CONFIDENCE.T function

PRO

The CONFIDENCE.T function in Jspreadsheet Formulas Pro is a statistical tool that provides the confidence interval for a population mean, based on a Student's t-distribution. It gives you a range in which the true mean of a population is likely to fall, with a specified level of confidence. Essentially, it helps you make predictions about a large group based on a smaller sample. This function is particularly useful in fields like market research, where it's often impractical to gather data from every member of a population.

Documentation

Returns the confidence interval for a population mean, using a Student's t-distribution.

Syntax

CONFIDENCE.T(alpha, standard_dev, size)

Parameter	Description
`alpha`	The significance level used to compute the confidence level. Often represented as a decimal; for example, use 0.05 for a 95% confidence level.
`standard_dev`	The sample standard deviation. Assumes the population standard deviation is unknown, which is why a t-distribution is used. Must be greater than 0.
`size`	The sample size.

Behavior

The CONFIDENCE.T function is used to calculate the confidence interval for a population mean, using a Student's T distribution. The function requires three arguments: alpha, standard_dev, and size. alpha is the significance level used to compute the confidence level, standard_dev is the population standard deviation, and size is the sample size.

If any required arguments are empty or omitted, the function returns an error.
Texts that cannot be coerced to numbers return #VALUE!.
Booleans are treated as integers 0 (false) and 1 (true).
If the value of alpha is ≤ 0 or ≥ 1, the function will return a #NUM! error.
If the standard_dev ≤ 0, it will return a #NUM! error.
If size is < 1, it will return a #NUM! error.

Common Errors

Error	Description
#VALUE!	If any of the supplied arguments are non-numeric.
#NUM!	If `alpha` ≤ 0 or ≥ 1, `standard_dev` ≤ 0, or `size` < 1.

Best practices

Always check your data to make sure there are no non-numeric values before using the CONFIDENCE.T function.

Make sure your alpha value is between 0 and 1 (exclusive), standard_dev is more than 0, and size is greater than or equal to 1; otherwise, you will get a #NUM! error.

Be aware that the CONFIDENCE.T function assumes your data follows a Student's T distribution. If your data does not meet this assumption, the results may not be accurate.

Remember that the CONFIDENCE.T function gives you the radius of the confidence interval, not the whole range. To get the whole range, subtract the result from the mean to get the lower limit and add the result to the mean to get the upper limit.

Usage

A few examples using the CONFIDENCE.T function.

| Formula                         | Result (approx.) | Description                                                 |
|---------------------------------|------------------|-------------------------------------------------------------|
| CONFIDENCE.T(0.05, 1.5, 30)     | ≈ 0.5601         | 95% CI, sample std dev = 1.5, sample size = 30             |
| CONFIDENCE.T(0.01, 2, 50)       | ≈ 0.7580         | 99% CI, higher confidence, wider margin                     |

Interactive Spreadsheet Demo

<html>
<script src="https://jspreadsheet.com/v11/jspreadsheet.js"></script>
<script src="https://jsuites.net/v5/jsuites.js"></script>
<link rel="stylesheet" href="https://jsuites.net/v5/jsuites.css" type="text/css" />
<link rel="stylesheet" href="https://jspreadsheet.com/v11/jspreadsheet.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>
// Set your JSS license key (The following key only works for one day)
jspreadsheet.setLicense('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');

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

// Create a new spreadsheet
jspreadsheet(document.getElementById('spreadsheet'), {
  worksheets: [{
    data: [
    [
        "Sample Size",
        "Standard Dev",
        "Alpha",
        "Confidence Interval"
    ],
    [
        25,
        2.3,
        0.05,
        "=CONFIDENCE.T(C2,B2,A2)"
    ],
    [
        40,
        1.8,
        0.01,
        "=CONFIDENCE.T(C3,B3,A3)"
    ],
    [
        15,
        3.2,
        0.1,
        "=CONFIDENCE.T(C4,B4,A4)"
    ]
]
  }]
});
</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('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');

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

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

    // Worksheet data
    const data = [
    [
        "Sample Size",
        "Standard Dev",
        "Alpha",
        "Confidence Interval"
    ],
    [
        25,
        2.3,
        0.05,
        "=CONFIDENCE.T(C2,B2,A2)"
    ],
    [
        40,
        1.8,
        0.01,
        "=CONFIDENCE.T(C3,B3,A3)"
    ],
    [
        15,
        3.2,
        0.1,
        "=CONFIDENCE.T(C4,B4,A4)"
    ]
];

    // 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 Size",
        "Standard Dev",
        "Alpha",
        "Confidence Interval"
    ],
    [
        25,
        2.3,
        0.05,
        "=CONFIDENCE.T(C2,B2,A2)"
    ],
    [
        40,
        1.8,
        0.01,
        "=CONFIDENCE.T(C3,B3,A3)"
    ],
    [
        15,
        3.2,
        0.1,
        "=CONFIDENCE.T(C4,B4,A4)"
    ]
]

        return {
            data
        };
    }
}
</script>

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

// Set your JSS license key (The following key only works for one day)
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 Size",
        "Standard Dev",
        "Alpha",
        "Confidence Interval"
    ],
    [
        25,
        2.3,
        0.05,
        "=CONFIDENCE.T(C2,B2,A2)"
    ],
    [
        40,
        1.8,
        0.01,
        "=CONFIDENCE.T(C3,B3,A3)"
    ],
    [
        15,
        3.2,
        0.1,
        "=CONFIDENCE.T(C4,B4,A4)"
    ]
]
            }]
        });
    }
}

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