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Statistics are used to gain understanding of a population by describing characteristics of the population We discussed several population characteristics: µ σ p ρ β mean standard deviation proportion Pearson correlation slope of linear association And we discussed how to estimate those using statistics computed from a small sample from the population X̅ s p̂ r b sample mean sample standard deviation sample proportion sample correlation slope of best linear fit line We repeatedly applied two general methods of statistical inference Hypothesis tests Confidence intervals Both of which follow the general steps of 1. Assume certain values for the population characteristics 2. Derive the behavior (distribution) of the sample statistics if the assumptions in step 1 were true. 3. Use that distribution to estimate the probability of the observed sample statistic occurring (p-value). 4. If the probability is low, we rule out the value of the population statistic assumed in step 1 Take-home message #1 The evidence we gain from statistics is from ruling out things. o Our evidence is much better when we disprove things, o It is much more nebulous if we fail to disprove. Take-home message #2 Statistical significance and clinical significance are different. o Statistical significance says that our study has given us enough evidence to disprove certain values of a parameter of interest. o Clinical significance is an indication that the magnitude of an effect is important in the clinical setting o Our goal with statistics should be to find statistically significant evidence of effects that are clinical significant.