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Statistical Power
In frequentist statistics, power is the probability of detecting a given effect (if that effect actually exists) using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic and significance level), the sample size (more data tends to provide more power), and the effect size (effects or correlations that are large relative to the variability of the data tend to provide more power). More formally, in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis (H_0) when the alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, where \beta is the probability of making a type II error (a false negative) conditional on there being a true effect or association. Background Statistical testing uses data from samples to assess, or make inferences about, a statistical population. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequentist
Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies frequentist statistics, in which the well-established methodologies of statistical hypothesis testing and confidence intervals are founded. History of frequentist statistics Frequentism is based on the presumption that statistics represent probabilistic frequencies. This view was primarily developed by Ronald Fisher and the team of Jerzy Neyman and Egon Pearson. Ronald Fisher contributed to frequentist statistics by developing the frequentist concept of "significance testing", which is the study of the significance of a measure of a statistic when compared to the hypothesis. Neyman-Pearson extended Fisher's ideas to apply to multiple hypotheses. They posed that the ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Size (statistics)
In statistics, the size of a test is the probability of falsely rejecting the null hypothesis. That is, it is the probability of making a type I error. It is denoted by the Greek letter α (alpha). For a simple hypothesis, :\alpha = P(\text H_0 \mid H_0). In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses. :\alpha = \sup_ P(\text H_0 \mid h). A test is said to have significance level 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 \alpha, is the ... \alpha if its size is less than or equal to \alpha . In many cases the size and level of a test are equal. References Statistical hypothesis testing {{statistics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric Test
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Statistics
Parametric statistics is a branch of statistics which leverages models based on a fixed (finite) set of parameters. Conversely nonparametric statistics does not assume explicit (finite-parametric) mathematical forms for distributions when modeling data. However, it may make some assumptions about that distribution, such as continuity or symmetry, or even an explicit mathematical shape but have a model for a distributional parameter that is not itself finite-parametric. Most well-known statistical methods are parametric. Regarding nonparametric (and semiparametric) models, Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies". Example The normal family of distributions all have the same general shape and are ''parameterized'' by mean and standard deviation. That means that if the mean and standard deviation are known and if the distribution is normal, the probability o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Statistics
Bayesian statistics ( or ) is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation, which views probability as the limit of the relative frequency of an event after many trials. More concretely, analysis in Bayesian methods codifies prior knowledge in the form of a prior distribution. Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. For example, in Bayesian inference, Bayes' theorem can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequentist Statistics
Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies frequentist statistics, in which the well-established methodologies of statistical hypothesis testing and confidence intervals are founded. History of frequentist statistics Frequentism is based on the presumption that statistics represent probabilistic frequencies. This view was primarily developed by Ronald Fisher and the team of Jerzy Neyman and Egon Pearson. Ronald Fisher contributed to frequentist statistics by developing the frequentist concept of "significance testing", which is the study of the significance of a measure of a statistic when compared to the hypothesis. Neyman-Pearson extended Fisher's ideas to apply to multiple hypotheses. They posed that the ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Replication Crisis
The replication crisis, also known as the reproducibility or replicability crisis, refers to the growing number of published scientific results that other researchers have been unable to reproduce or verify. Because the reproducibility of empirical results is an essential part of the scientific method, such failures undermine the credibility of theories that build on them and can call into question substantial parts of scientific knowledge. The replication crisis is frequently discussed in relation to psychology and medicine, wherein considerable efforts have been undertaken to reinvestigate the results of classic studies to determine whether they are reliable, and if they turn out not to be, the reasons for the failure. Data strongly indicate that other natural science, natural and social sciences are also affected. The phrase "replication crisis" was coined in the early 2010s as part of a growing awareness of the problem. Considerations of causes and remedies have given rise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publication Bias
In 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 Statistical significance, 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 of experiments, design, papers with statistically significant results are three times more likely to be published than those with null results. This unduly motivates researchers to manipulate their practices to ensure statistically significant results, such as by data dredging. Many factors contribute to publication bias. For instance, once a scientific finding is well established, it may become newsworthy to publish reliable papers that fail to reject the null hypothesis. Most commonly, investigators simply decline to submit results, leading to non-response ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pilot Studies
A pilot experiment, pilot study, pilot test or pilot project is a small-scale preliminary study conducted to evaluate feasibility, duration, cost, adverse events, and improve upon the study design prior to performance of a full-scale research project. Implementation Pilot experiments are frequently carried out before large-scale quantitative research, in an attempt to avoid time and money being used on an inadequately designed project. A pilot study is usually carried out on members of the relevant population. A pilot study is used to formulate the design of the full-scale experiment which then can be adjusted. The pilot study is potentially a critical insight to clinical trial design, recruitment and sample size of participants, treatment testing, and statistical analysis to improve the power of testing the hypothesis of the study. Analysis from the pilot experiment can be added to the full-scale (and more expensive) experiment to improve the chances of a clear outcome. Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research Question
A research question is "a question that a research project sets out to answer". Choosing a research question is an essential element of both quantitative and qualitative research. Investigation will require data collection and analysis, and the methodology for this will vary widely. Good research questions seek to improve knowledge on an important topic, and are usually narrow and specific. To form a research question, one must determine what type of study will be conducted such as a qualitative, quantitative, or mixed study. Additional factors, such as project funding, may not only affect the research question itself but also when and how it is formed during the research process. Literature suggests several variations on criteria selection for constructing a research question, such as the FINER or PICOT methods. Definition The answer to a research question will help address a research problem or question. Specifying a research question, "the central issue to be resolved by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Testing
Multiple comparisons, multiplicity or multiple testing problem occurs in statistics when one considers a set of statistical inferences simultaneously or estimates a subset of parameters selected based on the observed values. The larger the number of inferences made, the more likely erroneous inferences become. Several statistical techniques have been developed to address this problem, for example, by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made. Methods for family-wise error rate give the probability of false positives resulting from the multiple comparisons problem. History The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Tel Aviv. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
