Statistical hypothesis testingA statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .
Null hypothesisIn scientific research, the null hypothesis (often denoted H0) is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.
Effect sizeIn statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening.
StatisticsStatistics (from German: Statistik, () "description of a state, a country") 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".
Alternative hypothesisIn statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc.
Selection biasSelection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed. It is sometimes referred to as the selection effect. The phrase "selection bias" most often refers to the distortion of a statistical analysis, resulting from the method of collecting samples. If the selection bias is not taken into account, then some conclusions of the study may be false.
BiasBias is a disproportionate weight in favor of or against an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, or a belief. In science and engineering, a bias is a systematic error. Statistical bias results from an unfair sampling of a population, or from an estimation process that does not give accurate results on average. The word appears to derive from Old Provençal into Old French biais, "sideways, askance, against the grain".
Publication biasIn published academic research, publication bias occurs when the outcome of an experiment or research study biases the decision to publish or otherwise distribute it. Publishing only results that show a significant finding disturbs the balance of findings in favor of positive results. The study of publication bias is an important topic in metascience. Despite similar quality of execution and design, papers with statistically significant results are three times more likely to be published than those with null results.
Test statisticA test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.
Statistical significanceIn 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 .
Observational errorObservational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken.
Design of experimentsThe design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.
Reporting biasIn epidemiology, reporting bias is defined as "selective revealing or suppression of information" by subjects (for example about past medical history, smoking, sexual experiences). In artificial intelligence research, the term reporting bias is used to refer to people's tendency to under-report all the information available. In empirical research, authors may be under-reporting unexpected or undesirable experimental results, attributing the results to sampling or measurement error, while being more trusting of expected or desirable results, though these may be subject to the same sources of error.
Survivorship biasSurvivorship bias or survival bias is the logical error of concentrating on entities that passed a selection process while overlooking those that did not. This can lead to incorrect conclusions because of incomplete data. Survivorship bias is a form of selection bias that can lead to overly optimistic beliefs because multiple failures are overlooked, such as when companies that no longer exist are excluded from analyses of financial performance.
Optimal designIn the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design.
Testing hypotheses suggested by the dataIn statistics, hypotheses suggested by a given dataset, when tested with the same dataset that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning (double dipping) would be involved: something seems true in the limited data set; therefore we hypothesize that it is true in general; therefore we wrongly test it on the same, limited data set, which seems to confirm that it is true.
Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
Confirmation biasConfirmation bias is the tendency to search for, interpret, favor, and recall information in a way that confirms or supports one's prior beliefs or values. People display this bias when they select information that supports their views, ignoring contrary information, or when they interpret ambiguous evidence as supporting their existing attitudes. The effect is strongest for desired outcomes, for emotionally charged issues, and for deeply entrenched beliefs.
Sample size determinationSample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power.
Statistical assumptionStatistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.
