Dichotomous thinking

Last updated

Dichotomous thinking or binary thinking in statistics is the process of seeing a discontinuity in the possible values that a p-value can take during null hypothesis significance testing: it is either above the significance threshold (usually 0.05) or below. When applying dichotomous thinking, a first p-value of 0.0499 will be interpreted the same as a p-value of 0.0001 (the null hypothesis is rejected) while a second p-value of 0.0501 will be interpreted the same as a p-value of 0.7 (the null hypothesis is accepted). The fact that first and second p-values are mathematically very close is thus completely disregarded and values of p are not considered as continuous but are interpreted dichotomously with respect to the significance threshold. A common measure of dichotomous thinking is the cliff effect. [1] A reason to avoid dichotomous thinking is that p-values and other statistics naturally change from study to study due to random variation alone; [2] [3] decisions about refutation or support of a scientific hypothesis based on a result from a single study are therefore not reliable. [4]

Dichotomous thinking is very often associated with p-value reading [5] [6] [7] but it can also happen with other statistical tools such as interval estimates. [1] [8]

See also

Related Research Articles

Biostatistics is a branch of statistics that applies statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results.

<span class="mw-page-title-main">Statistics</span> Study of the collection and analysis of data

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

<span class="mw-page-title-main">Statistical hypothesis test</span> Method of statistical inference

A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p-value computed from the test statistic. Roughly 100 specialized statistical tests have been defined.

In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study.

In scientific research, the null hypothesis is the claim that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null". In contrast with the null hypothesis, an alternative hypothesis is developed, which claims that a relationship does exist between two variables.

In frequentist statistics, power is a measure of the ability of an experimental design and hypothesis testing setup to detect a particular effect if it is truly present. In typical use, it is a function of the test used, the assumed distribution of the test, and the effect size of interest. High statistical power is related to low variability, large sample sizes, large effects being looked for, and less stringent requirements for statistical significance.

The Mann–Whitney test is a nonparametric statistical test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.

In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Even though reporting p-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience.

<span class="mw-page-title-main">Data dredging</span> Misuse of data analysis

Data dredging is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. This is done by performing many statistical tests on the data and only reporting those that come back with significant results.

In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false.

In statistical hypothesis testing, p-rep or prep has been proposed as a statistical alternative to the classic p-value. Whereas a p-value is the probability of obtaining a result under the null hypothesis, p-rep purports to compute the probability of replicating an effect. The derivation of p-rep contained significant mathematical errors.

<span class="mw-page-title-main">Multiple comparisons problem</span> Statistical interpretation with many tests

In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values.

In statistics, and especially in the statistical analysis of psychological data, the counternull is a statistic used to aid the understanding and presentation of research results. It revolves around the effect size, which is the mean magnitude of some effect divided by the standard deviation.

In science, a null result is a result without the expected content: that is, the proposed result is absent. It is an experimental outcome which does not show an otherwise expected effect. This does not imply a result of zero or nothing, simply a result that does not support the hypothesis.

Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. It complements hypothesis testing approaches such as null hypothesis significance testing (NHST), by going beyond the question is an effect present or not, and provides information about how large an effect is. Estimation statistics is sometimes referred to as the new statistics.

A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition, while a false negative is the opposite error, where the test result incorrectly indicates the absence of a condition when it is actually present. These are the two kinds of errors in a binary test, in contrast to the two kinds of correct result. They are also known in medicine as a false positivediagnosis, and in statistical classification as a false positiveerror.

<span class="mw-page-title-main">Replication crisis</span> Observed inability to reproduce scientific studies

The replication crisis is an ongoing methodological crisis in which the results of many scientific studies are difficult or impossible to reproduce. Because the reproducibility of empirical results is an essential part of the scientific method, such failures undermine the credibility of theories building on them and potentially call into question substantial parts of scientific knowledge.

