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Evaluating F-Tests

EvaluatingF-Tests

EvaluatingF-Tests

Thearticle “Factor selection and structural identification in theinteraction ANOVA model” offers an in-depth analysis of variousANOVA models. It emphasizes the factor that normal ANOVA tests areoften followed by a post hoc hypothesis analysis in order to meet theobjectives of the analysis. Here, the objectives are to identify thesignificant factors and to establish which levels differsignificantly in these factors. In order to meet these requirementssimultaneously, ANOVA models such as CAS ANOVA are used. However,this model faces the limitation of assuming a main effects onlymodel. The study proposes a new interaction model that addresses thislimitation. The interaction model, GASH ANOVA, can accomplish bothtasks simultaneously and still adhere to the heredity-typeconstraint. The article then uses a memory trial study to apply thismodel to real data analysis (Post &amp Bondell, 2013).

Thenull hypothesis of the real data example was that there is nosignificant difference between the memory capacity young and oldpeople. The alternative hypothesis of the study was that there is asignificant difference between the memory capacity of young and oldpeople. The independent variable in this case study was age while thedependent variable was the memory capacity. The independent variablewas measured in terms of age groups and the test was conducted ongroups of ten individuals per treatment for each age group. Thedependent variables were learning outcomes such as counting, imagery,adjectives, and rhyming. A fifth subgroup was intentionally informedthat they will be required to recall what they heard, while the otherfour subgroups were not informed. The dependent variables were thusmeasured using standard analysis. The specific levels at which thedata was measured are GASH-ANOVA, Naive, and BH/Bonferroni p-value.The mean and standard deviation of the data was also analyzed. Theresults of the study confirm that the GASH-ANOVA method offers thebest analysis of data. This is because the method identifiessignificant differences between the levels of the learning groupfactor more. Thus, the assumptions of the study were met (Post andBondell, 2013).

GASH-ANOVAhas the advantage of not requiring a post hoc hypothesis test sinceall the objectives of a study are achieved simultaneously. However,some post hoc tests were tested alongside GASH ANOVA in the study inorder to offer a comparative analysis. These include Bonferroniapproach, Benjamin and Hochberg method, and the Naïve method. Thepossible implication of the study is that GASH ANOVA is moreeffective in determining the factors that differ and the significanceof their difference simultaneously. Being interactive, the method ismore realistic since it adheres to the heredity-type constraint. Inthe study, GASH ANOVA method indicates that there is significantdifference between the memory capacity of the young and the old (Post&amp Bondell, 2013).

Inthe hypothetical data, some of the results were analyzed using the ttest while others were analyzed using the F test (NHIM, 2013). It isessential to use either test depending on the type of data availableor the hypothesis being tested. T-tests often identify thesignificant factors and the significance of their difference usingthe means of the two factors. This is applied on small samples whosevariance is not stated or is unknown. The F-test is used to offer anin-depth analysis of the differences between two factors based on thedifferences in their variance. This is applicable on large samplesizes and it is often used to test linear hypothesis (Rosner, 2011).

References

“ACornucopia of Statistical Goodies:Understanding t-tests, ANOVA, and Calculating Percent Change”(2013). NationalInstitute of Mental Health.

Post,J. &amp Bondell, H. (2013). “Factor selection and structuralidentification in the interaction ANOVA model.” Biometrics.

Rosner,B. (2011). Fundamentalsof biostatistics.Boston: Brooks/Cole, Cengage Learning.