In A Study Of Simulated Juror Decision-Making
In A Study Of Simulated Juror Decision Making Braden Maguire Sigal
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, 4 a verdict of not guilty by reason of self-defense, and four a verdict of not guilty by reason of insanity. What type of chi-square test would the researchers use to determine whether the distribution of verdicts differed from what could have been expected by chance?
Paper For Above instruction
In the study conducted by Braden-Maguire, Sigal, and Perrino (2005), the researchers aimed to analyze whether the distribution of juror verdicts significantly differed from what would be expected under chance conditions. The verdicts in question included guilty, not guilty by reason of self-defense, and not guilty by reason of insanity, with observed frequencies of 27, 4, and 4 respectively, out of a total of 80 participants. To determine if these observed frequencies significantly deviate from expected frequencies, a suitable statistical test must be selected.
The appropriate statistical analysis for this situation is the chi-square goodness-of-fit test. This test is designed to compare observed frequencies of categorical data against expected frequencies to assess whether the observed distribution deviates significantly from what would be anticipated if the null hypothesis were true. Specifically, the goodness-of-fit chi-square test evaluates whether the distribution of jury verdicts differs from an equal distribution across all categories or any hypothesized distribution.
In applying the chi-square goodness-of-fit test, the researchers would first establish their null hypothesis, which typically posits that jurors are equally likely to assign any of the verdicts or that the distribution follows a specified expected distribution. Expected frequencies are then calculated based on the null hypothesis. For example, if the null hypothesis presumes that verdicts are equally probable, the expected frequencies for each category would be based on dividing the total number of participants (80) equally across the three verdict categories, resulting in approximately 26.67 for each category.
The formula for the chi-square goodness-of-fit statistic is:
\[
\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}
\]
where \( O_i \) is the observed frequency for category \( i \), and \( E_i \) is the expected frequency for that category. The sum is taken over all categories.
Applying this formula to the data:
- For guilty verdicts: \( O = 27 \), \( E \approx 26.67 \)
- For not guilty by reason of self-defense: \( O = 4 \), \( E \approx 26.67 \)
- For not guilty by reason of insanity: \( O = 4 \), \( E \approx 26.67 \)
The calculated chi-square statistic would then be compared to critical values from the chi-square distribution table with degrees of freedom equal to the number of categories minus one (df = 2). If the calculated value exceeds the critical value at a specified significance level, it suggests that the distribution of verdicts significantly differs from the expected distribution under the null hypothesis.
In conclusion, the researchers would employ a chi-square goodness-of-fit test to determine whether the observed verdict distribution among participants significantly deviates from the expected distribution. This statistical test provides insight into whether juror decision-making was influenced by factors beyond mere chance, illustrating the influence of case details on verdicts.
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