some knowledge about comare means of two group

Question

I'm studying a bout statistic. I can compute very well. But i don't really know well.

I want to know clearly about theory. And i have this problem:

An experimenter wishes to compare two treatments A and B and obtains some data observations $x_i$ using treatment A and some data observations $y_i$ using treatment B. It turns out that mean(x)> mean(y) and so the experimenter concludes that treatment A results in larger data values on average than treatment B.

How do you feel about the experimenter’s conclusion?

What other information would you like to know?

As my opinion, I thik their conclusion is nor right. Because, just base on average of sample take random from a population. We can point out any conclusion. It's not evidence to give any conclusion. But in the second question, I don't know what do we need more?

More, If we have a test with null hypthesis:

$H_o:\mu_X-\mu_Y=0$

and $H_0 $ is rejected. So the last result is $\mu_X>\mu_Y=0$ .

That right because I see many book do the same thing. But why we can have that?

Answer 1

You need to know if the difference is significant.

How to do that ? The experimenter should have done a T-test to test if the difference is significant or not, and give the p-value. If the p-value is smaller than 5%, then we conclude to a significant difference. The p-value is the probability that the test statistics we compute is at least as extreme as what we observe, under the null hypothesis.

If you want to make a T-test yourself, you need to know all the observations, and test the following assumptions :

• Normality of the observations (with a Shapiro-Wilk test ; if you reject the normality, try a Wilcoxon test, it is non-parametric).
• Equality of variances of the two samples (with a F-test ; if you reject the equality of variances, try a Welch test).
• Independance of the observations (you can't test that, but use your common sense when the experimenter describe the experience).