Misuse of p-values is common in scientific research and scientific education. p-values are often used or interpreted incorrectly; the American Statistical Association states that p-values can indicate how incompatible the data are with a specified statistical model. From a Neyman–Pearson hypothesis testing approach to statistical inferences, the data obtained by comparing the p-value to a significance level will yield one of two results: either the null hypothesis is rejected, or the null hypothesis cannot be rejected at that significance level. From a Fisherian statistical testing approach to statistical inferences, a low p-value means either that the null hypothesis is true and a highly improbable event has occurred or that the null hypothesis is false.

<span class="mw-page-title-main">Equivalence test</span> Tool used to draw statistical inferences from observed data

Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined as an effect large enough to be deemed interesting, specified by an equivalence bound. The alternative hypothesis is any effect that is less extreme than said equivalence bound. The observed data are statistically compared against the equivalence bounds. If the statistical test indicates the observed data is surprising, assuming that true effects are at least as extreme as the equivalence bounds, a Neyman-Pearson approach to statistical inferences can be used to reject effect sizes larger than the equivalence bounds with a pre-specified Type 1 error rate. 

<span class="mw-page-title-main">Valentin Amrhein</span> German / Swiss professor of zoology (born 1971)

Valentin Amrhein is a German-Swiss professor of zoology at the University of Basel and science journalist. Together with Sander Greenland and others, he is a critic of significance thresholds in science and he draws attention to misunderstandings of p-values. He is author of a comment in the journal Nature on statistical significance that had the highest online attention score of all research outputs ever screened by Altmetric.

References

  1. 1 2 Lai, Jerry (2019). "DICHOTOMOUS THINKING: A PROBLEM BEYOND NHST" (PDF). ICOTS8. Retrieved 23 October 2018.
  2. ↑ Cumming, Geoff (2014). "The New Statistics: Why and How". Psychological Science. 25 (1): 7–29. doi:10.1177/0956797613504966. ISSN   0956-7976. PMID   24220629. S2CID   3484092.
  3. ↑ Berner, Daniel; Amrhein, Valentin (2022). "Why and how we should join the shift from significance testing to estimation". Journal of Evolutionary Biology. 35 (6): 777–787. doi:10.1111/jeb.14009. ISSN   1010-061X. PMC   9322409 . PMID   35582935.
  4. ↑ Amrhein, Valentin; Greenland, Sander; McShane, Blake (2019). "Scientists rise up against statistical significance". Nature. 567 (7748): 305–307. doi: 10.1038/d41586-019-00857-9 . PMID   30894741. S2CID   84186074.
  5. ↑ Rosenthal, Robert; Gaito, John (1963). "The Interpretation of Levels of Significance by Psychological Researchers". The Journal of Psychology. 55 (1). Informa UK Limited: 33–38. doi:10.1080/00223980.1963.9916596. ISSN   0022-3980.
  6. ↑ Nelson, Nanette; Rosenthal, Robert; Rosnow, Ralph L. (1986). "Interpretation of significance levels and effect sizes by psychological researchers". American Psychologist. 41 (11). American Psychological Association (APA): 1299–1301. doi:10.1037/0003-066x.41.11.1299. ISSN   1935-990X.
  7. ↑ Besançon, Lonni; Dragicevic, Pierre (2019). "The Continued Prevalence of Dichotomous Inferences at CHI". Extended Abstracts of the 2019 CHI Conference on Human Factors in Computing Systems. New York, New York, USA: ACM Press. pp. 1–11. doi:10.1145/3290607.3310432. ISBN   978-1-4503-5971-9.
  8. ↑ Helske, Jouni; Helske, Satu; Cooper, Matthew; Ynnerman, Anders; Besancon, Lonni (2021). "Can Visualization Alleviate Dichotomous Thinking? Effects of Visual Representations on the Cliff Effect". IEEE Transactions on Visualization and Computer Graphics. 27 (8). Institute of Electrical and Electronics Engineers (IEEE): 3397–3409. arXiv: 2002.07671 . doi:10.1109/tvcg.2021.3073466. ISSN   1077-2626. PMID   33856998. S2CID   233230810.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.