27 Introducing hypothesis tests
You have studied how to construct confidence intervals, which answer estimation-type RQs, and indicate the precision with which a statistic estimates a parameter. Now, you begin studying decision-type RQs, which help you make decisions about the value of unknown parameters based on the value of the statistic (Table 27.1). This is called hypothesis testing.
The word hypothesis means 'a possible explanation'.
Scientific hypotheses refer to potential scientific explanations that can be tested by collecting data. For example, an engineer may hypothesise that replacing sand with glass in the manufacture of concrete will produce desirable characteristics (Devaraj et al. 2021).
Statistical hypotheses refer to statistical explanations that are required to determine whether the evidence (i.e., data) supports the scientific hypotheses. The statistical hypotheses are the foundation of the logic of hypothesis testing.
This book discusses statistical hypotheses.
The decision-making process (Chap. 15) previously discussed was:
- Assumption: Make an assumption about the population. Initially, assume that the sampling variation explains any discrepancy between the observed sample and assumed value of the population parameter.
- Expectation: Based on the assumption about the parameter, describe the distribution of the values of the sample statistic that might reasonably be observed from all the possible samples that might be obtained (due to sampling variation).
- Observation: Observe the data from one of the many possible samples, and compute the observed sample statistic from this sample.
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Decision: If the observed sample statistic is:
- unlikely to happen by chance, it contradicts the assumption about the population parameter, and the assumption is probably wrong. The evidence suggests that the assumption is wrong (but it is not certainly wrong).
- likely to happen by chance, it is consistent with the assumption about the population parameter, and the assumption may be correct. No evidence suggests the assumption is wrong (though it may be wrong).
In this Part, we explore decision-type relational or interventional RQs with a comparison. Decision-type RQs with a connection are discussed in Chaps. 36 and 37.
| Estimation (CI) | Decision (Tests) | |
|---|---|---|
| Descriptive RQs | ||
| Proportions for one sample | Chap. 20 | Chap. 28 |
| Means for one sample | Chap. 22 | Chap. 29 |
| Mean differences (paired data; within-individual) | Chap. 23 | Chap. 31 |
| Relational/Interventional RQs (Comparison) | ||
| Comparing two means (between-individuals) | Chap. 24 | Chap. 32 |
| Comparing two odds (between-individuals) | Chap. 25 | Chap. 33 |
| Relational/Interventional RQs (Connection) | ||
| Correlation | Sect. 36.4 | |
| Regression | Sect. 37.6 | Sect. 37.6 |