# t-Test help: Two-Sample - Difference between assuming equal vs. unequal variances?

#### bryan

##### New Member
Hello all,

I'm needing some help here. I'm trying to figure out whether or not my statistics problem would use the "t-Test: Two-Sample Assuming Unequal Variances" or "t-Test: Two-Sample Assuming Equal Variances".

I have been trying to find the answer online but the light bulb upstairs is not going on for me.

Would anyone care to share with me the difference between these 2 types of t-Tests?

#### Englund

##### TS Contributor
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

The t test assuming unequal variances that most statistical softwares uses, uses the Aspin-Welch (WA) test. This test "estimates" the degrees of freedom. I would recommend you to use WA if you dont know that there are equal variances between groups, which you usually do not know since otherwise you wouldn't want to make hypothesis tests.

I would not recommend anyone to use the OTS for any real world problem, and the arguing for that is: i) if we are dealing with samples generated from populations with different variances, WA is a better choice of test; ii) if the samples are of unequal sample sizes, we are better off with WA; iii) if one is testing for equal variances in advance in order to decide whether OTS is appropriate, the power of this test is going to be low, meaning that the risk of falsely not rejecting the hypothesis that the variances are equal will be high, which leads to; iv) different nominal levels of the test we decide upon since we are testing for equal variances in advance; v) and the final argument is, if the OTS is a good choice of test, WA seems to be approximately equally good.

Google "Behrens-Fisher problem" if you're more interested in this problem.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

You run a different test before the ttest, or it may be apart of the ttest if you are using a program. An Equality of Variance test. There can be different names for this test, searching for Satterthwaite may help you.

Based on the results of this equality of variance test you then select the appropriate ttest.

#### bryan

##### New Member
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

In my case, for the sake of making things easy we'll call it Team A vs. Team B

Team A
1629
1680
1676
1619

Team B
1495
1514
1527
1520

I want to conduct a test to show statistical significance between the scores of these 2 groups.

In Excel 2007, when I conduct a "t-Test: Two-Sample Assuming Unequal Variances" test I get. . .

t-Test: Two-Sample Assuming Unequal Variances

Variable 1 Variable 2
Mean 1651 1514
Variance 991.3333333 188.6666667
Observations 4 4
Hypothesized Mean Difference 0
df 4
t Stat 7.976448383
P(T<=t) one-tail 0.000669412
t Critical one-tail 2.131846782
P(T<=t) two-tail 0.001338824
t Critical two-tail 2.776445105

How should I articulate the statistical significance here?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

Depends on who you are presenting these data to. p-value: 0.0013 for two-tailed test.

#### bryan

##### New Member
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

Depends on who you are presenting these data to. p-value: 0.0013 for two-tailed test.
So would this be a proper summary. . .

"After conducting a T-test, the p value showed Team A to have scored a statistically significant score compared to Team B."

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

With that sentence I don't know which was larger.

#### bryan

##### New Member
Re: t-Test help: Two-Sample - Difference between assuming equal vs. unequal variance

With that sentence I don't know which was larger.
Can you help me out with how to properly word it please, that's also what I'm having difficulty with.