DocumentationFormulasFunctionsZtest

ZTEST function

PRO BASIC

The ZTEST function in Jspreadsheet Formulas Pro returns the one-tailed probability of a z-test: the chance that the sample mean would be at least as large as the observed mean if the population mean were x. It is used to test a hypothesis about a mean when the sample is large or the population standard deviation is known. It is the compatibility version of Z.TEST and returns the same values.

Documentation

Returns the one-tailed probability of a z-test.

Category

Statistical

Syntax

ZTEST(array, x, [sigma])

Parameter Description
array The range or array of data to test against x.
x The hypothesized population mean.
[sigma] Optional. The known population standard deviation. When omitted, the sample standard deviation is used.

Behavior

The ZTEST function returns 1 - NORM.S.DIST((AVERAGE(array) - x) / (sigma / SQRT(n)), TRUE), the upper-tail probability.

  • x is required in Jspreadsheet. Calling the function with only array returns #N/A, unlike Excel, where x is optional.
  • When sigma is omitted the sample standard deviation is used. sigma must be positive; 0 returns #NUM!.
  • The array needs at least two numeric values. A single value returns #DIV/0!.
  • When the sample mean equals x the result is 0.5.
  • Text passed as x or an array without numbers returns #VALUE!.

Common Errors

Error Description
#NUM! Returned when sigma is less than or equal to 0.
#DIV/0! Returned when array has fewer than two numeric values.
#VALUE! Returned when x is text or when array contains no numbers.

Best practices

  • Always pass x, since the function does not accept the one-argument form.
  • Make sure the array has at least two numeric values and no headers, since a single value returns #DIV/0! and a range without numbers returns #VALUE!.
  • When providing sigma, validate that it is positive, because 0 returns #NUM!.
  • Use absolute references for the array when the formula is copied to other cells.

Usage

A few examples using the ZTEST function.

// A2:A6 = 2, 4, 6, 8, 10
ZTEST(A2:A6, 3)
// Returns 0.016947

ZTEST(A2:A6, 3, 2)
// Returns 0.000398, using a known standard deviation of 2

ZTEST(A2:A6, 6)
// Returns 0.5, the sample mean equals x

ZTEST(A2:A6)
// Returns #N/A because x is required

Interactive Spreadsheet Demo

<html>
<script src="https://jsuites.net/v6/jsuites.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jspreadsheet@13/dist/index.min.js"></script>
<link rel="stylesheet" href="https://jsuites.net/v6/jsuites.css" type="text/css" />
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/jspreadsheet@13/dist/jspreadsheet.min.css" type="text/css" />

<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Material+Icons" />
<script src="https://cdn.jsdelivr.net/npm/@jspreadsheet/formula-pro/dist/index.min.js"></script>

<div id="spreadsheet"></div>

<script>
// You can use the following license for quick testing on localhost, StackBlitz, or CodeSandbox.
// The license is valid for one day, after which the spreadsheet will become read-only.
// For a longer trial period, you can create a free account and generate a demo license with an extended expiration date.
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

// Create a new spreadsheet
jspreadsheet(document.getElementById('spreadsheet'), {
  worksheets: [{
    data: [
    [
        "Sample A",
        "Sample B",
        "",
        "Formula",
        "Result"
    ],
    [
        2,
        1,
        "",
        "ZTEST x=3",
        "=ZTEST(A2:A6, 3)"
    ],
    [
        4,
        3,
        "",
        "ZTEST x=6",
        "=ZTEST(A2:A6, 6)"
    ],
    [
        6,
        5,
        "",
        "ZTEST sigma=2",
        "=ZTEST(A2:A6, 3, 2)"
    ],
    [
        8,
        7,
        "",
        "AVERAGE A",
        "=AVERAGE(A2:A6)"
    ],
    [
        10,
        11
    ]
]
  }]
});
</script>
</html>

import React, { useRef } from "react";
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/react";
import formula from "@jspreadsheet/formula-pro";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";

