# Microsoft Knowledge Base

## Pooled Variance Wrong in t-Test Two-Sample Unequal Variances

Last reviewed: September 12, 1996
Article ID: Q100982

• Microsoft Excel for Windows, version 4.0, 4.0a
• Microsoft Excel for the Macintosh, version 4.0

## SYMPTOMS

In Microsoft Excel 4.0, the pooled variance returned by the two-sample assuming unequal variances t-Test tool is incorrect. The value returned is 3.5, or, if you ran a two-sample assuming EQUAL variances t-Test, the returned value will be the same pooled variance returned by that test.

## STATUS

Microsoft has confirmed this to be a problem in the versions of Microsoft Excel listed above. We are researching this problem, and will post more information here in the Microsoft Knowledge Base as it becomes available.

The example below illustrates this behavior.

### Steps to Reproduce Problem

1. On a new worksheet, enter the following values:

```      A1: 61           B1: 55
A2: 71           B2: 63
A3: 68           B3: 61
A4: 73           B4: 65
A5: 71           B5: 64
A6: 70           B6: 63
A7: 69           B7: 62
A8: 74           B8: 66
```
2. From the Options menu, choose Analysis Tools. From the list of tools, select t-Test: Two-Sample Assuming Unequal Variances and choose OK.
3. In the dialog box, enter the following values:

```      Variable 1 Input Range: \$A\$1:\$A\$8
Variable 2 Input Range: \$B\$1:\$B\$8
Output Range: \$C\$1```
4. Choose OK to perform the analysis.

The pooled variance returned will be 3.5. The correct pooled variance is 6.714 (as is indicated on page 49 of "User's Guide 2," version 4.0).

If you perform a two-sample assuming EQUAL variances t-Test with these same numbers, you will receive a pooled variance of 13.69643. This value is correct. However, if you then perform another two-sample assuming UNEQUAL variances t-Test with the same numbers, you will still receive a pooled variance of 13.69643; this value is incorrect.