# Unpaired t-Test with equal sample sizes and unequal variances [duplicate]

I have two samples of $n=10$ with the following values

Sample 1:

• Mean = $3$
• $s_{d} = 0.4$

Sample 2:

• Mean = $3.35$
• $s_{d} = 0.3$

but the observations of both samples are unknown and I want to know the common $s_{d}$ to calculate $t_{0}$

Note: this is no homework is only an exercise from the tutorial, which has not been solved.

## marked as duplicate by whuber♦Dec 1 '13 at 21:57

• is this homework? – John Nov 30 '13 at 19:09
• no it's normal exercise – Ben Ishak Nov 30 '13 at 19:33
• What is this $t_0$? – Glen_b Dec 1 '13 at 0:56
• $t_{0} = (d- µ_{0}) / (s_{d} / \sqrt{n})$ for paired t-test – Ben Ishak Dec 1 '13 at 14:21

i may suggest the following solution

$$s_{d_{1}-d_{2}} = \sqrt{1/_n * (s_{d1}^2 + s_d{2}^2)} = \sqrt{1/_{10} * (0.4^2 + 0.3^2)} = 0.158$$

$$t = d_{1} - d_{2} / s_{d_{1}-d_{2}} = -0.35 / 0.158 = -2.215$$

• This unfortunately is incorrect. The duplicate question shows how to combine the SDs into a pooled SD, because their squares are variances and that thread concerns combining variances. – whuber Dec 1 '13 at 21:57
• i still not sure if my solution was correct, but the thread that you sepposed is not the same as my problem, as he has 2 matrices with all values $(x_{i}, y_{i})$ but i have only the SDs and the means – Ben Ishak Dec 2 '13 at 17:10
• Your problem is identical to that one, but happens to be much simpler: the squares of your SDs are one-by-one covariance matrices and your means are the means of vectors of dimension 1. – whuber Dec 2 '13 at 17:12
• [this][1] what i was looking for [1] = en.wikipedia.org/wiki/… – Ben Ishak Jan 18 '14 at 14:44