# Independent samples test for mean without normal distribution with T-score

I have two independent samples of male and female order value.
Female number of observations = 26887
Male number of observations = 12928
Female mean order value = 133.03
Male mean order value = 145.24
Female sample variance = 10,406.38
Male sample variance = 17,563.87

Pooled variance = 12,730.36
T-score = 0.11
p-value = 0.50926

Same on the image

Terrible p-value 🤦‍♂️

Samples distribution is far from normal

Questions:
1. What is the reason for such a bad p-value?
2. How can I improve it?
3. Is CLT applicable here?

• The reason for such a high p-value is that you have made a calculation error somewhere (a Welch t-test gives an absolute t-value of about 9.24; an equal variance two sample t test gives an absolute t-value of about 10.11) . Please show what formulas you used, giving explicit steps – Glen_b -Reinstate Monica Feb 8 at 9:54
• Added screenshots of the formulas – Svetoslav Dimitrov Feb 8 at 9:57
• Yep, the error is quite plain. – Glen_b -Reinstate Monica Feb 8 at 9:58
• However, I meant "please show the algebraic formulas" not "please show me spreadsheet formulas" – Glen_b -Reinstate Monica Feb 8 at 10:06

Your calculation of the test statistic is wrong. You're dividing the difference in means by the pooled standard deviation, rather than the standard error of the difference in means.

The formula for the (equal-variance) two sample t-test statistic would be:

$$\frac {{\bar {x}}_{1}-{\bar {x}}_{2}}{s_{p}\cdot {\sqrt {{\frac {1}{n_{1}}}+{\frac {1}{n_{2}}}}}}$$

but you seem to have

$$\frac {\bar{x}_1-\bar{x}_2}{s_{p}}$$