Exploring Statistical Methods and Their Applications in Public Health and Personal Life

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Exploring Statistical Methods and Their Applications in Public Health and Personal Life1.For each of the followingbullets below,answer the questions as posted andin additionalso includea linkto a webpageor attach an image orpdfthat shows an example of the test.oRandom Effect--Givean example of a situation where use of a random effectinatwo-way factorial ANOVAcouldlogically be employed.Talk briefly about why a random effect wouldbe appropriate in thatcase instead of a fixed effect.Also provide a link, image or PDF.Answer:•Example Situation:Suppose a study is conducted on the effectiveness of a new drug where patientsare grouped by hospitals, and each hospital administers the treatment. In a two-way factorial ANOVA, hospitalsare treated as a random effect because hospitals are not of primary interest, but rather, they serve as randomsamples representing a larger population of hospitals.•Why Random Effect is Appropriate:A random effect is appropriate here because the goal is not to makeinferences about specific hospitals but rather about general variations across different hospital settings. It isassumed that these hospitals are randomly selected, and the effect of the hospital will be treated as a randomsample from the larger population of hospitals.•Link/Example:Random Effects in ANOVA (This provides further explanation of random effects.)oInteraction--Givean example of two factors that could potentially display interaction.Describe the two factors and talkabout why it would make sense tothink that those factors mightinteract with each other.Also provide a link, image orPDF.Answer:•Example of Interaction:Suppose a study on the effect of two factors—"exercise type" (e.g., runningvs. swimming) and "diet type" (e.g., high-protein vs. high-carb)—on weight loss over a six-month period. Theremay be an interaction between exercise type and diet type such that the effect of exercise on weight loss could bestronger with a high-protein diet than with a high-carb diet, or vice versa.•Why Interaction Makes Sense:This makes sense because the combination of diet and exercise may producedifferent effects on weight loss than when each factor is considered independently. For instance, one exercisetype may be more effective with a particular diet, creating an interaction between the two factors.•Link/Example:Interaction in ANOVA (Example of interaction in statistical models.)oANOVA--Givean example of a research question that would be better handled by ANOVA (one-way or two-way) thanat-test. Discuss what type ofANOVA would make the most sense to address the research question and write out the nulland alternative hypotheses.Also provide a link, image or PDF.Answer:o. ANOVA:•Research Question Example:A research question might be: "Does the type of teaching method (Traditional,Online, Hybrid) affect student performance on a standardized test?" This would be better handled by a one-wayANOVA, as there are multiple groups (teaching methods) being compared to see if they differ in terms of student

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