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Statement that says there is no relationship between the two measured items

Null Hypothesis

The statistical power of a research design is the probability that the study will reject the null hypothesis, given a specific sample size and an expected relationship strength. For instance, if a design has a power of $$.80$$, it means there is an $$80\%$$ chance of correctly rejecting the null hypothesis when the expected relationship exists in the population. It is essentially the complement of the probability of making a Type II error, so researchers strive for high statistical power to avoid missing a real effect.

Statistical Power

Critics of null hypothesis testing argue that the strict convention of rejecting the null hypothesis only when $$p < .05$$ is logically flawed. This rigid threshold creates an artificial divide where a result of $$p = .04$$ is deemed significant and worthy of publication, while a nearly identical result of $$p = .06$$ is dismissed as not significant. This arbitrariness can prevent valuable research from being published and exacerbates the file drawer problem by suppressing non-significant findings.

Arbitrariness of the p-value Threshold

Bayesian statistics is an approach to inferential statistics where a researcher specifies the prior probability that the null hypothesis and alternative hypotheses are true before conducting a study. Once the study is conducted, the probabilities are updated based on the newly collected data. This approach offers a potential alternative to traditional null hypothesis testing by providing a logical framework for quantifying uncertainty using probability distributions.

Bayesian Statistics

A Type I error is a false positive in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are statistically significant—thereby rejecting the null hypothesis—when, in reality, the null hypothesis is true and there is no actual relationship in the population. These errors happen because random sampling error can occasionally produce extreme results even when no true effect exists. The predetermined alpha level dictates the probability of committing this error when the null hypothesis is true.

Type I Error

A Type II error is a false negative in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are not statistically significant—thereby retaining the null hypothesis—when, in reality, the null hypothesis is false and a true relationship does exist in the population. In practical research, Type II errors typically happen because a study lacks adequate statistical power to detect the underlying relationship, often due to an insufficiently large sample size.

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