PHI function

PRO BASIC

The PHI function in Jspreadsheet Formulas Pro is used to calculates the standard normal probability density function (PDF) for a given value. In simpler terms, it returns the height of the standard normal curve at a specific point. In simpler terms, it's a tool used in statistics to determine the probability that a certain event will occur. You provide a specific value, and the PHI function calculates the likelihood of an event happening with that value or lower. This function is incredibly useful in a variety of fields, including data analysis, financial forecasting, and risk management.

Documentation

Returns the value of the standard normal probability density function (PDF) at a specified value.

Syntax

PHI(z)

Parameter	Description
`z`	The value for which you want to calculate the standard normal CDF. The standard normal distribution has a mean of zero and a standard deviation of one.

Behavior

The PHI function returns the value of the standard normal cumulative distribution function at a given value. The standard normal cumulative distribution function has a mean of 0 and a standard deviation of 1. Here is how it behaves under different scenarios:

Empty cells: If the function is applied to an empty cell, the function will return an error because it requires a numeric input.
Text: The function cannot be used with text. If text is used as an argument, the function will return an error.
Booleans: Booleans are interpreted as 0 for FALSE and 1 for TRUE.
Errors: If an error is passed as an argument, the function will return that error.
Non-numeric values: The function will return an error because it requires a numeric input.

Common Errors

Error	Description
#VALUE!	Occurs when the function is used with a non-numeric argument.
#N/A	Occurs when the function is used with no arguments.

Best practices

Always ensure that the input to the PHI function is a number. Non-numeric values will result in an error.

Use the PHI function to create a probability plot of your data to visualize how closely it follows a standard normal distribution.

Remember that Boolean values will be interpreted as 0 for FALSE and 1 for TRUE. This may lead to unintended results if Boolean values are used as arguments.

Usage

A few examples using the PHI function.

PHI(0) → Returns 0.3989, the peak value of the standard normal distribution at the mean.  
PHI(1.96) → Returns 0.0584, the density at z = 1.96 (commonly used in confidence intervals).  
PHI(-2.5) → Returns 0.0175, the density at z = -2.5.

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: [
    [
        "Z-Score",
        "Probability",
        "Description"
    ],
    [
        0,
        "=PHI(A2)",
        "Mean (50th percentile)"
    ],
    [
        1.96,
        "=PHI(A3)",
        "95th percentile"
    ],
    [
        -1.96,
        "=PHI(A4)",
        "5th percentile"
    ],
    [
        2.58,
        "=PHI(A5)",
        "99.5th percentile"
    ]
]
  }]
});
</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 = [
    [
        "Z-Score",
        "Probability",
        "Description"
    ],
    [
        0,
        "=PHI(A2)",
        "Mean (50th percentile)"
    ],
    [
        1.96,
        "=PHI(A3)",
        "95th percentile"
    ],
    [
        -1.96,
        "=PHI(A4)",
        "5th percentile"
    ],
    [
        2.58,
        "=PHI(A5)",
        "99.5th percentile"
    ]
];

    // 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 = [
    [
        "Z-Score",
        "Probability",
        "Description"
    ],
    [
        0,
        "=PHI(A2)",
        "Mean (50th percentile)"
    ],
    [
        1.96,
        "=PHI(A3)",
        "95th percentile"
    ],
    [
        -1.96,
        "=PHI(A4)",
        "5th percentile"
    ],
    [
        2.58,
        "=PHI(A5)",
        "99.5th percentile"
    ]
]

        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('ZjllODVkNDRhMTc3MGNkMzMyZTdlODRlOWRjZGQxNjdhZDRiZmViYzgzMzQ1NTExNzQ2MzY5NjY4Y2U0YjEzMTJjZTQ5ODZlYTIzM2FiNWNlNjFiM2E1ODY0YjZhYjcxZWFkOTUxMDliY2I0ZWZiZDVlNWEzMWJiZTE0ODg0ZmUsZXlKamJHbGxiblJKWkNJNklpSXNJbTVoYldVaU9pSktjM0J5WldGa2MyaGxaWFFpTENKa1lYUmxJam94TnpVNE5UQXpPVEUwTENKa2IyMWhhVzRpT2xzaWFuTndjbVZoWkhOb1pXVjBMbU52YlNJc0ltTnZaR1Z6WVc1a1ltOTRMbWx2SWl3aWFuTm9aV3hzTG01bGRDSXNJbU56WWk1aGNIQWlMQ0p6ZEdGamEySnNhWFI2TG1sdklpd2lkMlZpWTI5dWRHRnBibVZ5TG1sdklpd2lkMlZpSWl3aWJHOWpZV3hvYjNOMElsMHNJbkJzWVc0aU9pSXpOQ0lzSW5OamIzQmxJanBiSW5ZM0lpd2lkamdpTENKMk9TSXNJbll4TUNJc0luWXhNU0lzSW1Ob1lYSjBjeUlzSW1admNtMXpJaXdpWm05eWJYVnNZU0lzSW5CaGNuTmxjaUlzSW5KbGJtUmxjaUlzSW1OdmJXMWxiblJ6SWl3aWFXMXdiM0owWlhJaUxDSmlZWElpTENKMllXeHBaR0YwYVc5dWN5SXNJbk5sWVhKamFDSXNJbkJ5YVc1MElpd2ljMmhsWlhSeklpd2lZMnhwWlc1MElpd2ljMlZ5ZG1WeUlpd2ljMmhoY0dWeklpd2labTl5YldGMElsMHNJbVJsYlc4aU9uUnlkV1Y5');

// 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: [
    [
        "Z-Score",
        "Probability",
        "Description"
    ],
    [
        0,
        "=PHI(A2)",
        "Mean (50th percentile)"
    ],
    [
        1.96,
        "=PHI(A3)",
        "95th percentile"
    ],
    [
        -1.96,
        "=PHI(A4)",
        "5th percentile"
    ],
    [
        2.58,
        "=PHI(A5)",
        "99.5th percentile"
    ]
]
            }]
        });
    }
}

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