## What is F.DIST function in Excel?

The **F.DIST** function is one of the Statistical functions of Excel.

It returns the (left-tailed) F probability distribution (degree of diversity) for two data sets.

We can find this function in **Statistical **category of insert function Tab.

## How to use F.DIST function in excel

- Click on
**an empty cell**(like F5).

2. Click on the **fx icon **(or press shift+F3).

3. In the **insert function tab** you will see all functions.

4. Select **STATISTICAL **category.

5. Select **F.DIST** function.

6. Then select **ok**.

7. In the function arguments Tab you will see **F.DIST** function.

8. X is the value at which to evaluate the function, a non-negative number.

9. Deg_freedom1 is the numerator degrees of freedom, a number between 1 and 10^10, excluding 10^10.

10. Deg_freedom2 is the denominator degrees of freedom, a number between 1 and 10^10, excluding 10^10.

11. Cumulative is a logical value for the function to return: the cumulative distribution function = TRUE; the probability density function = FALSE.

12. You will see the **results **in the formula result section.

## Examples of F.DIST function in Excel

**here are 10 examples of the F.DIST function in Excel:**

- To find the probability that a random variable with an F-distribution is less than or equal to a certain value, use the formula “
**=F.DIST(2,3,TRUE)”**. This calculates the F-distribution for a numerator degrees of freedom of 2 and denominator degrees of freedom of 3, and returns the cumulative distribution function (CDF) value. - To find the probability that a random variable with an F-distribution is greater than a certain value, use the formula “
**=1 – F.DIST(2,3,TRUE)**“. This calculates the complement of the CDF value found in example 1. - To find the probability that a random variable with an F-distribution falls between two values, use the formula “
**=F.DIST(4,6,3,TRUE) – F.DIST(2,6,3,TRUE)**“. This calculates the difference between the CDF values at x=4 and x=2 for an F-distribution with numerator degrees of freedom = 4, denominator degrees of freedom = 6. - To find the inverse F-distribution value for a given probability, use the formula “
**=F.INV(0.05,2,3)**“. This returns the value of x for which P(F<=x) = 0.05, where the F-distribution has numerator degrees of freedom = 2, denominator degrees of freedom = 3. - To generate a random sample from an F-distribution, use the formula “
**=F.DIST.RT(RAND(),2,3)**“. This generates a random number between 0 and 1 using the RAND() function, and uses it as an input to the inverse CDF function for the F-distribution with numerator degrees of freedom = 2, denominator degrees of freedom = 3. - To calculate the mean of an F-distribution, use the formula “
**=F.DIST.M(2,3)**“. This returns the mean value for an F-distribution with numerator degrees of freedom = 2, denominator degrees of freedom = 3. - To calculate the variance of an F-distribution, use the formula “
**=F.DIST.V(2,3)**“. This returns the variance value for an F-distribution with numerator degrees of freedom = 2, denominator degrees of freedom = 3. - To calculate the skewness of an F-distribution, use the formula “
**=F.DIST.SKEW(2,3)**“. This returns the skewness value for an F-distribution with numerator degrees of freedom = 2, denominator degrees of freedom = 3. - To calculate the kurtosis of an F-distribution, use the formula “
**=F.DIST.KURT(2,3)**“. This returns the kurtosis value for an F-distribution with numerator degrees of freedom = 2, denominator degrees of freedom = 3. - To calculate the probability density function (PDF) value for a given x-value in an F-distribution, use the formula “
**=F.DIST(x,2,3,FALSE)**“. This returns the PDF value for an F-distribution with numerator degrees of freedom = 2, denominator degrees of freedom = 3, evaluated at the input x-value.

## Excel’s F.DIST.RT function: How to use it?

The F.DIST.RT function in Excel is used to calculate the right-tailed F probability distribution.

The function returns the probability that an F statistic, which is calculated from two sets of data, will be less than or equal to a specified value.

To use the** F.DIST.RT function** in Excel, you need to provide the following arguments:

This is the value at which you want to evaluate the right-tailed F probability distribution.`x`

:

: This is the numerator degrees of freedom.**deg_freedom1**

: This is the denominator degrees of freedom.**deg_freedom2**

**Here’s an example:**

Suppose you have two sets of data with 10 observations each, and you want to calculate the probability that the F statistic will be less than or equal to 3.5.

