How to use the CHISQ.TEST function

What is the CHISQ.TEST function?

The CHISQ.TEST function calculates the test for independence, the value returned from the chi-squared statistical distribution and the correct degrees of freedom. Use this function to check if hypothesized results are valid.

The CHITEST function is outdated and you will find it in the compatibility category, the function has been replaced with the CHISQ.TEST function.

1. Introduction

What is a test for independence?

A test for independence is a statistical hypothesis test that checks if two categorical variables are related or independent based on observed data, commonly done using Pearson's chi-squared test or G-test to compare observed and expected frequency counts.

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 an hypothesis?

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.

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.

2. Syntax

CHISQ.TEST(actual_range,expected_range)

3. Arguments

actual_range	Required. A range of data.
expected_range	Required. A range of data.

4. Example 1

A researcher wants to test if there is a significant difference between the observed frequencies of different blood types in a population and the expected frequencies based on theoretical probabilities. The data consists of the observed and expected frequencies for each blood type.

Observed frequencies of blood types:

Blood Type A: 120
Blood Type B: 95
Blood Type AB: 30
Blood Type O: 155

To calculate the expected frequencies based on theoretical probabilities we need to know the probabilities of each blood type in the general population.

The theoretical probabilities for the ABO blood group system are as follows:

Blood Type A: 0.25 (or 25%)
Blood Type B: 0.25 (or 25%)
Blood Type AB: 0.09 (or 9%)
Blood Type O: 0.41 (or 41%)

Determine if the observed frequencies differ significantly from the expected frequencies?

The image above shows the observed frequencies in cell range B19:C22 and the expected frequencies in cell range B27:D30. There are four categories of blood types (A, B, AB, and O), the degrees of freedom would be 3 (4 categories - 1).

Formula in cell C23:

Formula in cell D27:

Copy cell D27 to cells below as far as needed.

Formula in cell C32:

The CHISQ.TEST function returns 0.0934952080113268

Formula in cell C33:

Formula in cell C34:

The χ2 statistic for the observed frequencies is approx. 6.41 with 3 degrees of freedom. This is lower than the decision rule calculated in cell C34. The observed frequencies does not differ significantly from the expected frequencies.

5. Example 2

A quality control manager at a manufacturing plant wants to test if the frequencies of defective products across different production lines are significantly different from the expected frequencies based on historical data. The data includes the observed and expected frequencies of defective products for each production line.

Observed frequencies of defective products:

Production Line 1: 18
Production Line 2: 25
Production Line 3: 12
Production Line 4: 30
Production Line 5: 19

Expected frequencies of defective products based on historical data:

Production Line 1: 22
Production Line 2: 24
Production Line 3: 20
Production Line 4: 28
Production Line 5: 10

Determine if the observed frequencies of defective products differ significantly from the expected frequencies?

The image above shows the observed frequencies in cell range C19:C23 and the expected frequencies in cell range C28:C32. There are five categories of production lines (1, 2, 3, 4, and 5), the degrees of freedom would be 4 (5 categories - 1).

Formula in cell C34:

The CHISQ.TEST function returns 0.0158438623483097

Formula in cell C35:

Formula in cell C36:

The χ2 statistic for the observed frequencies is approx. 12.21 with 4 degrees of freedom. This is higher than the decision rule calculated in cell C36. The observed frequencies does differ significantly from the expected frequencies.

6. Function not working

Independence is indicated by a low number of χ2.

The CHISQ.TEST function returns

• #N/A error value if the number of data points in the arguments doesn't match.

6.1 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.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. 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.

6.2 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:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. 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.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. 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.
6. 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..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. 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.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. 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 D3 converted to hard-coded value using the F9 key. The CHISQ.TEST function requires the same number of data points in both arguments 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

6.3 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.

7. How is the function calculated?

CHISQ.TEST function equation:

Aij = actual frequency in the i-th row, j-th column

Eij = expected frequency in the i-th row, j-th column

r = number of rows

c = number of columns

Functions in 'Statistical' category

The CHISQ.TEST function function is one of 73 functions in the 'Statistical' category.

Excel function categories

Excel categories

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