When we investigate in psychology, within the inferential statistics we find two important concepts: the type I error and type II error . These arise when we are testing hypotheses with a null hypothesis and an alternative hypothesis.

In this article we will see what exactly they are, when we commit them, how we calculate them and how we can reduce them.

Parameter estimation methods

Inferential statistics are responsible for drawing or extrapolating conclusions from a population, based on information from a sample. In other words, it allows us to describe certain variables that we want to study, at a population level.

Within it, we find the parameter estimation methods , which aim to provide methods that allow us to determine (with certain precision) the value of the parameters we want to analyse, from a random sample of the population we are studying.

Parameter estimation can be of two types: point (when a single value of the unknown parameter is estimated) and interval (when a confidence interval is set where the unknown parameter would “fall”). It is within this second type, the estimation by intervals, where we find the concepts that we analyze today: the type I error and type II error.

Type I error and type II error: what are they?

Type I error and type II error are types of errors that we can make when in an investigation we are faced with the formulation of statistical hypotheses (such as the null hypothesis or H0 and the alternative hypothesis or H1). That is, when we are carrying out hypothesis testing. But to understand these concepts, we must first contextualize their use in interval estimation.

As we have seen, the estimation by intervals is based on a critical region from the parameter of the null hypothesis (H0) that we propose, as well as on the confidence interval from the sample estimator.

That is, the objective is to establish a mathematical interval where the parameter we want to study would fall . To do this, a series of steps must be carried out.

1. Hypothesis formulation

The first step is to formulate the null hypothesis and the alternative hypothesis, which, as we will see, will lead us to the concepts of type I and type II error.

Null hypothesis (H0)

The null hypothesis (H0) is the hypothesis raised by the researcher, and provisionally accepted as true . It can only be rejected by a process of falsification or refutation.

Normally, what is done is to state the absence of effect or the absence of difference (for example, it would be to state that: “There is no difference between cognitive therapy and behavioral therapy in the treatment of anxiety”).

1.2. Alternative hypothesis (H1)

The alternative hypothesis (H1), on the other hand, is the candidate to supplant or replace the null hypothesis. It often states that there are differences or effects (e.g., “There are differences between cognitive and behavioral therapy in the treatment of anxiety”).

2. Determination of significance or alpha level (α)

The second step within interval estimation is to determine the significance level or alpha level (α) . This is set by the researcher at the beginning of the process; it is the maximum probability of error that we accept to commit when rejecting the null hypothesis.

It usually takes small values, such as 0.001, 0.01 or 0.05. That is, it would be the maximum “cap” or error that we are willing to make as researchers. When the significance level is worth 0.05 (5%), for example, the confidence level is 0.95 (95%), and the two add up to 1 (100%).

Once we establish the level of significance, four situations can occur: that two types of errors occur (and this is where type I and type II error come in), or that two types of correct decisions occur. In other words, the four possibilities are:

2.1. Right decision (1-α)

It consists of accepting the null hypothesis (H0) as true . That is, we do not reject it, we maintain it, because it is true. Mathematically it would be calculated in the following way: 1-α (where α is the type I error or significance level).

2.2. Right decision (1-β)

In this case, we also make a correct decision; it consists in rejecting the null hypothesis (H0) as being false. It is also called power of proof . It is calculated: 1-β (where β is the type II error).

2.3. Type I error (α)

The type I error, also called alpha (α), is made by rejecting the null hypothesis (H0) as being true . Thus, the probability of making a type I error is α, which is the level of significance we have established for our hypothesis test.

If, for example, the α that we had established is 0.05, this would indicate that we are willing to accept a 5% probability of being wrong when rejecting the null hypothesis.

2.4. Type II error (β)

The type II or beta error (β), is made by accepting the null hypothesis (H0) being false . In other words, the probability of making a type II error is beta (β), and depends on the power of the test (1-β).

To reduce the risk of making a type II error, we may choose to ensure that the test is sufficiently powerful. To do this, we must ensure that the sample size is large enough to detect a difference when it actually exists.

Bibliographic references:

  • Botella, J. Sueró, M. Ximénez, C. (2012). Data analysis in psychology I. Madrid: Pirámide.
  • Lubin, P. Macià, A. Rubio de Lerma, P. (2005). Mathematical Psychology I and II. Madrid: UNED.
  • Pardo, A. San Martín, R. (2006). Data analysis in psychology II. Madrid: Pirámide.