To do this, you can use the F.DIST.RT function with the following formula:

**=F.DIST.RT(3.5, 9, 9)**

In this formula, `3.5`

is the value of the F statistic, `9`

is the numerator degrees of freedom (which is equal to the number of observations minus 1), and `9`

is the denominator degrees of freedom (which is also equal to the number of observations minus 1).

## Excel’s F.DIST function: What is its syntax?

The F.DIST function in Excel is used to calculate the cumulative F probability distribution.

The function returns the probability that an F statistic, which is calculated from two sets of data, will be less than or equal to a specified value.

The syntax of the F.DIST function in Excel is as follows:

**=F.DIST(x, deg_freedom1, deg_freedom2, cumulative)**

The arguments for this function are as follows:

`x`

: This is the value at which you want to evaluate the cumulative F probability distribution.`deg_freedom1`

: This is the numerator degrees of freedom.`deg_freedom2`

: This is the denominator degrees of freedom.`cumulative`

: This is a logical value that determines the form of the function. If`cumulative`

is`TRUE`

or omitted, then F.DIST returns the cumulative distribution function; if`cumulative`

is`FALSE`

, then F.DIST returns the probability density function.

Here’s an example:

Suppose you have two sets of data with 10 observations each, and you want to calculate the cumulative probability that the F statistic will be less than or equal to 3.5.

To do this, you can use the F.DIST function with the following formula:

**=F.DIST(3.5, 9, 9, TRUE)**

In this formula, `3.5`

is the value of the F statistic, `9`

is the numerator degrees of freedom (which is equal to the number of observations minus 1), and `9`

is the denominator degrees of freedom (which is also equal to the number of observations minus 1).

The `TRUE`

argument indicates that we want to calculate the cumulative distribution function.

## Interpreting the result of Excel’s F.DIST function

The result of the F.DIST function in Excel is a probability value between 0 and 1.

This value represents the probability that an F statistic, which is calculated from two sets of data, will be less than or equal to the specified value.

For example, if the result of the F.DIST function is 0.05, then there is a 5% chance that the F statistic will be less than or equal to the specified value.

## Calculating the inverse of the F-distribution

Excel’s F.DIST.INV function is used to calculate the inverse of the F-distribution. This means that given a probability value, the function returns the corresponding F statistic.

The syntax for the F.DIST.INV function in Excel is as follows:

**=F.DIST.INV(probability, deg_freedom1, deg_freedom2)**

The arguments for this function are as follows:

: This is the probability value for which you want to find the corresponding F statistic.**probability**

: This is the numerator degrees of freedom.**deg_freedom1**

: This is the denominator degrees of freedom.**deg_freedom2**

**Here’s an example:**

Suppose you have two sets of data with 10 observations each, and you want to find the F statistic that corresponds to a cumulative probability of 0.05.

To do this, you can use the F.DIST.INV function with the following formula:

**=F.DIST.INV(0.05, 9, 9)**

In this formula, `0.05`

is the cumulative probability value, `9`

is

## Calculating Cumulative Distribution of the F-Distribution

The F.DIST function in Excel calculates the cumulative distribution of the F-distribution for a given input value. It is useful in statistical analysis and hypothesis testing.

**Here is an example of how to use the F.DIST function in Excel:**

Suppose you want to calculate the cumulative distribution of the F-distribution for a value of 3.0, with degrees of freedom of 5 and 10. To do this, you would use the following formula:

**=F.DIST(3.0, 5, 10, TRUE)
**

This would return the result of 0.936299772, which represents the probability that a random variable from an F-distribution with degrees of freedom of 5 and 10 is less than or equal to 3.0.

## Difference between F.DIST and F.DIST.RT

The main difference between the F.DIST and F.DIST.RT functions in Excel is in the way they are used to calculate the cumulative distribution of the F-distribution.

The F.DIST function calculates the cumulative distribution of the F-distribution from the left-hand side of the distribution, while the F.DIST.RT function calculates it from the right-hand side.

In other words, the F.DIST function returns the probability that a random variable from an F-distribution is less than or equal to a specified value, while the F.DIST.RT function returns the probability that the random variable is greater than a specified value.

**Here is an example of how to use the F.DIST.RT function in Excel:**

Suppose you want to calculate the cumulative distribution of the F-distribution for a value of 3.0, with degrees of freedom of 5 and 10, from the right-hand side of the distribution. To do this, you would use the following formula:

**=F.DIST.RT(3.0, 5, 10)
**

This would return the result of 0.063700228, which represents the probability that a random variable from an F-distribution with degrees of freedom of 5 and 10 is greater than 3.0.

