How to use the CHISQ.DIST function
What is the CHISQ.DIST function?
The CHISQ.DIST function calculates the probability of the chi-squared distribution. Use this function to check if a hypothesize is valid. It allows you to calculate the cumulative distribution or the probability density function.
The CHISQ.DIST function was introduced in Excel 2010 and has replaced the CHIDIST function.
Table of Contents
1. Introduction
What is a chi-squared distribution?
The chi-squared distribution is a theoretical probability distribution modeling the sum of squared standard normal random variables used in inferential statistics for estimation, confidence intervals, and hypothesis testing.
What is the probability of the chi-squared distribution?
The probability of the chi-squared distribution determines the likelihood that the sum of squared standard normal variables will take on a value less than or equal to a given number, depending on its degrees of freedom parameter.
What is a hypothesize?
In statistics, a hypothesis is an assumption about some aspect of a population parameter or probability model that can be tested using observations and data to determine if there is sufficient evidence in the sample to support the assumed hypothesis.
What is a cumulative chi-squared distribution?
The cumulative chi-squared distribution function gives the probability that the sum of squared standard normals will result in a value less than or equal to a specified number x, giving the accumulated area under the probability density curve.
What is a probability density function of a chi-squared distribution?
A chi-squared probability density function is a function that defines the relative likelihood of different outcomes for the sum of squared standard normals based on its degrees of freedom parameter, integrating to a total area of 1 over the domain.
What is inferential statistics for estimation?
Inferential statistics for estimation involve using a random sample to estimate characteristics and parameters about a larger population using statistical techniques like confidence intervals and point estimation to quantify uncertainty about the estimates.
What is confidence intervals?
A confidence interval provides a range of plausible values for an unknown population parameter centered around a sample estimate, describing the uncertainty around the estimate at a specified level of confidence.
What is the sum of squared standard normal variables?
The sum of squared standard normal variables refers to summing multiple independent normally distributed random variables each with a mean of 0 and variance of 1, which results in a chi-squared distribution that can be used for statistical modeling and analysis.
2. Syntax
CHISQ.DIST(x,deg_freedom,cumulative)
3. Arguments
| x | Required. A numerical value representing a point in the probability distribution you want to be evaluated. |
| deg_freedom | Required. A numerical value representing the degrees of freedom. |
| cumulative | Required. A boolean value. TRUE - Cumulative distribution function FALSE - Probability density function |
What are the degrees of freedom?
The degrees of freedom in a chi-squared distribution refers to the number of standard normal random variables being squared and summed, which affects the shape of the distribution and occurs in statistical tests as the sample size minus the number of estimated parameters.
What is a boolean value?
A Boolean value is a logical data type having only two possible states - true or false - which logic gates and circuits are based on.
4. Example 1
What is the probability density function for a chi-squared distribution with a degree of freedom of one for an x value of 1.3?
The CHISQ.DIST function has three arguments:
- x - which is specified in cell C16 and is 1.3 in this example.
- deg_freedom - The degree of freedom is 1 and is specified in cell C17.
- cumulative - FALSE meaning the CHISQ.DIST function calculates the density probability function.
The image above shows a chart demonstrating both the cumulative chi-squared distribution (blue line) and the density probability function (orange line) between x values of 0 to 10. These distribution lines change based on the degree of freedom value. In this example the degree of freedom is 1.
Formula in cell C20:
The formula in cell C6 returns approx. 0.183. This value can be found in the chart above. The orange line shows the density probability function, the x value is found on the x-axis. 1.3 on the x-axis corresponds to the 0.18 value on the y-axis based on the orange line.
5. Example 2
What is the cumulative distribution function for a chi-squared distribution with a degree of freedom of two, for an x value of 2?
The CHISQ.DIST function has three arguments:
- x - which is specified in cell C16 and is 2 in this example.
- deg_freedom - The degree of freedom is 2 and is specified in cell C17.
- cumulative - TRUE meaning the CHISQ.DIST function calculates the cumulative distribution function.
The image above shows a chart demonstrating both the cumulative chi-squared distribution (blue line) and the density probability function (orange line) between x values of 0 to 10. These distribution lines change based on the degree of freedom value, note that the chart lines are different than in example 1, section 4. In this example the degree of freedom is 2.
Formula in cell C20:
The formula in cell C6 returns approx. 0.632. This value can be found in the chart above. The orange line shows the density probability function, the x value is found on the x-axis. 0.632 corresponds to the area below the orange line between 0 and 2.
The blue line shows the cumulative distribution function, 2 on the x-axis corresponds to 0.632 on the y-axis based on the blue line.
6. Example 3
What is the complement of the cumulative distribution function for a chi-squared distribution with a degree of freedom of eight, for an x value of 8?
The complement of the cumulative distribution function is the area below the orange line from x value 8 to infinity. We can calculate the cumulative probability for x value 8 and then calculate the complement by subtracting 1 with the cumulative probability from the CHISQ.DIST function.
Formula in cell C20:
The blue line shown in the image above demonstrates the cumulative distribution function for chi squared distribution with the following arguments:
- x - which is specified in cell C16 and is 8 in this example.
- deg_freedom - The degree of freedom is 8 and is specified in cell C17.
- cumulative - TRUE meaning the CHISQ.DIST function calculates the cumulative distribution function.
Number 8 on the x-axis corresponds to value approx. 0.57 on the left y-axis, however, we need the complement meaning the area below the orange line. The orange line shows the density probability function of a chi squared distribution from 8 on the x-axis to infinity. 1 minus 0.57 is approx. 0.43.
7. Function not working
The CHISQ.DIST function returns
- #VALUE! error value if x, deg_freedom or cumulative argument is non-numeric.
- #NUM! error value if:
- x < 0 (zero)
- deg_freedom < 1
- deg_freedom > 10^10
deg_freedom argument is converted into integers.
7.1 Troubleshooting the error value
When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.
- The first line describes the error if you press with left mouse button on it.
- The second line opens a pane that explains the error in greater detail.
- The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
- This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
- The fifth line lets you edit the formula in the Formula bar.
- The sixth line opens the Excel settings so you can adjust the Error Checking Options.
Here are a few of the most common Excel errors you may encounter.
#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.
#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.
#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.
#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.
#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.
#NAME error - The #NAME error happens if you misspelled a function or a named range.
#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.
#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.
#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.
7.2 The formula returns an unexpected value
To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:
- Select the cell containing the formula you want to examine in detail.
- Go to tab “Formulas” on the ribbon.
- Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control. - Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
- Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
- Press "Close" button to dismiss the dialog box.
There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..
- Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
- Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
- Press F9: This will calculate and display the result of just that selected portion.
- Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
- Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.
The image above shows cell reference C16 converted to hard-coded value using the F9 key. The CHISQ.DIST function requires numerical values which is not the case in this example. We have found what is wrong with the formula.
Tips!
- View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
- Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
- Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.
Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button
7.3 Other errors
Floating-point arithmetic may give inaccurate results in Excel - Article
Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.
'CHISQ.DIST' function examples
The following article has a formula that contains the CHISQ.DIST function.
Table of Contents How to use the BETADIST function How to use the BETAINV function How to use the BINOMDIST […]
Functions in 'Statistical' category
The CHISQ.DIST function function is one of 73 functions in the 'Statistical' category.
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