Hypothesis Testing

Inferential statistics are used to make decisions about the population based on sample information. In order to reach statistical decisions, broad statements or hypotheses are formed about the probability distribution of the population. Hypothesis testing is the formal statistical process used to evaluate the probability or likelihood a hypothesis is true. The two major procedures for hypothesis testing are the classical approach and the probability value or p value method.

In classical or traditional hypothesis testing, four major steps are employed: (1) statement of the null and alternative hypotheses (H0 and HA); (2) determination of an analysis plan; (3) calculation of the test statistic; and (4) evaluation of the hypothesis statements. In the first step, the H0 and HA identify the parameter(s) being tested (e.g., mean, proportion, total) in order to determine whether the sample is coming from the same or different population. The H0 assumes any observed difference between the sample and population is due to chance (i.e., sampling error) and not influenced by a predictor variable. Conversely, the alternative or research hypothesis (HA) states a change or difference exists between the sample and population that is due to a nonrandom cause. The two hypotheses are written as mutually exclusive and exhaustive such that if one statement is accepted then the other statement must be rejected.

Hypothesis statements are formatted as either directional or nondirectional (equal to or not equal to a parameter value). The correct format depends on whether the researcher is interested in testing for a range of values or an exact value. For example, a professor believes that students who sleep more than 6 hours per night have test scores higher than the overall average (μ = 75). In a directional format, the H0 is that the test scores for these students are equal to or less than the expected average (H0 ≤ 75), and the alternative is then what the professor suspects, higher than average test scores for this group (HA > 75). If the professor only speculates that the test scores for this group are different than the average (rather than higher or lower), then a nondirectional format is used (H0: μ = 75 and HA: μ ≠ 75). This example is set up for a one-sample test using a single-point parameter, the population mean (μ), for comparison. Other statistical tests have hypothesis statements that are formatted slightly differently based on the number of samples, relationships, and parameters examined.

[Page 803]The second major step in hypothesis testing is deciding the appropriate sample statistic from which the decision to reject or not reject the H0. The proper statistical test is determined by the research question being asked and whether the data meet the test requirements. Parametric statistics assume a random sample drawn from a normally distributed population with variables measured at the interval or ratio scale; nonparametric statistics are for data sets that do not meet these requirements. The sample size also impacts the calculation and interpretation of most statistical tests. Small samples (n < 30) utilize the Student t distribution, whereas large samples (n ≥ 30) employ the z (also known as Gaussian or normal) distribution.

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