Type I error and type II error: what are they and what do they indicate in statistics?

When we do research in psychology, Within inferential statistics we find two important concepts: type I error and type II error.. These arise when we are performing hypothesis tests 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.

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Parameter estimation methods

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

Inside it we find parameter estimation methods, whose objective is to provide methods that allow to determine (with some precision) the value of the parameters that we want to analyze, from a random sample of the population that we are studying.

Parameter estimation can be of two types: punctual (when a single value of the parameter is estimated unknown) and by intervals (when a confidence interval is established where the parameter would "fall" a stranger). It is within this second type, the estimation by intervals, where we find the concepts we are analyzing today: type I error and type II error.

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

The type I error and type II error are types of errors that we can commit when in an investigation we are before 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 tests. 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 in the confidence interval from the estimator of the sample.

That is, the goal is 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 error and type II error.

1.1. Null hypothesis (H0)

The null hypothesis (H0) is the hypothesis that the researcher proposes, and that he provisionally accepts as true.. You can only reject it through a process of falsification or rebuttal.

Normally, what is done is to state the absence of effect or the absence of differences (for example, it would be state that: “There are no differences between cognitive therapy and behavior 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. This usually states that there are differences or effect (for example, "There are differences between cognitive therapy and behavior therapy in the treatment of anxiety").

• You may be interested in: "Cronbach's alpha (α): what it is and how it is used in statistics"

2. Determination of the level of significance or alpha (α)

The second step in interval estimation is determine the significance level or the alpha (α) level. 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. In other words, 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 (and this is where the type I error and type II error come in), or that two types of decisions are produced correct. That is, the four possibilities are:

2.1. Correct decision (1-α)

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

2.2. Correct decision (1-β)

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

23. Type I error (α)

The type I error, also called alpha (α), is committed by rejecting the null hypothesis (H0) being this true. Thus, the probability of making a type I error is α, which is the significance level that 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 (β) error is made when accepting the null hypothesis (H0) when it is false.. That is, the probability of committing a type II error is beta (β), and it 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 powered. To do this, we must ensure that the sample size is large enough to detect a difference when it actually exists.