# CHISQ.TEST

The `CHISQ.TEST` formula calculates the test for independence of two categorical ranges of data using the chi-squared distribution. It returns the probability that any observed differences between the two ranges are due to chance. This formula is commonly used in hypothesis testing to determine whether there is a significant association between two variables.

## Usage

Use the `CHISQ.TEST` formula with the syntax shown below, it has 2 required parameters:

Parameters:
1. observed_range (required):
The range of observed categorical data.
2. expected_range (required):
The range of expected categorical data, with the same dimensions as the observed range.

## Examples

Here are a few example use cases that explain how to use the `CHISQ.TEST` formula in Google Sheets.

### Testing for association between two variables

Suppose you have two categorical variables and you want to test whether there is a significant association between them. You can use the `CHISQ.TEST` formula to calculate the probability that any observed differences between the two variables are due to chance.

### Testing goodness of fit

Suppose you have a categorical variable and you want to test whether the observed frequencies of the categories fit a specified distribution. You can use the `CHISQ.TEST` formula to calculate the probability that any differences between the observed and expected frequencies are due to chance.

### Testing homogeneity of proportions

Suppose you have two or more populations and you want to test whether they have the same proportions of a categorical variable. You can use the `CHISQ.TEST` formula to calculate the probability that any observed differences between the populations are due to chance.

## Common Mistakes

`CHISQ.TEST` not working? Here are some common mistakes people make when using the `CHISQ.TEST` Google Sheets Formula:

### Incorrect range size

One common mistake is to provide observed_range and expected_range that have different sizes. Make sure both ranges have the same number of cells.

### Incorrect range reference

Another common mistake is to provide incorrect range references for observed_range and expected_range. Double-check the cell references to ensure they are correct.

### Invalid input data

The CHISQ.TEST formula requires non-negative input values. If any of the values in the observed_range or expected_range are negative, the formula will return an error. Check your data to ensure it meets this requirement.

### Not enough data

The CHISQ.TEST formula requires at least one degree of freedom. If the number of cells in the observed_range or expected_range is less than 2, the formula will return an error. Make sure you have enough data to perform the test.

### Incorrectly interpreting results

One common mistake is to misinterpret the results of the CHISQ.TEST formula. Remember that the formula returns a p-value, which is the probability of getting the observed result by chance alone. A small p-value (less than 0.05) suggests that the observed and expected data are significantly different, while a large p-value (greater than 0.05) suggests that they are not significantly different.

The following functions are similar to `CHISQ.TEST` or are often used with it in a formula:

• `CHISQ.DIST`

The `CHISQ.DIST` function calculates the probability density function or the cumulative distribution function of a chi-squared distribution. This function is commonly used in hypothesis testing to determine the significance of the difference between expected and observed values. The output of this function can be used to make decisions about the null hypothesis.

• `CHISQ.INV`

The CHISQ.INV function returns the inverse of the right-tailed probability of the chi-squared distribution. It is commonly used in hypothesis testing where the null hypothesis is that the observed data follows a chi-squared distribution. The function returns the value of the chi-squared random variable at which the cumulative distribution function equals the given probability. This function is useful for finding critical values after performing a chi-squared test.

• `F.TEST`

The `F.TEST` function returns the result of an F-test, which tests the equality of variances between two datasets. It is commonly used to compare the variances of two datasets to determine if they are significantly different. If the result is less than or equal to a critical value, the variances are considered equal. If the result is greater than the critical value, the variances are considered unequal.

• `T.TEST`

The `T.TEST` function calculates the probability associated with a Student's t-test. This function is commonly used in statistics to determine whether two samples are likely to have come from the same two underlying populations that have the same mean. It returns the probability that the two samples are different. The function assumes that the two samples are independent of each other and have equal variances.

• `Z.TEST`

The `Z.TEST` formula returns the probability of a certain value occurring in a normal distribution. This formula is commonly used to test whether two samples have the same mean by comparing their Z scores. The formula returns a value between 0 and 1, with a result closer to 1 indicating a higher likelihood that the value could occur by chance.

You can learn more about the `CHISQ.TEST` Google Sheets function on Google Support.