Question

After the affordable care act was passed into law, states debated on whether they should adopt the Medicaid expansion. Was a state’s decision to adopt the Medicaid expansion influenced by its majority party affiliation? To test this claim, the following data is available.

What criticism might you have of the data analysis? Researchers might take issue with the variables chosen, or the setup of this particular test. There are no wrong answers, here, but your reasoning should be supported by statistical theory or supporting evidence.

States	Medicaid Expanded	Medicaid Not Expanded
Voted Democrat in 2012 presidential election	22	4
Voted Republican in 2012 presidential election	6	18

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 22 4 26 row 2 6 18 24 TOTALS 28 22 N = 50 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formula E-TABLE col1 col2 row 1 14.56 11.44 row 2 13.44 10.56 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 22 14.56 7.44 55.354 3.8018 4 11.44 -7.44 55.354 4.8386 6 13.44 -7.44 55.354 4.1186 18 10.56 7.44 55.354 5.2418 ᴪ^2 o = 18.0008 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =3.8415 since our test is right tailed,reject Ho when ᴪ^2 o > 3.8415 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 18.0008 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415 we got | ᴪ^2| =18.0008 & | ᴪ^2 α | =3.8415 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 18.0008 critical value: 3.8415 p-value:0 decision: reject Ho

we have enough evidence to support the claim that state’s decision to adopt the Medicaid expansion influenced by its majority party affiliation.