// Set license
jspreadsheet.setLicense('NGZmMGY0MjA5NGEwZGVhMmU5MTA5MmQ0ZDE2MGFmNDRhYzBhMjBjYzAxMGZjMjIwY2NkNDE5MzVhZDI0ODc5NzFlNTNlNzYyZWI2NzdjMWFlMTBmZDk0MWUzZGE4NDk4YTZhMzliMzgyMTdjNmMxMTZmMjYzNWU3NzgyY2MxOTMsZXlKamJHbGxiblJKWkNJNklpSXNJbTVoYldVaU9pSktjM0J5WldGa2MyaGxaWFFpTENKa1lYUmxJam94TnpreE9EY3dPRGt3TENKa2IyMWhhVzRpT2xzaWFuTndjbVZoWkhOb1pXVjBMbU52YlNJc0ltTnZaR1Z6WVc1a1ltOTRMbWx2SWl3aWFuTm9aV3hzTG01bGRDSXNJbU56WWk1aGNIQWlMQ0p6ZEdGamEySnNhWFI2TG1sdklpd2lkMlZpWTI5dWRHRnBibVZ5TG1sdklpd2liRzlqWVd4b2IzTjBJbDBzSW5Cc1lXNGlPaUl6TkNJc0luTmpiM0JsSWpwYkluWTNJaXdpZGpnaUxDSjJPU0lzSW5ZeE1DSXNJbll4TVNJc0luWXhNaUlzSW5ZeE15SXNJbU5vWVhKMGN5SXNJbVp2Y20xeklpd2labTl5YlhWc1lTSXNJbkJoY25ObGNpSXNJbkpsYm1SbGNpSXNJbU52YlcxbGJuUnpJaXdpYVcxd2IzSjBaWElpTENKaVlYSWlMQ0oyWVd4cFpHRjBhVzl1Y3lJc0luTmxZWEpqYUNJc0luQnlhVzUwSWl3aWMyaGxaWFJ6SWl3aVkyeHBaVzUwSWl3aWMyVnlkbVZ5SWl3aWMyaGhjR1Z6SWl3aVptOXliV0YwSWl3aWNHbDJiM1FpWFN3aVpHVnRieUk2ZEhKMVpYMD0=');

// Set the extensions
jspreadsheet.setExtensions({ formula });

export default function App() {
    // Spreadsheet array of worksheets
    const spreadsheet = useRef();

    // Worksheet data
    const data = [
    [
        "Sample A",
        "Sample B",
        "",
        "Formula",
        "Result"
    ],
    [
        2,
        1,
        "",
        "ZTEST x=3",
        "=ZTEST(A2:A6, 3)"
    ],
    [
        4,
        3,
        "",
        "ZTEST x=6",
        "=ZTEST(A2:A6, 6)"
    ],
    [
        6,
        5,
        "",
        "ZTEST sigma=2",
        "=ZTEST(A2:A6, 3, 2)"
    ],
    [
        8,
        7,
        "",
        "AVERAGE A",
        "=AVERAGE(A2:A6)"
    ],
    [
        10,
        11
    ]
];

    // Render component
    return (
        <Spreadsheet ref={spreadsheet}>
            <Worksheet data={data} />
        </Spreadsheet>
    );
}

<template>
    <Spreadsheet ref="spreadsheet">
        <Worksheet :data="data" />
    </Spreadsheet>
</template>

<script>
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/vue";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";
import formula from "@jspreadsheet/formula-pro";

// Set license
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

export default {
    components: {
        Spreadsheet,
        Worksheet,
    },
    data() {
        // Worksheet data
        const data = [
    [
        "Sample A",
        "Sample B",
        "",
        "Formula",
        "Result"
    ],
    [
        2,
        1,
        "",
        "ZTEST x=3",
        "=ZTEST(A2:A6, 3)"
    ],
    [
        4,
        3,
        "",
        "ZTEST x=6",
        "=ZTEST(A2:A6, 6)"
    ],
    [
        6,
        5,
        "",
        "ZTEST sigma=2",
        "=ZTEST(A2:A6, 3, 2)"
    ],
    [
        8,
        7,
        "",
        "AVERAGE A",
        "=AVERAGE(A2:A6)"
    ],
    [
        10,
        11
    ]
]

        return {
            data
        };
    }
}
</script>

import { Component, ViewChild, ElementRef } from "@angular/core";
import jspreadsheet from "jspreadsheet";
import formula from "@jspreadsheet/formula-pro";

// You can use the following license for quick testing on localhost, StackBlitz, or CodeSandbox.
// The license is valid for one day, after which the spreadsheet will become read-only.
// For a longer trial period, you can create a free account and generate a demo license with an extended expiration date.
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

@Component({
    standalone: true,
    selector: "app-root",
    template: `<div #spreadsheet></div>`
})
export class AppComponent {
    @ViewChild("spreadsheet") spreadsheet: ElementRef;
    // Worksheets
    worksheets: jspreadsheet.worksheetInstance[];

    // Create a new data grid
    ngAfterViewInit() {
        // Create spreadsheet
        this.worksheets = jspreadsheet(this.spreadsheet.nativeElement, {
            worksheets: [{
                data: [
    [
        "Sample A",
        "Sample B",
        "",
        "Formula",
        "Result"
    ],
    [
        2,
        1,
        "",
        "ZTEST x=3",
        "=ZTEST(A2:A6, 3)"
    ],
    [
        4,
        3,
        "",
        "ZTEST x=6",
        "=ZTEST(A2:A6, 6)"
    ],
    [
        6,
        5,
        "",
        "ZTEST sigma=2",
        "=ZTEST(A2:A6, 3, 2)"
    ],
    [
        8,
        7,
        "",
        "AVERAGE A",
        "=AVERAGE(A2:A6)"
    ],
    [
        10,
        11
    ]
]
            }]
        });
    }
}