Question

In a study of simulated juror decision making, Braden-Maguire, Sigal, and Perrino (2005) investigated the type of verdict assigned by study participants after they read a 12-page summation of a case involving a battered woman who had shot and killed her husband. Of the 80 participants, 27 assigned a verdict of guilty, 49 a verdict of not guilty by reason of self-defense, and 4 a verdict of not guilty by reason of insanity. What type of chi-square test would the researchers use to determine if the distribution of verdicts differs from what would be expected by chance

Answer 1

Independence chi-square test

Explanation:

The Chi-Square Test for independence is a type of statistical hypothesis test that is used to determine the existence of an association or relationship between nominal or categorical variables

The chi-square is given by the following formula;

`\chi^2 = \XXL\sum (\left (O_i - E_i \right)^2)/(E_i)`

The number of participants = 80

The number that assigned a verdict of guilty = 27

The number that assigned a verdict of not guilty by reason of self defense = 49

The number that assigned a verdict of not guilty by reason of insanity = 4

Independence Chi Square test

The table of values is presented as follows;

Expected Value = (Row sum * Column Sum)/(Grand Total)

Expected Value for Guilty = 27 × 80/80 = 27

Expected Value for Self Defense = 49 × 80/80 = 49

Expected value for Insanity = 4 × 80/80 = 4

`\begin{array}{ccc}Category&Observed&Expected\\Guilty&27&27\\SelfDe&49&49\\Insanity&4&4\end{array}`