PoliSci341_ProblemSet4_(2010).doc

NAME: Brittany Harrison . STATA Problem Set Due on Tuesday, November 23rd at 4pm. Answers should be type-written. Include tables where necessary. No emailed assignments will be accepted. ***Students are expected to do their own work on the problem set. If you have questions about the material, please contact me.*** Use the ?nes2000.dta? file, which can be found under Course Documents in Blackboard A researcher is interested in examining whether there was a significant difference in the age of voters versus non-voters (i.e., whether turnout is related to age). Evaluate this research question by performing a T-Test (difference of means) analysis. Briefly summarize (in words) your findings. The variable for age is called ?age?, which ranges from 18 to 97. The turnout variable is called ?vote00?, and is coded as follows: 0 = did not vote, 1 = voted. . ttest age, by (vote00) Two-sample t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- 0 | 368 43.10326 .9355096 17.94619 41.26363 44.94289 1. voted | 1178 49.39559 .4786161 16.42707 48.45655 50.33462 ---------+-------------------------------------------------------------------- combined | 1546 47.8978 .4325556 17.00774 47.04934 48.74626 ---------+-------------------------------------------------------------------- diff | -6.292325 1.003305 -8.260309 -4.32434 ------------------------------------------------------------------------------ diff = mean(0) - mean(1. voted) t = -6.2716 Ho: diff = 0 degrees of freedom = 1544 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000 According to the confidence interval (t= -6.2716), we can see that it contains no zeros, so we can reject the null hypothesis and conclude that the difference in the two means presented is statistically significant. In other words, we can say that the age of a person is related to whether or not that person votes. A researcher is interested in examining whether there was a significant difference in the feelings towards the Democratic Party in different regions of the country. Evaluate this research question by performing an analysis of variance (ANOVA) test. Include a Scheffe test. Briefly summarize (in words) your findings. The variable for feelings about the Republican Party is called ?demtherm?, which ranges from 0 to 100 (where 100 is the most favorable opinion of the Democratic Party) The region variable is called ?region?, and is coded as follows: 1 = northeast, 2 = north central, 3 = south, 4 = west. . oneway demtherm region, tabulate census | Summary of c2a. thermometer dem region of | party interview | Mean Std. Dev. Freq. ------------+------------------------------------ 1. northe | 60.477419 24.179837 310 2. north | 58.098851 24.889005 435 3. south | 59.2416 26.609249 625 4. west | 58.084656 23.329112 378 ------------+------------------------------------ Total | 58.926201 25.068738 1748 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 1373.57921 3 457.859737 0.73 0.5351 Within groups 1096513.9 1744 628.735035 ------------------------------------------------------------------------ Total 1097887.48 1747 628.441603 Bartlett's test for equal variances: chi2(3) = 9.1617 Prob>chi2 = 0.027 After analyzing the data, it appears that the Prob > F is actually above 0.05 (it?s 0.5351), which would mean that we accept the null hypothesis that states that all the means are the same. In other words, there appears to be no significant difference in the feelings towards the Democratic Party when looking at different regions of the country. . oneway demtherm region, scheffe Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 1373.57921 3 457.859737 0.73 0.5351 Within groups 1096513.9 1744 628.735035 ------------------------------------------------------------------------ Total 1097887.48 1747 628.441603 Bartlett's test for equal variances: chi2(3) = 9.1617 Prob>chi2 = 0.027 Comparison of c2a. thermometer dem party by census region of interview (Scheffe) Row Mean-| Col Mean | 1. north 2. north 3. south ---------+--------------------------------- 2. north | -2.37857 | 0.653 | 3. south | -1.23582 1.14275 | 0.918 0.912 | 4. west | -2.39276 -.014194 -1.15694 | 0.671 1.000 0.919 In the Scheffe test we can see the difference between the means of two specific variables. We can also see the significance level which, if below 0.05, means that the difference is significant statistically. According to this, none of the pairs of variables show any statistically significant difference. This would further support the conclusion we found in the ANOVA test. There appears to be no significant difference in the feelings towards the Democratic Party when looking at different regions of the country. A researcher is interested in examining the relationship between race and vote choice in the 2000 election. Assess this relationship by performing a Chi-square analysis. Briefly