Question

We plan to investigate whether blood pressure is affected by eating lasagna
lunch every day. Describe how to submit such an investigation to get pairwise independence observations.

Answer 1

In order to investigate we have to collect the data.

Table for the observed values

	blood pressure affected	blood pressure not affected	Total
eat lasagna lunch	a	b	a+b
do not eat lasagna lunch	c	d	c+d
Total	a+c	b+d	a+b+c+d

To get pairwise independence observations we will perform chi-square test for independence

The null hypothesis: The variables eating lasagna lunch and blood pressure are independent

The alternate hypothesis: The variables eating lasagna lunch and blood pressure are dependent

we will make a table for the expected values

	blood pressure affected	blood pressure not affected
eat lasagna lunch	(a+b)(a+c)/(a+b+c+d)	(a+b)(b+d)/(a+b+c+d)
do not eat lasagna lunch	(a+c)(c+d)/(a+b+c+d)	(c+d)(b+d)/(a+b+c+d)

Test statistics :

d.f = (number of rows-1)(no of columns-1)=(2-1)(2-1)=1

let us take

We will accept the null hypothesis if and can conclude that the observations are pairwise independence.