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

When we research psychology, in inferential statistics we find two important concepts: type I error and type II error. These arise when we perform hypothesis testing with a null hypothesis and an alternate hypothesis.

In this article, we’ll see what exactly they are, when we hire them, how we calculate them, and how we can reduce them.

    Parameter estimation methods

    Inferential statistics are responsible for extracting 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 the population level.

    Within it we find the methods of parameter estimation, Which aim to provide methods 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: point (when estimating a single unknown parameter value) and interval (when a confidence interval is set where the unknown parameter would “fall”). It is in this second type, interval estimation, that 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?

    Type I error and Type II error are types of errors that we can make when, in a survey, we are confronted with the formulation of statistical hypotheses (Like the null hypothesis or H0 and the alternative hypothesis or H1). In other words, when we are doing hypothesis testing. But to understand these concepts, we must first contextualize their use in interval estimation.

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

    In other words, 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 performed.

    1. Formulation of hypotheses

    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 proposed by the researcher, and which he accepts provisionally as true.. It can only be rejected by a process of falsification or refutation.

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

    1.2. Alternative hypothesis (H1)

    The alternative hypothesis (H1), on the other hand, is the aspirant to supplant or replace the null hypothesis. This usually indicates that there are differences or effects (eg, “there are differences between cognitive therapy and behavior therapy in treating anxiety”).

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

      The second step of interval estimation is determine the significance level or alpha (α) level. This is defined by the researcher at the start of the process; it is the maximum probability of error that we accept to make by 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 “limit” or the maximum error that we are prepared to make as researchers. When the significance level is 0.05 (5%), for example, the confidence level is 0.95 (95%) and the two add up to 1 (100%).

      Once we have established the level of significance, 4 situations can occur: that two types of errors occur (and this is where the type I error and the type II error come into play), or two kinds of correct decisions occur. In other words, the four possibilities are:

      2.1. Good decision (1-α)

      It consists in accepting the null hypothesis (H0) being this true. In other words, we don’t 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 the level of significance).

      2.2. Good decision (1-β)

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

      2.3. Type I error (α)

      Type I error, also called alpha (α), it is committed by rejecting the null hypothesis (H0) being this true. So, the probability of making a Type I error is α, which is the level of significance that we established for our hypothesis test.

      If, for example, α we set is 0.05, that would indicate that we are willing to accept a 5% probability of making a mistake by rejecting the null hypothesis.

      2.4. Type II error (β)

      The type II or beta (β) error is made by accepting the null hypothesis (H0) being this 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 make sure the test has enough power. To do this, we need to make sure that the sample size is large enough to detect a difference when it actually exists.

      Bibliographical references:

      • Botella, J. Serum, M. Ximénez, C. (2012). Data Analysis in Psychology I, Madrid: Pyramid.
      • 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: Pyramid.

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