# Discussion: Case Statistical Test

# Discussion: Case Statistical Test

## Discussion: Case Statistical Test

Discussion: Case Statistical Test

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Module XI Discussion Construct a quantitative research question and state the appropriate statistical test that should be conducted and why. Post your initial response by Wednesday at midnight. Respond to one student by Sunday at midnight. Both responses should be a minimum of 150 words, scholarly written, APA formatted, and referenced. A minimum of 2 references are required (other than your text). Refer to the Grading Rubric for Online Discussion in the Course Resource section.

A **statistical hypothesis**, sometimes called **confirmatory data analysis**, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.^{[1]} A **statistical hypothesis test** is a method of statistical inference. Commonly, two statistical data sets are compared, or a data set obtained by sampling is compared against a synthetic data set from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis that proposes no relationship between two data sets. The comparison is deemed *statistically significant* if the relationship between the data sets would be an unlikely realization of the null hypothesis according to a threshold probability—the significance level. Hypothesis tests are used when determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance.

The process of distinguishing between the null hypothesis and the alternative hypothesis is aided by considering two conceptual types of errors. The first type of error occurs when the null hypothesis is wrongly rejected. The second type of error occurs when the null hypothesis is wrongly not rejected. (The two types are known as type 1 and type 2 errors.)

Hypothesis tests based on statistical significance are another way of expressing confidence intervals (more precisely, confidence sets). In other words, every hypothesis test based on significance can be obtained via a confidence interval, and every confidence interval can be obtained via a hypothesis test based on significance.^{[2]}

Significance-based hypothesis testing is the most common framework for statistical hypothesis testing. An alternative framework for statistical hypothesis testing is to specify a set of statistical models, one for each candidate hypothesis, and then use model selection techniques to choose the most appropriate model.^{[3]} The most common selection techniques are based on either Akaike information criterion or Bayes factor.

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