Question

1. We want to compare whether people give a higher taste rating to Ulker or Eti petit-beurre biscuits. A blind tasting is executed to avoid psychological effects, (i.e., subjects don't know the brand of the biscuits). Describe how to design a study involving independent samples and dependent samples.

1. (15 pts.) Design involving independent samples
2. (15 pts.) Design involving dependent samples

Answer 1

Let's call the two biscuit types as treatment A and B.

a. In order to draw independent samples, we need two groups. For that we can randomly select individuals for the two groups. Let's assume we have chosen n memebers for each of the groups. (there's no hard and fast rule that the group sizes must be equal. It's just for convinience)

-Give all the subjects in first group, the treatment A (in a blind fashion, so that they don't know which biscuit they are exactly eating). Record their responses: X1,...,Xn

-Do the same with the subjects in the second group, with treatment B. Let the responses be Y1,...,Yn

We can assume:

and that the two samples are independent.

Now we can test Vs. an alternative of your choice using an independent samples t-test.

b. For a dependent sample.

Select n individuals randomly and give the two biscuits to each of them (without telling them, which one is what).

Thus, each individual gives two scores, to treatment A and B respectively. Let the scores be (X,Y)

Thus, we have n iid paired observations: (X1,Y1),...,(Xn,Yn) (paired as the two responses come from the same individual.)

We can assume that

Now we can test Vs. an alternative of our choice using a paired sample t-test.