Your question shows problems in understanding the concepts. 1.stat. hypotheses testing is about deciding which of two hypotheses is most likely true. 2. In general we are interested in more specific things so We do not test whether populations are different. Suppose for example that we would like to compare the mean scores on a test to see if on the ave. scores of men are lower than women's. That is do women get higher scores on the ave. than men. We already know the populations are different, one male the other female. What we are testing is one the ave. are men's score's lower than women's and what is the probability that our conclusion is correct. Thus we would be testing if the mean score of one group was higher than the other. Give that if you have only the mean and s.d. of each of two groups, All you can say is how your sample means relate which is not enough information to test a hypothesis. Best, David Booth

Following David Eugene Booth's response, you should formulate the null and alternative hypotheses and some related information such as the effect size, the level of significance, the power of the test and the sample sizes; but doing this after having the average of the data and the standard deviation is not a good research practice.

You may apply t test to make analyze two sets of data. This will give you a detail view. Using SPSS you can do that easily. If you want to analyze from the resent view you have to know that what type of information you can infer from these information. You can deal one hypothesis with this. You have to make your hypothesis and then draw the results from it

If you know the mean, SD, and the number of cases in each group then you can simulate a t-test. Some software will let you do this.

Jerry Miller How can you simulate the t-test without the original data. There are an awful lot of ways to get those parameters. e.g. Bootstrap works only because you are sampling from the original data not simulated. Have I misunderstood? D. Booth

Someone would have to have the original data in order to produce the means and standard deviations in the first place. But often researchers only have the mean and standard deviation available, and not the original data. In that case you can still do a t-test, where the null hypothesis Ho is that there are no differences between the means of the two groups, and H1 is that the means are in fact different. This can be done using the ordinary arithmetic means and standard deviations. Both groups should be normally distributed or at least have a n > 30. By "simulation" I meant you're plugging in the means and SDs without determining them yourself from the raw data; "compute" would have been better.

Jerry Miller Thank you I understand now and you are,of course, correct in what you say except without the original data you can't do the assumption checks you recommend. I am assuming the question was asked because the original data was, for some reason, not available. Thank you for clarifying. Best wishes, David Booth

Hi all,

With only the average and the standard deviation we cannot do anything, not even a descriptive analysis. Sample sizes are also needed. We also don't know if the samples are related or independent. If we assume that they are independent and we have the sample sizes, we can replace the values in the T or Welch formulas, but this is arithmetic and not statistical inference. What if the "significance" is about variances? We would have similar arithmetic possibilities and problems. As a consequence, the same term "significant" is not clear. This is why I agree with David Eugene Booth. I apologize if this comment sounds a bit rough.