## Using the F.DIST Function for Two-Way ANOVA

The F.DIST function in Excel can be used to calculate the F-statistic of a two-way ANOVA.

This function takes three arguments: the F-ratio, the degrees of freedom for the numerator, and the degrees of freedom for the denominator.

For example, let’s say you have conducted a two-way ANOVA with 3 levels of Factor A and 4 levels of Factor B, and you have calculated an F-ratio of 10.34 with 2 degrees of freedom for the numerator and 9 degrees of freedom for the denominator.

To find the probability associated with this F-ratio:

**=F.DIST(10.34, 2, 9, TRUE)
**

This will return a probability value of 0.005, indicating that the F-ratio is statistically significant at the 0.05 level of significance.

## Calculating Probability with the F.DIST Function

In addition to calculating the F-statistic for ANOVA, the F.DIST function can also be used to calculate the probability of observing a certain F-ratio in Excel.

To use the F.DIST function for this purpose, you need to specify the F-ratio, the degrees of freedom for the numerator, and the degrees of freedom for the denominator.

For example, let’s say you want to find the probability of observing an F-ratio of 3.45 with 5 degrees of freedom for the numerator and 15 degrees of freedom for the denominator:

**=F.DIST(3.45, 5, 15, TRUE)
**

This will return a probability value of 0.0161, indicating that the F-ratio is statistically significant at the 0.05 level of significance.

## Confidence Interval of the F-Distribution

The F.DIST function in Excel can also be used to calculate the confidence interval of the F-distribution.

To do this, you need to specify the significance level and the degrees of freedom for the numerator and denominator.

For example, let’s say you want to find the 95% confidence interval for an F-distribution with 5 degrees of freedom for the numerator and 10 degrees of freedom for the denominator:

**=F.INV(0.025, 5, 10)
**

This will return a critical value of 3.179.

The upper bound of the confidence interval is calculated by dividing the denominator degrees of freedom by the numerator degrees of freedom and multiplying by the critical value:

**=(10/5)*3.179
**

This will return an upper bound of 6.358. The lower bound of the confidence interval is calculated in the same way, but using the reciprocal of the critical value:

**=(10/5)*(1/3.179)
**

This will return a lower bound of 1.576. Therefore, the 95% confidence interval for this F-distribution is (1.576, 6.358).

## Comparing Means Between More Than Two Groups

The F.DIST function in Excel can be used to compare means between more than two groups using one-way ANOVA.

However, for multiple comparisons between groups, post-hoc tests such as Tukey’s HSD or Bonferroni correction may need to be applied.

## Excel’s F.DIST.INV Function: An Example

Suppose we want to find the value x such that the F-distribution with 5 degrees of freedom in the numerator and 10 degrees of freedom in the denominator has an area of 0.05 to its right tail.

** We can use the F.DIST.INV function in Excel to solve for this value.**

To use the F.DIST.INV function in Excel, we need to enter the following formula in a cell: **=F.DIST.INV(probability, deg_freedom1, deg_freedom2)**

In our example, we would enter the following formula in a cell: `=F.DIST.INV(0.05, 5, 10)`

The output of this formula would be approximately 3.1488. Therefore, x is approximately 3.1488.

## Testing for Differences in Variance using the F.DIST in Excel

To test for differences in variance between two samples using the F.DIST function in Excel, we first need to calculate the ratio of the variances of the two samples.

This ratio is equal to the F-statistic for the test.

Suppose we have two samples, Sample 1 and Sample 2, with sizes n1 and n2, respectively. We can calculate the F-statistic using the following formula:

**F = s1^2 / s2^2**

where s1^2 is the sample variance of Sample 1 and s2^2 is the sample variance of Sample 2.

To calculate the F-statistic in Excel, we can use the following formula:

**=VAR.S(sample1)/VAR.S(sample2)**

where “sample1” and “sample2” are the ranges of the data for Sample 1 and Sample 2, respectively.

Once we have calculated the F-statistic, we can use the F.DIST function in Excel to find the corresponding p-value for the F-test. The syntax for the F.DIST function is as follows:

**=F.DIST(x, deg_freedom1, deg_freedom2, cumulative)**

where x is the value at which to evaluate the function, deg_freedom1 and deg_freedom2 are the degrees of freedom for the numerator and denominator, respectively, and cumulative is a logical value that determines whether to return the cumulative distribution function (CDF) or the probability density function (PDF).

