Question

Figure out what type of statistical analysis would be best for the following scenarios (between z-test, t-test, one-way ANOVA, two-way ANOVA, regression). Please also indicate what the levels/factors, null/alternative hypotheses, or the random variables are.

1) The length an illness remains infectious on a surface, depending on the surface of the material. The materials include, copper, iron, gold, plastic.

2) If taking a certain drug will help patients shorten the duration of the illness that they have contracted.

3) The relationship between the duration of an illness and the patients age

 

Answer 1

(1) There are 4 different levels and only measurement is length of illness. We want to check if the average length of illness is the same across the surface. Since we have more than 2 populations here (surfaces), we use a One Way ANOVA.

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(2) We need to have 2 populations here,where both populations have the same illness. Based on that, one set of people will be given the drug, and the other set will not be given a drug (Control / placebo group).

The times for both populations are then monitored to see the time taken and to check the average time for Drug group is lesser than the average time for placebo / without drug group.

In this case we would do a 2 sample t test for 2 means.

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(3) Here we want to check the relationship between 2 variables. One is a dependent variable (duration of illness) and the other being the independent variable (patients age). This would be done by find the regression equation, calculating r, the correlation coefficient and testing to see if r is 0, which would help us to know if there is a relationship or not.

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