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FactorialANOVA compares two or more independent variables. It consists of morethan one independent variable separating the experimental sample into4 or more groups. Factorial ANOVA uses two independent variablesagainst one dependent variable. It is possible to examine how thedifferent factors interact (Sukal, 2013).

Inthis example, 2×2 factorial design where two values are applied attwo distinct levels. The effect of two quantities of drug 100mg, and200mg will be tested in male and female patients. The two quantitiesof the drug represent two factors. Gender is the second factor.

Thequestion is

Doesthe quantity of drug taken has an effect on control of hypertensionand is there a difference in the effect of the drug between males andfemales?

Theeffects of two quantities 100mg and 200mg will be tested amongst bothsexes where males take 100mg and the second group takes 200mg. Thesame would apply to females (Sukal, 2013). The other aspect tested isthe effect of the drug itself on males and females.

Theindependent variables are the quantity of drug and gender and onedependent variable hypertension (Collinset al., 2014).Both sex and quantity are independent because they can be manipulatedunlike the disease.

Genderis a categorical variable that is nominal and can further beclassified as a dichotomous variable with categories, male, andfemales (Collinset al., 2014).The quantity of drug is a quantitative variable because it has anumerical value. The variable is of ratio type as there can be 0mgtested.

Thevariables qualify for the statistical test as this kind of testrequires two variables that can be manipulated and one that cannot bemanipulated.

Thereare three possible hypotheses:

H01:The main effect ‘quantity’ is not significant

X11oomg≠ X1200mg

H02: Themain effect ‘gender’ is not significant

X1males≠X1females

H03:There is no interaction effect

X11oomg.male≠ X1100mg.femaleX1200mg.males≠X1200mg.females

Theprimary type of error here is type I error and type II errors, typeerror I am rate of false positives whereas Type II error is thepossibility of missing the effect when it is there

(Collinset al., 2014).

References

Collins,L. M., Dziak, J. J., Kugler, K. C., &amp Trail, J. B. (2014).Factorial experiments: efficient tools for evaluation of interventioncomponents. Americanjournal of preventive medicine,47(4),498-504.

Sukal,M. (2013). Research methods: Applying statistics in research. SanDiego, CA: Bridgepoint Education, Inc.