8: Inferential Statistics
- Page ID
- 45180
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Statistical methods are important in biology because results of experiments are usually not clear-cut and therefore tests to support decisions between competing hypotheses are needed.
We will limit ourselves to a general discussion with examples, but beginning in this chapter, we start our introductions of specific types of statistical tests. As a reminder, our statistical philosophy is frequentist and follows the Null Hypothesis Significant Testing or NHST approach. Discussion of Bayesian statistical approaches are included as appropriate.
Thus, all statistical tests we will talk about share the following requirements or properties.
- The type of data we have dictates which test or tests are appropriate.
- We start with a clear description of the null hypotheses.
- Set the Type I error rate, alpha \((\alpha)\). By convention, 5% is often used (Cowles and David 1982)
- We must be aware of the assumptions our statistical tests make and what, if any, modifications to them we can make.
- Correct computation of the test statistic and degrees of freedom.
- Comparison of the critical value and the test statistic value, with interpretation and significance testing (p-value, Bayesian Factor, cf. discussion in Goodman 2008).
We can provide a flow-chart of these steps (Fig. \(\PageIndex{1}\)).
While we want to avoid the impression that statistical analysis is simply a matter of following a step-by-step protocol as in Fig. \(\PageIndex{1}\), it nevertheless may be helpful to think of it as such, understanding all the while that there are caveats and assumptions that accompany the choices we make while following the protocol.
- 8.1: The null and alternative hypotheses
- Defining the basic components of the NHST framework, including test statistics, p-values, and null and alternative hypotheses.
- 8.2: The controversy over proper hypothesis testing
- The controversy over whether a p-value should be interpreted as evidence for a hypothesis. Limitations of the frequentist NHST approach, and discussion of the alternative of Bayesian statistics. Correct interpretation of p-values, and common incorrect interpretations.
- 8.3: Sampling distribution and hypothesis testing
- Sampling distribution and how it is applied in hypothesis testing, including discussion of sampling error and confidence intervals.
- 8.4: Tails of a test
- All possible hypotheses involving one or two groups, their classification into one- or two-tailed comparisons, and how different tail distributions are interpreted. Includes example cases.
- 8.5: One sample t-test
- Applying the one-sample \(t\)-test to evaluate data from a single sample population, when the true population parameters are unknown.
- 8.6: Confidence limits for the estimate of population mean
- Determining confidence limits for population mean estimate, using the \(t\) distribution.