Excel - FTEST Function



FTEST Function

The FTEST function in Excel is a statistical function that is used to determine whether the two independent samples have equal variances. Implementing the F test manually is tedious, prone to error, and produces inaccurate results. An F-test returns the two-tailed probability that the variances in array1 and array2 are not significantly different.

After performing the F-test function, you can decide whether to accept the alternative hypothesis or reject the null hypothesis. If the output is statistically significant, the null hypothesis should be rejected.

The FTEST function replaces the F.TEST function in Excel 2010.

Compatibility

This advanced Excel function is compatible with the following versions of MS-Excel −

  • Excel for Microsoft 365
  • Excel for Microsoft 365 for Mac
  • Excel for the web
  • Excel 2021
  • Excel 2021 for Mac
  • Excel 2019
  • Excel 2019 for Mac
  • Excel 2016

Syntax

The syntax of FTEST function is as follows −

FTEST (arr1, arr2)

Arguments

You can use the following arguments with the FTEST function −

Argument Description Required / Optional
Arr1 It specifies the first data range Required
Arr2 It specifies the second data range Required

Points to Remember

  • Only numeric values, arrays, names, and references that address the numeric values are valid inside the arguments.
  • If the number of data points in arr1 or arr2 is less than 2, or if the variance of arr1 or arr2 is zero, FTEST returns the #DIV/0! error value.
  • If an array or reference argument comprises text, logical values, or empty cells, those values are ignored. However, cells with the value zero are included.
  • The F-test value returned by the LINEST function differs from that returned by the FTEST function. LINEST returns the F statistic, whereas FTEST returns the probability.
  • More than two arguments are not possible inside the F-test function.
  • This function follows the F distribution, and the data range must be independent.
  • Mathematically, the F test formula is represented by $\mathrm{F \: = \: \frac{v_1^2}{v_2^2}}$
  • One Way Anova is a perfect example of F-test.
  • Make sure that two samples are independent and that the sample dataset is distributed normally.

Examples of FTEST Function

Practice the following examples to learn the use of the FTEST function in Excel.

Example 1

Only numeric values, arrays, names, and references that address the numeric values are valid inside the arguments.

Solution

Firstly, assume the sample worksheets shown in the screenshot below. For instance, the delivery time of medicine across Delhi city is showcased in the range "B3:B7," and the delivery period across Agra city is specified in the range "C3:C7." Enter the formula =FTEST(B3:B7, C3:C7) in the C8 cell and press "Enter" to obtain the output.

Excel FTEST Function 1

Excel FTEST Function 2

Example 2

If the number of data points in arr1 or arr2 is less than 2, or if the variance of arr1 or arr2 is zero, FTEST returns the #DIV/0! error value.

Solution

In this example, consider the sample data where the first sample comprises only a single data value and the other sample contains multiple data values.

Will the F test perform correctly for the given sample data?

Lets observe in the below worksheet. You may enter the formula =FTEST(C4:C8, D4:D8) in the D9 cell and press the Enter tab.

Excel FTEST Function 3

Excel FTEST Function 4

As you can notice in the screenshot, the error occurred while performing the FTEST function. If the data values are smaller than 2 in the given arrays, then a "#DIV/0!" error will occur.

Example 3

If an array or reference argument comprises text, logical values, or empty cells, those values are ignored. However, cells with the value zero are included.

Solution

Firstly, you can consider the sample dataset that contains empty, numeric, and non-numeric values. Now, you can enter the formula =FTEST(B5:B9, C5:C9) in the C10 cell. Press the Enter tab.

Excel FTEST Function 5

Excel FTEST Function 6

Here, the values of cell references like B6, C5, B7, and C9 are ignored as these cell references do not contain the numeric value. Therefore, the resulting value is 0.197276.

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