# Two Sample T-Test With Unequal Variables

#### graham_ashe

##### New Member
I need to perform an independent samples t-test with unequal variables on these two sample sets. There are 30 samples in each. So far, I've come up with the following information.

t(43) = 7.81, p < 0.001

degrees of freedom = 43
t statistic = 7.81
p statistic = <0.001

I need confirmation if that's correct. Also, what does this say about the statistics? Is it valid enough? I'm trying to show that the difference between the averages of the two groups is statistically significant. Thanks if you can help.

Set 01

1.073
0.598
0.876
1.434
0.636
0.705
0.524
0.561
0.401
0.516
0.916
1.243
0.628
0.615
0.537
1.166
0.635
0.615
0.909
0.728
1.180
1.223
0.582
0.833
0.964
1.038
0.636
1.077
0.427
0.602

Set 02

0.244
0.283
0.516
0.237
0.427
0.413
0.457
0.293
0.365
0.152
0.500
0.232
0.343
0.335
0.476
0.329
0.523
0.192
0.478
0.523
0.293
0.198
0.304
0.679
0.241
0.314
0.246
0.109
0.276
0.617

#### JohnM

##### TS Contributor
Looks OK to me. The probability of getting a t statistic that large, if the null hypothesis is in fact true, is less than .001.

So, you have enough evidence to reject Ho.

#### graham_ashe

##### New Member
JohnM said:
Looks OK to me. The probability of getting a t statistic that large, if the null hypothesis is in fact true, is less than .001.

So, you have enough evidence to reject Ho.
What about the degrees of freedom? Is it right? It looks a bit low to me. I wonder what that implies.

#### JohnM

##### TS Contributor
Since your group variances are significantly different, it looks like the software automatically performed the Welch's t-test, which adjusts the d.o.f. downward, making it a less powerful test (when the variances are not equal, the Welch test requires more evidence of inequality than a standard t test before it will find a significant result).

The formula for the adjusted d.o.f. can be found at this link:

http://web.uccs.edu/lbecker/spss80/ttest.htm#5.%20Independent%20Samples:%20Running%20the%20t%20Test