Effect size in the context of Null hypothesis

⭐ Core Definition: Effect size

In 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 one parameter for a hypothetical population, or 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, and the risk of a particular event (such as a heart attack). Effect sizes are a complementary tool for statistical hypothesis testing, and play an important role in statistical power analyses to assess the sample size required for new experiments. Effect size calculations are fundamental to meta-analysis, which aims to provide the combined effect size based on data from multiple studies. The group of data-analysis methods concerning effect sizes is referred to as estimation statistics.

Effect size is an essential component in the evaluation of the strength of a statistical claim, and it is the first item (magnitude) in the MAGIC criteria. The standard deviation of the effect size is of critical importance, as it indicates how much uncertainty is included in the observed measurement. A standard deviation that is too large will make the measurement nearly meaningless. In meta-analysis, which aims to summarize multiple effect sizes into a single estimate, the uncertainty in studies' effect sizes is used to weight the contribution of each study, so larger studies are considered more important than smaller ones. The uncertainty in the effect size is calculated differently for each type of effect size, but generally only requires knowing the study's sample size (N), or the number of observations (n) in each group.

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👉 Effect size in the context of Null hypothesis

The null hypothesis (often denoted ${\textstyle H_{0}}$ ) is the claim in scientific research 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 (often denoted $H_{A}$ or $H_{1}$ ) is developed, which claims that a relationship does exist between two variables.

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⭐ Core Definition: Effect size
👉 Effect size in the context of Null hypothesis
Effect size in the context of Meta-analysis
Effect size in the context of Experimental economics
Effect size in the context of Fisher's geometric model

Effect size in the context of Meta-analysis

Meta-analysis is a method of synthesis of quantitative data from multiple independent studies addressing a common research question. An important part of this method involves computing a combined effect size across all of the studies. As such, this statistical approach involves extracting effect sizes and variance measures from various studies. By combining these effect sizes the statistical power is improved and can resolve uncertainties or discrepancies found in individual studies. Meta-analyses are integral in supporting research grant proposals, shaping treatment guidelines, and influencing health policies. They are also pivotal in summarizing existing research to guide future studies, thereby cementing their role as a fundamental methodology in metascience. Meta-analyses are often, but not always, important components of a systematic review.

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Effect size in the context of Experimental economics

Experimental economics is the application of experimental methods to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).

A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.

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Effect size in the context of Fisher's geometric model

Fisher's geometric model (FGM) is an evolutionary model of the effect sizes and effect on fitness of spontaneous mutations proposed by Ronald Fisher to explain the distribution of effects of mutations that could contribute to adaptative evolution.

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Effect size in the context of Null hypothesis

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⭐ Core Definition: Effect size

👉 Effect size in the context of Null hypothesis

Effect size in the context of Meta-analysis

Effect size in the context of Experimental economics

Effect size in the context of Fisher's geometric model