summarize (in words) your findings. The variable for race is called ?race?, and is coded as follows: 1 = White, 2 = Black, 3 = Hispanic, 4 = Native American, 5 = Asian, 6 = Other The variable for vote choice in 2000 is called ?who2000?, and is coded as follows: 0 = Gore, 1 = Bush. . tabulate race who2000, column chi +-------------------+ | Key | |-------------------| | frequency | | column percentage | +-------------------+ | who2000 racial self id | Gore Bush | Total -------------------+----------------------+---------- 1. white | 427 484 | 911 | 72.87 91.84 | 81.85 -------------------+----------------------+---------- 2. black | 106 8 | 114 | 18.09 1.52 | 10.24 -------------------+----------------------+---------- 3. hispanic | 23 15 | 38 | 3.92 2.85 | 3.41 -------------------+----------------------+---------- 4. native american | 3 7 | 10 | 0.51 1.33 | 0.90 -------------------+----------------------+---------- 5. asian | 12 6 | 18 | 2.05 1.14 | 1.62 -------------------+----------------------+---------- 6. other | 15 7 | 22 | 2.56 1.33 | 1.98 -------------------+----------------------+---------- Total | 586 527 | 1,113 | 100.00 100.00 | 100.00 Pearson chi2(5) = 93.1395 Pr = 0.000 According to the Chi-square analysis, white people voted for Bush the most in the 2000 election, accounting for 91.84% of the vote for that candidate. Black people had a strong voting relationship with Gore, accounting for 18.09% of the vote. It should also be noted, however, that a decent number of white people voted for Gore as well, representing 72.87% of the vote for him in the election. Hispanics tended to vote for Gore in the 2000 election, representing 3.92% of all the votes for Gore. Native Americans developed a strong voting relationship with Bush in the 2000 election, representing 1.33% of his overall vote. Asians voted for Al Gore the most out of all the other candidates in the 2000 election. This accounted for 2.05% of his total votes. All other races not represented in a particular category tended to vote for Al Gore the most, accounting for 2.56% of the vote for this candidate. Also, the relationship between these variables is definitely statistically significant, as the level of significance is well below 0.05. A researcher is interested in examining the relationship between religiosity (how often someone reads the bible) and public opinion about abortion. Assess this relationship by performing a Gamma analysis. Briefly summarize (in words) your findings. The variable for religiosity is called ?bible1?, and is coded as follows: 1 = several times per day, 2 = once a day, 3 = few times a week, 4 = one a week or less, 5 = never. The abortion variable is called ?abortion?, and is coded as follows: 1 = never permit, 2 = permit only in case of rape, incest, or health of mother in danger, 3 = permit when a ?clear need? exists, 4 = always permit. . tabulate bible1 abortion, column gamma +-------------------+ | Key | |-------------------| | frequency | | column percentage | +-------------------+ how often does r | abortion scale read the bible | 1. never 2. rape, 3. clear 4. always | Total ---------------------+--------------------------------------------+---------- 1. several times/day | 30 19 7 7 | 63 | 14.49 3.70 2.69 0.97 | 3.71 ---------------------+--------------------------------------------+---------- 2. once/day | 52 85 19 26 | 182 | 25.12 16.57 7.31 3.61 | 10.71 ---------------------+--------------------------------------------+---------- 3. a few times/week | 50 99 40 53 | 242 | 24.15 19.30 15.38 7.36 | 14.24 ---------------------+--------------------------------------------+---------- 4. once/week or less | 46 163 101 228 | 538 | 22.22 31.77 38.85 31.67 | 31.65 ---------------------+--------------------------------------------+---------- 5. never | 29 147 93 406 | 675 | 14.01 28.65 35.77 56.39 | 39.71 ---------------------+--------------------------------------------+---------- Total | 207 513 260 720 | 1,700 | 100.00 100.00 100.00 100.00 | 100.00 gamma = 0.4770 ASE = 0.024 According to the Gamma analysis, people who read the Bible several times a day believe that abortion is never acceptable. They represent 14.49 % of the people that believe that abortion is never acceptable. The people who read the Bible once a day also believe that abortion is never acceptable, although they are a bit more accepting of rape cases than people who read the Bible several times a day. The people who read the Bible once a day represent 25.12% of the people who believe abortion is never acceptable and 16.57% of the people that believe abortion is acceptable only in cases of rape, incest, or health of the mother. The people who read the Bible a few times a week also believe that abortion is never acceptable, but tend to side with those who consider it acceptable only in cases of rape, incest, or health of the mother