In the 05' VCAA paper, there was a question that said
Q. 'What conclusions can be drawn from the descriptive statistics that Rhonda provided?
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And the answer was:
None, because these are descriptive statistics.
This question was very poorly answered. It is clear that students did not understand the limitations of descriptive statistics.
Can somebody explain to me why it's 'none'? I don't understand what they mean by the explanation of 'these are descriptive statistics' nor the 'limitations'
Descriptive Statistics = Mean, Median, Mode, Range, IQR, etc etc
Inferential Statistics = t-tests, ANOVA, MANOVA, etc.
Descriptive Statistics provide information about the sample that you have yourself. However, it is not a comparison between the sample and population, hence you can't use Descriptive Stats to make determinations about the populations (and hence the conclusion).
For example, if you have Group A and Group B with the means of 7.1 and 7.2 each, you might think that this means that Group B is better than Group A. But it could also mean that you managed to get the 7.2 figure through luck, that due to various factors, you've managed to arrive at a mean of 7.2, when in another repetition of the experiment, you might get a figure of 6.9.
One way of determining this is through the usage of tests of significance, for example the t-tests. This provides inferential statistics that you can use to help determine whether Group B's 7.2 mean is more significantly different than Group As.