# Help with T test assuming equal variance results (p value and t critical value not leading to same answer)

Using the p value and negative t value with t critical value my results are said to be significantly different but using the positive t value with the t critical positive value the results are not significant. What am I doing wrong?

male scores female scores
3.13 4.53
3.95 4.34
3.61 4.26
2.61 4.63
3.50 4.53
4.21 4.26
3.68 3.76
4.00 3.68
2.82 3.82
4.58 4.26
3.84 3.97
3.68 4.63
3.89 4.92
3.45 4.74
4.87 3.82
3.42
4.05

t-Test: Two-Sample Assuming Equal Variances

Mean male scores - 3.72291021671827 | Mean female scores - 4.27719298245614

Variance male scores - 0.32610090435066 | Variance female scores - 0.152836037462076

Observation male scores - 17 | Observation female scores - 15

Pooled Variance 0.245243966

Hypothesized Mean Difference 0

df 30

t Stat -3.159565118

P(T<=t) one-tail 0.001796723

t Critical one-tail 1.697260887

P(T<=t) two-tail 0.003593446

t Critical two-tail 2.042272456

• It would be best if there is some way you can provide this information in a textual format rather than as an image/screenshot, as it allows other people to reproduce the example much more easily ... Commented Mar 11 at 17:02

As @PeterFlom said, you need to compare the absolute value of t. 3.16 is (a lot) larger than 2.04 (the critical value for p=0.05), so the p-value is (a lot) lower than 0.05.

It is more straightforward to ignore the p-value and "significance", and instead focus on the difference and the confidence interval of the difference. For your data, the difference is 0.55 and the 95% confidence interval runs from 0.20 to 0.91. You can't completely interpret that without knowing what the measurement is and how large of a difference is scientifically relevant. The CI does not include zero, but is pretty wide.

Here are the values in plain text, in case others want to do different analyses.

Male: 3.13 3.95 3.61 2.61 3.50 4.21 3.68 4.00 2.82 4.58 3.84 3.68 3.89 3.45 4.87 3.42 4.05

Female: 4.53 4.34 4.26 4.63 4.53 4.26 3.76 3.68 3.82 4.26 3.97 4.63 4.92 4.74 3.82

You are comparing the result to the wrong thing.

You are doing a two-tail t-test. Your test statistic is -3.16. The critical value (2 tail) is 2.04, but this is in either direction, so you compare the absolute value of your test statistic to this critical value.

After all, you could just have easily written the test in the other direction. You don't say what your variable is, but let's say it's height. Then you are testing whether males and females are the same height. It's arbitrary whether you say "males are taller" or "females are shorter".

All this assumes you are doing a two tail test but, usually, you should be.