Mean (statistics) in the context of Effect size

⭐ Core Definition: Mean (statistics)

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.

The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x₁, x₂, ..., x_n is typically denoted using an overhead bar, ${\bar {x}}$ . If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the sample mean ( ${\bar {x}}$ ) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted $\mu$ or $\mu _{x}$ .

↓ Menu

HINT:

👉 Mean (statistics) in the context of 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.

↓ Explore More Topics

In this Dossier

⭐ Core Definition: Mean (statistics)
👉 Mean (statistics) in the context of Effect size
Mean (statistics) in the context of Probability density function
Mean (statistics) in the context of Short stature

Mean (statistics) in the context of Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words. While the absolute likelihood for a continuous random variable to take on any particular value is zero, given there is an infinite set of possible values to begin with. Therefore, the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample.

More precisely, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of a continuous variable's PDF over that range, where the integral is the nonnegative area under the density function between the lowest and greatest values of the range. The PDF is nonnegative everywhere, and the area under the entire curve is equal to one, such that the probability of the random variable falling within the set of possible values is 100%.

View the full Wikipedia page for Probability density function

↑ Return to Menu

Mean (statistics) in the context of Short stature

Short stature refers to a height of a human that is below typical. Whether a person is considered short depends on the context. Because of the lack of preciseness, there is often disagreement about the degree of shortness that should be called short. Dwarfism is the condition of being very short, often caused by a medical condition. In a medical context, short stature is typically defined as an adult height that is more than two standard deviations below a population’s mean for age and sex, which corresponds to the shortest 2.3% of individuals in that population.

Shortness in children and young adults nearly always results from below-average growth in childhood, while shortness in older adults usually results from loss of height due to kyphosis of the spine or collapsed vertebrae from osteoporosis. The most common causes of short stature in childhood are constitutional growth delay or familial short stature.

View the full Wikipedia page for Short stature

↑ Return to Menu

Mean (statistics) in the context of Effect size

Mean (statistics) Study page number 1 of 1

Play TriviaQuestions Online!

Skip to study material about Mean (statistics) in the context of "Effect size"

⭐ Core Definition: Mean (statistics)

👉 Mean (statistics) in the context of Effect size

Mean (statistics) in the context of Probability density function

Mean (statistics) in the context of Short stature