Hi Bodine, thank you for the opportunity to help you with your question!
a. For two groups, 'men' and 'women', we are provided the mean value of a certain measure, say X, and its standard deviation. Women show a higher mean value of X than men and also a greater deviation (or dispersion) around the mean value.
b. Although it might appear that given the data, women have higher value of X than men, we cannot be completely sure if that is the case. Certainty, in statistical terms, implies performing tests e.g. a 2 samples t-test which examines the hypothesis that the mean value of X is significantly different for men compared to women.
In order to be absolutely certain, one would need to know all the values of X for the two groups and then perform a 2 samples t-test and check for the p-value. If p < 0.05, then we can be confident in saying that the mean values of X are indeed statistically different for men vs. women.
I hope this helps. Feel free to ask me any further questions.
Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 17th, 2015
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