p Value

Hypothesis Testing

Hypothesis testing is one of the main methods used for statistical inference. In hypothesis testing, researchers set up a hypothesis about a population parameter(s) and, based on data from a random sample drawn from this population, test its [Page 1144]tenability. The tested hypothesis is called the null hypothesis. Null hypotheses are represented by H0. Null hypotheses may specify a value or a range of values for population parameter(s), differences or relationships between population parameters, or an effect in the population. For example, H0 can state that a population mean is 100 (H0: μ = 100) or that the difference between two populations’ means is greater than 50 (H0: μ1 – μ2 ≥ 50). In the most common application of hypothesis testing, H0 of no association, no difference, or no effect is used, and this type of H0 is often referred to as a nil null hypothesis. An example of a nil null hypothesis might be that there is no difference between two population means (H0: μ1 = μ2).

The H0 is tested against a statistical alternative hypothesis. If H0 is rejected, the alternative hypothesis holds true for the population. Alternative hypotheses are commonly symbolized as Ha, although some use other symbols, such as H1. Generally, H0 is tested using data from a sample(s), however, both H0 and Ha always refer to population parameters. For the H0 that there is no difference between two population means (H0: μ1 = μ2), an Ha would be that these population means are not the same (Ha: μ1 ≠ μ2). A nondirectional Ha about parameters is called a two-sided or two-tailed Ha. For example, Ha: μ1 ≠ μ2 denotes a difference between two population means but does not indicate which of these means is larger or smaller. On the other hand, a one-sided or one-tailed Ha specifies the direction of the relationship. For the H0: μ1 = μ2, a one-sided Ha would be Ha: μ1 < μ2 or Ha: μ1 > μ2.

Often, Ha states researchers’ expectations or assumptions about the study's outcome and is commonly referred to as the research hypothesis. In many cases, researchers would like to reject H0 and hold Ha tenable for the population. However, this is not always the case. For example, when testing the effectiveness of a cheap drug compared to a more expensive drug, H0 can be that the cheap drug's effectiveness is the same as the expensive drug's. In this situation, researchers probably would not want to reject the H0.

After establishing H0 and Ha, data are collected from a sample and then used to test the tenability of the hypotheses about population parameters. The hypothesis that is tested is always H0, not Ha. The hypothesis testing process is a form of indirect proof—proof by contradiction. The testing process starts with the assumption that H0 is true for the population. If the magnitude of the difference between the obtained statistic (e.g.,

or SD) and the population parameter as stated in H0 is highly unlikely to be observed in a sample belonging to a population where H0 is true, then H0 is rejected in favor of Ha. If the observed difference is not sufficiently unlikely, then H0 is considered to be tenable for the population, and researchers fail to reject H0. Notice that researchers either reject or fail to reject H0; H0 is never accepted because it is never proved, but rather the evidence may be insufficient to disprove it.

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