The dominant method of inference in psychology is statistical testing (also called hypothesis testing; null hypothesis statistical testing).
This involves stating a pair of competing hypotheses about Reality, collecting relevant data, and using the data to make a choice between the two competing hypotheses. This choice is called a “statistical decision”. Statistical decision-making, which involves the possibility of incorrect decisions, is possible because we make reasonable assumptions about the nature of distributions of possible outcomes under various competing hypotheses. To understand this requires understanding: o the decision-making framework; and o the idea of “reasonable assumptions about the nature of distributions of possible outcomes under competing hypotheses”. Examples
Experiment concerning attitudes about tanning. The investigators suspected that individuals who are exposed to not-tan models will express less favorable attitudes toward tanning (lower values on a scale of 1 to 5) than individuals who are exposed to tan models.
Experiment concerning estimated confidence of the individual who answered geography questions. The investigators suspected that individuals presented with imprecise answers would estimate the answerer as less confident (lower values on a scale of 1 to 8) than individuals presented with precise answers.
The Decision-Making Framework
Formally, for the tanning experiment, one imagines two populations—a population of individuals exposed to not- tan models and a population of individuals exposed to tan models. Every individual in each population has some attitude toward tanning, and within each population, there is variability in attitude toward tanning. Thus, each population has a population mean and a population standard deviation.
The two competing hypotheses are: that the two population means are the same. (This is called the null hypothesis.) This is a sort of baseline idea that the investigators generally hope is not true (because if they thought it was true, they wouldn’t have bothered to do the study). that the population mean attitude of individuals exposed to not-tan models is lower than that of individuals exposed to tan models. (This is called the alternative hypothesis; it is sometimes called the research hypothesis.)
In the hypothesis-testing framework, what one wants to know is: Does the data provide sufficiently compelling evidence against the null hypothesis that the null hypothesis can be rejected (in favor of the alternative hypothesis)?
In the hypothesis-testing framework: one assumes that one or the other of the two hypotheses is a true statement about Reality. one makes a decision about the null hypothesis—either to retain it (generally a disappointment for the investigators) or to reject it.
For the tanning study, the hypotheses are: the null hypothesis H0: μNT = μT (which is equivalent to : μNT – μT = 0) the alternative hypothesis Ha: μNT < μT (which is equivalent to : μNT – μT < 0)
As indicated above, population means (e.g., μNT and μT) cannot be known—they must be estimated from sample information. (Sometimes the populations of interest don’t even really exist! But knowing something about them is nevertheless of interest.)
For attitudes toward tanning, the population means μNT and μT are estimated by conducting an experiment and using the sample means and standard deviations to estimate the population means and standard deviations, respectively.
The decision-making framework is as follows:
So, in this framework, two types of incorrect decision…