Finally, one needs to use the data to calculate test statistics and the associated p-values which provide the basis for testing hypotheses and drawing conclusions. Statistical testing is analogous to finding the signal-to-noise ratio (Carlin and Doyle, 2001). In our mice example, when sample means are compared, the signal is the difference between the means of the two mice lines and the noise is the standard error, a measurement of variability. The test statistic would be a ratio of these two quantities, and the general formula for a test statistic can be expressed as (Carlin and Doyle, 2001)
Test statistic a signal variation= n
where n is the sample size.
A p-value is the probability of obtaining a test statistic as extreme as or more extreme than the test statistic observed from the sample given that the null hypothesis is true. In other words, large negative or large positive values for the ratio in Equation (1) will result in small p-values. When the p-value for a test is equal to or smaller than the significance level (often set at 0.05 or 0.01), one rejects the null hypothesis in favor of the alternative hypothesis. Note that, as shown in Equation (1), the test statistic and therefore the p-value, are functions of the sample size, n. This implies that even a small difference between means can become statistically significant given a sufficiently large sample size.
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