Unpaired t-Test with equal sample sizes and unequal variances

Question

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

Sample 1:

Sample 2:

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.

$t_{0} = (d- µ_{0}) / (s_{d} / \sqrt{n})$ for paired t-test — Ben Ishak, Dec 01 '13 at 14:21

Ben Ishak · Accepted Answer · 2014-01-18T14:40:43.207

0

i may suggest the following solution

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

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

edited Jan 18 '14 at 14:40

answered Dec 01 '13 at 15:01

Ben Ishak

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 01 '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 02 '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 02 '13 at 17:12
[this][1] what i was looking for [1] = http://en.wikipedia.org/wiki/Student's_t-test#Equal_or_Unequal_sample_sizes.2C_unequal_variances – Ben Ishak Jan 18 '14 at 14:44

1 Answers1