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The critical value for a particular test (i.e., for a particular statistical hypothesis and alpha value) is the value of the test statistic such that if the observed test statistic is more extreme, the statistical hypothesis is rejected.
The critical value essentially is: if you get some statistic in your sample that is so different from the average, it is likely a real pattern, and not simply an artifact of your sample being unusual.
For example, at a 5% significance level (and degree of freedom equal to 1), the critical value for a one-tailed test is 6.314. My question is 'why this specific value?' Is it necessarily 6.314, or could it have been otherwise?
In hypothesis testing, the value corresponding to a specific rejection region is called the critical value, \(z_{crit}\) (“\(z\)-crit”) or \(z*\) (hence the other name “critical region”). Finding the critical value works exactly the same as finding the z-score corresponding to any area under the curve like we did in Unit 1.
In hypothesis tests, critical values determine whether the results are statistically significant. For confidence intervals, they help calculate the upper and lower limits. In both cases, critical values account for uncertainty in sample data you’re using to make inferences about a population.
Critical value is a value on a test distribution that is used to decide whether the null hypothesis should be rejected or not. Understand critical value using solved examples.
11 Οκτ 2024 · In statistics, the critical value plays an essential role in hypothesis testing and confidence interval estimation. It determines the threshold at which we either reject or fail to reject a hypothesis, making it crucial for drawing meaningful conclusions from data.
