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Modified t-Test Procedures
To safely conduct post hoc comparisons without inflating the risk of making a Type I error, researchers use modified -test procedures rather than standard -tests. Techniques such as the Bonferroni procedure, Fisher's least significant difference (LSD) test, and Tukey's honestly significant difference (HSD) test are designed specifically for this purpose. While their mathematical details differ, their shared goal is to keep the overall risk of mistakenly rejecting a true null hypothesis at an acceptable level (typically close to ) across multiple comparisons.
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Research Methods in Psychology - 4th American Edition @ KPU
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Modified t-Test Procedures
What is the primary statistical problem that arises when conducting multiple independent-samples t-tests to compare every pair of group means in an experiment?
A researcher conducts six separate t-tests to compare every pair of means among four experimental groups, using an alpha level of .05 for each test. Because each individual test maintains only a 5% chance of a Type I error, the overall probability of making at least one Type I error across all six tests also remains at 5%.
A researcher is comparing the mean scores of three different groups: a Control group, a New Treatment group, and a Traditional Treatment group. To find specific differences, they conduct three separate statistical comparisons (Control vs. New, Control vs. Traditional, and New vs. Traditional). Match each term to how it applies to this specific scenario of multiple comparisons.
A psychology researcher is analyzing data from an experiment with four distinct treatment conditions. Arrange the following testing scenarios in order of their cumulative probability of committing at least one Type I error (the familywise error rate), starting with the scenario that has the lowest probability (top) and ending with the highest probability (bottom).
You are designing the 'Data Analysis' section of a research proposal comparing four different types of memory training. Your goal is to identify all specific pairs of training types that differ from one another without exceeding an overall Type I error rate of . Which of the following represents the most effective plan to construct this statistically valid framework?
Match each statistical concept related to the problem of multiple comparisons with its correct description.
Arrange the following steps in the logical order that explains how the 'multiple comparisons' problem develops when analyzing group differences in a research study.
A researcher argues that their study maintains a total risk of only for a false positive because every individual comparison was tested at an alpha () of . When evaluating this argument, we find it to be statistically invalid because the _____ error rate compounds with each additional test, making the overall risk of at least one false positive much higher than intended.
When analyzing an experiment with multiple group means, conducting several independent-samples -tests simultaneously keeps the cumulative risk of mistakenly rejecting a true null hypothesis at exactly .
When evaluating a study design that performs multiple independent-samples -tests to compare all group means, a researcher must recognize that simultaneous tests compound the overall probability of committing a _____, requiring specialized statistical procedures to control the error rate.
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Bonferroni Procedure
Fisher's Least Significant Difference (LSD) Test
Tukey's Honestly Significant Difference (HSD) Test
Why do researchers use modified t-test procedures, such as the Bonferroni procedure or Tukey's honestly significant difference (HSD) test, rather than standard t-tests when conducting post hoc comparisons?
If a researcher decides to use standard t-tests rather than modified t-test procedures for multiple post hoc comparisons, they will successfully keep their overall risk of mistakenly rejecting a true null hypothesis at an acceptable level.
A researcher has found a significant difference in an ANOVA comparing the effects of four different study schedules on exam performance. After finding this overall difference, they must decide how to conduct follow-up tests. Match each of the researcher's subsequent actions or observations with the correct statistical term or procedure.
Arrange the following stages to represent the logical progression of identifying and managing error inflation when conducting post hoc comparisons in a study.
Suppose you are designing the statistical analysis protocol for a new research study evaluating the effectiveness of four distinct therapeutic interventions (, , , and ). After finding a significant overall effect in an initial ANOVA, you must construct a post hoc analysis plan that compares all six possible pairs of interventions while strictly maintaining the overall familywise alpha level at exactly . Which of the following analytical designs represents the most appropriate construction of this plan to prevent Type I error inflation?
Match each term associated with modified -test procedures used in post hoc comparisons with its correct description or identifying characteristic.
A researcher evaluates a study comparing five different antidepressant medications and discovers that the authors performed ten pairwise comparisons using standard -tests. The researcher correctly judges the study's conclusions to be unreliable because, without using a modified procedure like Tukey's HSD or the Bonferroni procedure, the authors failed to control for the inflation of the _____ error rate across the entire set of comparisons.
A researcher is studying the effects of three different diets on weight loss in rats. After finding a significant overall effect, they plan to run three post hoc comparisons. True or False: If they use standard -tests instead of a modified procedure like Tukey's HSD, they will successfully keep their overall risk of making a Type I error close to .
A research group analyzes their experiment comparing four therapy types and notices that the overall risk of making a Type I error was kept close to across all post hoc comparisons. By examining their analysis, you can determine that they must have used a modified -test procedure, such as the _____ procedure, rather than multiple standard -tests.
A researcher needs to evaluate and manage the risk of Type I error inflation when analyzing multiple group differences in a newly completed study. Order the following steps to represent the correct methodological sequence for identifying, evaluating, and addressing this statistical risk.