpser", "ported/special_math_common::bratio_apser", "ported/special_math_common::bratio_bpser", "ported/special_math_common::bratio_bup", "ported/special_math_common::bratio_brcomp", "ported/special_math_common::bratio_brcmp1", "ported/special_math_common::bratio_bfrac", "ported/special_math_common::bratio_bgrat", "ported/special_math_common::bratio_grat1", "ported/special_math_common::bratio_basym", "ported/special_math_common::bratio", "ported/statistical_tests_family::sample_mean", "ported/statistical_tests_family::sample_variance", "ported/statistical_tests_family::validate_positive_df", "ported/statistical_tests_family::t_probability", "ported/statistical_tests_family::t_test_paired_kernel", "ported/statistical_tests_family::t_test_equal_variance_kernel", "ported/statistical_tests_family::t_test_unequal_variance_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L345-L347", "state": "close", "suite": null, "summary": "Close: 2 of 8 recorded answers differ in the last bits, worst 2 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.TTEST.json", "name": "TTEST", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[T.TEST](FUNC.T.TEST.md) is the modern spelling; [TDIST](FUNC.TDIST.md) accepts a supplied t statistic; [F.TEST](FUNC.F.TEST.md) compares variances.\n\n\n", "how-to-implement": "\nCollect 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.\n\n| Type | Standard error SE | Degrees v |\n|---|---|---|\n| 1, paired differences d | `sqrt(s_d²/n)` | `n-1` |\n| 2, pooled | `sqrt(s_p²*(1/n1+1/n2))`, with `s_p²=((n1-1)*s1²+(n2-1)*s2²)/(n1+n2-2)` | `n1+n2-2` |\n| 3, unequal variances | `sqrt(a+b)`, with `a=s1²/n1,b=s2²/n2` | `(a+b)²/(a²/(n1-1)+b²/(n2-1))` |\n\nFor paired data set `t=abs(mean(d)/SE)`; otherwise set `t=abs((mean1-mean2)/SE)`. Reject zero SE. Retain fractional v for type three.\n\nThe 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`.\n\nFor 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.\n\nThese 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.\n\n\n", "quirks": "\nType 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.\n\nTTEST 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.\n\nThe 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.\n\n\n", "sources": "\n- [Microsoft: TTEST function](https://support.microsoft.com/en-us/excel/functions/ttest-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/statistical_tests_family.rs); implementation steps and the limits identified in the text.\n\n", "try-it": "\n`=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.\n\n\n", "version-differences": "\nNo 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.\n\n\n", "what-it-does": "\n`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.\n\n\n" }, "signature": { "display": "TTEST(array1, array2, tails, type)", "parameters": [ { "description": null, "name": "array1", "optional": false, "repeats": false }, { "description": null, "name": "array2", "optional": false, "repeats": false }, { "description": null, "name": "tails", "optional": false, "repeats": false }, { "description": null, "name": "type", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 4, "min": 4 }, "category": "Compatibility", "classification": { "arg_preparation_profile": "RefsVisibleInAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "RefOnly", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Student's t-test probability (older form of T.TEST)", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the probability associated with a Student's t-test", "microsoft_url": "https://support.microsoft.com/en-us/office/ttest-function-1696ffc1-4811-40fd-9d13-a0eaad83c7ae" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "TTEST" }, { "locale": "bg-BG", "name": "TTEST" }, { "locale": "cs-CZ", "name": "TTEST" }, { "locale": "da-DK", "name": "TTEST" }, { "locale": "de-DE", "name": "TTEST" }, { "locale": "el-GR", "name": "TTEST" }, { "locale": "en-AU", "name": "TTEST" }, { "locale": "en-GB", "name": "TTEST" }, { "locale": "en-US", "name": "TTEST" }, { "locale": "es-ES", "name": "PRUEBA.T" }, { "locale": "et-EE", "name": "TTEST" }, { "locale": "fi-FI", "name": "TTESTI" }, { "locale": "fr-FR", "name": "TEST.STUDENT*" }, { "locale": "he-IL", "name": "TTEST" }, { "locale": "hr-HR", "name": "TTEST" }, { "locale": "hu-HU", "name": "T.PRÓBA" }, { "locale": "id-ID", "name": "TTEST" }, { "locale": "it-IT", "name": "TTEST" }, { "locale": "ja-JP", "name": "TTEST" }, { "locale": "ko-KR", "name": "TTEST" }, { "locale": "lt-LT", "name": "TTEST" }, { "locale": "lv-LV", "name": "TTEST" }, { "locale": "nb-NO", "name": "TTEST" }, { "locale": "nl-NL", "name": "T.TOETS" }, { "locale": "pl-PL", "name": "TEST.T" }, { "locale": "pt-BR", "name": "TTEST" }, { "locale": "pt-PT", "name": "TESTET" }, { "locale": "ro-RO", "name": "TTEST" }, { "locale": "ru-RU", "name": "ТТЕСТ" }, { "locale": "sk-SK", "name": "TTEST" }, { "locale": "sl-SI", "name": "TTEST" }, { "locale": "sr-Latn-RS", "name": "TTEST" }, { "locale": "sv-SE", "name": "TTEST" }, { "locale": "th-TH", "name": "TTEST" }, { "locale": "tr-TR", "name": "TTEST" }, { "locale": "uk-UA", "name": "TTEST" }, { "locale": "vi-VN", "name": "TTEST" }, { "locale": "zh-CN", "name": "TTEST" }, { "locale": "zh-HK", "name": "TTEST" }, { "locale": "zh-TW", "name": "TTEST" } ], "signature": { "display": "TTEST(array1, array2, tails, type)", "parameters": [ { "description": null, "name": "array1", "optional": false, "repeats": false }, { "description": null, "name": "array2", "optional": false, "repeats": false }, { "description": null, "name": "tails", "optional": false, "repeats": false }, { "description": null, "name": "type", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "TTEST", "version_marker": null, "xlcall": { "code": "316", "symbol": "xlfTtest" } }, "microsoft": "https://support.microsoft.com/en-us/office/ttest-function-1696ffc1-4811-40fd-9d13-a0eaad83c7ae" }, "try_it": { "formula": "=TTEST({1,2,3},{0,2,4},2,3)" }, "url": "https://handbook.dnacalc.com/functions/TTEST.html", "variants": [], "versions": [] }