27 Introducing hypothesis tests

We have studied forming confidence intervals, which answer estimation-type RQs, and indicate the precision with which a statistic estimates a parameter.

Now, we begin looking at decision-type RQs, which help us 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 usually refer to the explanations that scientists or engineers are wishing to demonstrate are true; for example, an engineer may expect that replacing sand with glass in the manufacture of concrete produces desirable characteristics.436

Statistical hypotheses refer to the null hypothesis and the alternative hypothesis that are necessary for formal statistical hypothesis testing. These refer to the two possible statistical explanations for the difference between the proposed population parameter and the observed sample statistic.

We are discussing statistical hypotheses.

The decision-making process (Chap. 15) previously discussed was:

  1. Assumption: Make an assumption about the population.

  2. Expectation: Based on this assumption, the distribution of the possible values of the sample statistic can be described.

  3. Observation: If sample information is observed that is:

    • unlikely to happen by chance, it is contrary to that assumption about the population parameter, and the assumption is probably wrong. There is evidence to suggest that the assumption is wrong (but it is not certainly wrong).
    • likely to happen by chance, it is consistent with that assumption about the population parameter, and the assumption may be correct. There is no evidence to suggest 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. 35 and 36.)

TABLE 27.1: Confidence interrvals and hypothesis tests for different situations
Estimation type (CI) Decision type (Tests)
Descriptive RQs
Proportions for one sample Chap. 20
Means for one sample Chap. 22 Chap. 28
Mean differences (for paired data; within-individual comparisons) Chap. 23 Chap. 30
Relational/Interventional RQs (Comparison)
Means for two samples (between-individuals comparisons) Chap. 24 Chap. 31
Odds for two samples, comparing ORs (between-individuals comparisons) Chap. 25 Chap. 32
Relational/Interventional RQs (Connection)
Correlation Sect. 35.4
Regression Sect. 36.7 Sect. 36.7