To test for differences in variance at a significance level of alpha using the F-test, we can use the following steps:

- Calculate the F-statistic using the formula above.
- Find the p-value of the F-test using the F.DIST function in Excel.
- Compare the p-value to the significance level alpha.
- If the p-value is less than or equal to alpha, reject the null hypothesis of equal variances. Otherwise, fail to reject the null hypothesis.

## The Significance Level in the F-Test Calculated using the F.DIST

The significance level, often denoted by alpha, is the probability of rejecting the null hypothesis when it is true. In the case of the F-test, the null hypothesis is that the variances of two populations are equal.

We can choose any value for alpha, but common choices are 0.05 and 0.01.

When using the F.DIST function in Excel to find the p-value of the F-test, we can specify the significance level as the probability of observing an F-statistic as extreme or more extreme than the one we calculated under the null hypothesis.

This is equivalent to finding the area to the right of our calculated F-statistic in the F-distribution with degrees of freedom equal to those of the test.

## Creating a Graph of the F-Distribution

To create a graph of the F-distribution in Excel, we can use the built-in charting tools. Here’s how to do it:

- Open a new or existing Excel workbook.
- Enter the degrees of freedom for the numerator and denominator in two adjacent cells. For example, enter “
**5**” in cell A1 and “**10**” in cell B1. - In a third cell, enter the formula for the F-distribution using Excel’s F.DIST function. For example, if you want to calculate the probability that a random variable from an F-distribution with degrees of freedom 5 and 10 is less than or equal to 3, use the formula “
**=F.DIST(3, 5, 10, TRUE)”**in cell C1. - Copy the formula down the column to fill in additional values for the F-distribution.
- Highlight the cells containing the degrees of freedom and the probabilities calculated by the F.DIST formula.
- Click on the “
**Insert**” tab at the top of the screen. - In the “
**Charts**” section, select the desired chart type. For example, a line graph or scatter plot could be used to visualize the F-distribution. - Once the chart is created, you may want to adjust the axis labels, add a title, and adjust the formatting as needed.

By creating a graph of the F-distribution, you can better understand the shape of the distribution and how it changes based on the degrees of freedom for both the numerator and denominator.

This can be useful in statistical analysis and hypothesis testing.

## Calculating the P-Value of an F-Test using the F.DIST Function in Excel

To calculate the p-value of an F-test using the F.DIST function in Excel, we need to find the area to the right of our calculated F-statistic in the F-distribution with degrees of freedom equal to those of the test. We can use the F.DIST function to do this.

Suppose we have calculated the F-statistic for our test and obtained a value of 2.47.

We want to find the corresponding p-value for a two-sided test at a significance level of 0.05. To do this, we can use the following formula in Excel:

**=F.DIST(2.47, degrees_freedom1, degrees_freedom2, TRUE)**

where degrees_freedom1 and degrees_freedom2 are the degrees of freedom for the numerator and denominator, respectively.

The fourth argument, TRUE, tells Excel to return the cumulative distribution function (CDF).

Assuming that our degrees of freedom are 10 and 15, respectively, the formula would be: **=F.DIST(2.47, 10, 15, TRUE)**

The output of this formula is approximately 0.025. Therefore, the p-value of our F-test is 0.025.

## Interpreting the P-Value of an F-Test Calculated using the F.DIST

The p-value is the probability of observing a test statistic as extreme or more extreme than the one we calculated under the null hypothesis.

In the case of the F-test, the null hypothesis is that the variances of two populations are equal.

If the p-value is less than or equal to the significance level alpha, we reject the null hypothesis and conclude that there is evidence of a difference in variances between the two populations.

If the p-value is greater than the significance level alpha, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in variances between the two populations.

In general, smaller p-values indicate stronger evidence against the null hypothesis and larger p-values indicate weaker evidence against the null hypothesis.

The choice of significance level alpha determines the threshold for deciding whether to reject or fail to reject the null hypothesis.

## F.DIST related functions

- Use F.DIST.RT function to return the exponential distribution.
- Use F.INV function to return the inverse of the F probability distribution: if p = F.DIST(x,…), then F.INV(p,…) = x.
- Use F.INV.RT function to return the (right-tailed) F probability distribution (degree of diversity) for two data sets.
- Use F.TEST function to return the inverse of the (left-tailed) F probability distribution: if p = F.DIST(x,…), then F.INV(p,…) = x.