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In null-hypothesis significance testing, the p-value [note 1] 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. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [ note 1 ] [ 1 ] [ 2 ] This number is often expressed as a percentage (%), ranging from 0% to 100%.
A possible null hypothesis is that the mean male score is the same as the mean female score: H 0: μ 1 = μ 2. where H 0 = the null hypothesis, μ 1 = the mean of population 1, and μ 2 = the mean of population 2. A stronger null hypothesis is that the two samples have equal variances and shapes of their respective distributions.
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
The specific calculation of the likelihood is the probability that the observed sample would be assigned, assuming that the model chosen and the values of the several parameters θ give an accurate approximation of the frequency distribution of the population that the observed sample was drawn
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]
[1] The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a ...