# Two Sample t-Test Assuming Unequal Variances

## Use a t-Test to determine if means (i.e., averages) are the same or different

**Prerequisite: **Before using the t-test, use an F-test to determine if the variances are *equal* or *unequal*.

If they are not equal go to: Two-Sample t-Test assuming equal variances.

(The QI Macros Stat Wizard will do this for you automatically.)

### Video Example: Analyze Data Sets with a Two Sample t-Test

**Example of a Two Sample t-Test Assuming Unequal Variances**

In this example, we want to compare two types of structural steel and want to know if the strengths (in 1000 lbs/sq. in.) are the same or different. Next we conduct some tests and enter the data into Excel:

**Warning: **While you can run a t-Test using Excel's Data Analysis Toolpak, if you don't enter the two columns in the correct order, Excel will give you incorrect results. The QI Macros have eliminated this problem.

**How to Perform a t-Test Assuming Unequal Variances** using QI Macros for Excel

- Select the data with the mouse and click on the QI Macros Menu, Statistical Tools and then t-Test two sample assuming unequal variances:
- The QI Macros will prompt for a significance level (default is .05):

- Next the QI Macros will prompt for the hypothesized difference in the means (default is 0):

The QI Macros will perform the calculations and interpret the results for you:

**What's Unique About t-Test Calculations in the QI Macros?**

**What's Unique About t-Test Calculations in the QI Macros?**

When you run the t-test, the QI Macros will compare the p-value (0.197) to the significance level (0.05) and interpret the results for you. Cannot Reject the Null Hypothesis because p > 0.05" and that the "Means are the same".

### Here is Some Guidance to Interpret the t-Test Results Yourself:

- The null hypothesis H0 is that the mean difference (x1-x2) = 0
- The alternative hypothesis Ha is that the mean difference <> 0

or in other words the means are the same

or in other words the means are not the same, they are different

If |
Then |

test statistic > critical value (i.e. t> tcrit) |
Reject the null hypothesis |

test statistic < critical value (i.e. t< tcrit) |
Cannot Reject the null hypothesis |

p value < a |
Reject the null hypothesis |

p value > a |
Cannot Reject the null hypothesis |

Since the null hypothesis is that the mean difference (x1-x2) = 0, this is a two-sided test. Therefore, use the two-tail values for your analysis.

Since the t statistic < t critical (1.355 < 2.145) and *p value > a (* 0.197 > 0.05) , we cannot reject the null hypothesis - the means are the same.

The two recipes produce steel with the same mean tensile strength at a 95% confidence level.

### Learn More...

- t-Test one sample
- Paired two sample t-Test
- Two-Sample t-Test assuming equal variances
- Statistics Wizard analyzes your data and selects the right statistical tests for you

Hypothesis Testing Quick Reference Card