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To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true. [5] [12] The null hypothesis is rejected if the p-value is less than (or equal to) a predetermined level, .
It is denoted by the Greek letter α (alpha). For a simple hypothesis, = (). In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses. [1]
In this method, before conducting the study, one first chooses a model (the null hypothesis) and the alpha level α (most commonly 0.05). After analyzing the data, if the p -value is less than α , that is taken to mean that the observed data is sufficiently inconsistent with the null hypothesis for the null hypothesis to be rejected.
How to calculate alpha. ... To figure the expected return for an investment’s level of risk, analysts use beta, which measures an asset’s volatility and can be used to gauge risk. If a stock ...
The Bonferroni correction can also be applied as a p-value adjustment: Using that approach, instead of adjusting the alpha level, each p-value is multiplied by the number of tests (with adjusted p-values that exceed 1 then being reduced to 1), and the alpha level is left unchanged.
To reduce the probability of committing a type I error, making the alpha value more stringent is both simple and efficient. To decrease the probability of committing a type II error, which is closely associated with analyses' power, either increasing the test's sample size or relaxing the alpha level could increase the analyses' power.
Power analyses can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size (in other words, producing an acceptable level of power). For example: "How many times do I need to toss a coin to conclude it is rigged by a certain amount?"
This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution. If the q s value is larger than the critical value q α obtained from the distribution, the two means are said to be significantly different at level α : 0 ≤ α ≤ 1 . {\displaystyle \ \alpha ...