Descriptive Statistics Scope / Methods Political Science - 2200 Words

Descriptive Statistics: Scope and Methods in Political Science (Statistics Project Sample) Content: by Political Science 2101PRIVATEScope and Methods in Political ScienceSecond Problem SetQUESTIOIN 1Below is a cross tabulation of two variables from a survey of students in PSC 2101 from the fall of 2012: (1) student political ideology and (2) student predictions regarding whether President Obama will be reelected. Calculate an appropriate measure of association for this cross tabulation, and interpret this statistic regarding the direction and strength of the association between the two variables.SOLUTION:The data from the above image has been summarized as shown below  Do you think president Obama will be re-elected in 2012   liberal Slightly liberal moderate Slightly conservative conservative total Respondent ID No 0 1 0 1 3 5 Maybe 4 1 1 1 2 9 Yes 17 13 7 5 1 41  Total answered 21 13 8 7 6 55 From the table above the variables under à ¢Ã¢â€š ¬Ã‹Å"do you think president Obama will be re-elected in 2012à ¢Ã¢â€š ¬ are the depen dent variables while the variables across respondent ID (no, yes and maybe) are the independent variables. They have been summarized in their orderly form.To calculate the Gamma, the following formula is usedGamma = Number of concordant pairs à ¢Ã¢â€š ¬ number of discordant pairsNumber of concordant pairs + number of discordant pairs= nc - ndnc + ndConcordant pairs are the numbers in a pair of observations where the elements of one pair have the properties such that they are greater than, equal to or less than another pair in relation to the elements in the other pair. They are indicated as shown below;nc1 = 170 nc2 = 40 nc3 = 52 nc4 = 0 total nc 262 Discordant pairs are the numbers in a pair of observable variables whereby if one pair has a larger value of the X value then automatically the other pair has a larger value of the Y value. They are indicated as shown below;nd1 = 0 nd2 = 104 nd3 = 0 nd4 = 13 total nd 117 Gamma = 0.382585752This test statistic assumes that there is a we ak significant relationship between the respondents and their views on whether president Obama will be re-elected in 2012QUESTION 2Below is a cross tabulation of two variables: (1) student gender and (2) student attitudes toward professors banning laptops during class. Calculate the chi square for this cross tabulation, and interpret this statistic regarding the statistical significance of the association between the two variables.SOLUTION:The observed summary is as shown belowObserved frequencies   gender   male female Total ban laptops no 17 23 40 maybe 5 7 12 yes 4 5 9  total 26 35 61 Before calculating the Chi-Square, we need do derive the null and alternative hypothesis required for this test.Null hypothesis:Ho: the two variables Ban laptops and Gender are independentAlternative hypothesis:H1: the two variables Ban laptops and Gender are not independent.Test statistic: Chi square = à ¢ [(oi à ¢Ã¢â€š ¬ ei)2 / ei]Where, [oi] = observed frequencie sAnd [ei] are the expected frequenciesObserved frequencies   gender   male female Total ban laptops no 17 23 40 ...