more so than the people who read the Bible several times a day. The people who read the Bible a few times a week represent 24.15% of the people that never believe abortion is acceptable and 19.30% of the people that believe it is ok in cases of rape, incest and a risk to the health of the mother. People who sporadically read the Bible once a week or less believe that abortion is acceptable when a clear need exists for it. There group represents 38.85% of people who believe this reasoning. Finally, people who never read the Bible overwhelmingly believe that abortion is always acceptable, with a startling 56.39% of people who share this view. According to the Gamma statistic, it is positive, so the relationship is also positive. This means that the more someone reads the Bible, the more they believe that abortion should never be permitted. The opposite is also true: the less someone reads the Bible, the less they believe that abortion should never be permitted. The ASE (approximate level of significance) is below 0.05, so there is a statistically significant relationship between these variables. This means that the frequency with which someone reads a Bible does have an effect on their public opinion about abortion. The same researcher that examined gender differences in Hillary Clinton attitudes wants to perform a more rigorous test. This researcher hypothesizes that the following variables will all be related to attitudes about Hillary: 1) Feelings towards Bill Clinton, 2) Partisanship, 3) Gender, 4) Race (i.e., is respondent black). The variable names and values are listed below. For each of the five variables, state your hypothesis. Do you expect a relationship to exist between each of these independent variables and the dependent variable (feelings about H. Clinton)? (Note: Your hypothesis may be that you expect there to be no relationship between these variables.) Feelings towards Bill Clinton: If people feel strongly for Bill Clinton, they will feel strongly for Hillary too. Partisanship: The more Republican a person is, the less likely they will support Hillary Clinton. Gender: If a person is female, they will feel more strongly for Hillary. Race: If the respondent is black, he or she will be less likely to support Hillary Clinton. Perform a multiple regression analysis: . regress hillary clintpre partyid7 gender black Source | SS df MS Number of obs = 1550 -------------+------------------------------ F( 4, 1545) = 544.89 Model | 861401.927 4 215350.482 Prob > F = 0.0000 Residual | 610615.815 1545 395.220592 R-squared = 0.5852 -------------+------------------------------ Adj R-squared = 0.5841 Total | 1472017.74 1549 950.301964 Root MSE = 19.88 ------------------------------------------------------------------------------ hillary | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- clintpre | .6045483 .0225407 26.82 0.000 .5603347 .648762 partyid7 | -2.942611 .323005 -9.11 0.000 -3.576186 -2.309037 gender | 7.709597 1.021193 7.55 0.000 5.706526 9.712667 black | 4.854246 1.597449 3.04 0.002 1.720848 7.987644 _cons | 20.89047 2.091856 9.99 0.000 16.78729 24.99365 ------------------------------------------------------------------------------ How much of the variation in attitudes towards Hillary are we explaining with these independent variables? According to the multiple regression analysis, these independent variables explain 58.41% of the variation in attitudes towards Hillary. (Adj R-squared) What is the relationship between each of these variables and the dependent variable? (Ex: As feelings towards Bill Clinton increase by X percent, feelings towards Hillary Clinton increase by Y percent) As feelings towards Bill Clinton increase by 1%, feelings towards Hillary Clinton increases by .60%. As a respondent becomes more Republican, his or her feelings towards Hillary Clinton decrease (become worse). Females are more likely to have strong feelings towards Hillary Clinton. Black respondents are more likely to have strong feelings towards Hillary Clinton. Which (if any) of these relationships are statistically significant? All of these variables are statistically significant according to the multiple regression analysis. (All significant levels [P>|t|] below 0.05) The variables you will need are as follows: Feelings towards Bill Clinton The variable for feelings about Bill Clinton is called ?clintpre?, which ranges from 0 to 100 (where 100 is the most favorable opinion of Bill Clinton) Partisanship The variable for partisanship is called ?partyid7?, and is coded as follows: 0 = strong Democrat, 1 = Democrat, 2 = weak Democrat, 3 = Independent, 4 = weak Republican, 5 = Republican, 6 = strong Republican Gender The gender variable is called ?gender?, and is coded as follows: 0 = male and 1 = female. Black The race variable is called ?black?, and is coded as follows: 0 = not black and 1 = black.