- The stacked bar chart below shows the level of trust in science among supporters of three different political parties. Each bar represents a political party and shows the proportion of its supporters who have low, medium, or high trust. Which statement is best supported by the chart?
Answer: The proportion of supporters with high trust in science is more than double for Party A compared to Party C.
Stacked bar charts show proportions. We must compare the size of the 'High Trust' segment relative to the total bar height for each party. For Party A, 'High Trust' is 60%. For Party B, it is 40%. For Party C, it is 20%. Thus, the proportion for Party A (60%) is three times, and therefore more than double, the proportion for Party C (20%). Choice A is incorrect because we cannot know the total number of people without knowing the sample size for each party. Choice B is incorrect because bar charts like this often standardize each party to 100% and do not reflect the size of the party. Choice D is incorrect because there is a very clear, strong relationship.
- Based on the sociologist's findings described in the passage, which concept from the elaboration paradigm is demonstrated?
Answer: Explanation, because the original relationship was shown to be a consequence of a third, antecedent variable.
The scenario describes a classic case of explanation (or spuriousness). An initial relationship between two variables vanishes when a third variable, which is causally prior to both, is controlled. Education is antecedent to both adult income and voting behavior. Because the relationship disappeared, it is explained by education. Replication would mean the relationship persisted. Specification would mean it persisted in one subgroup but not the other. Interpretation involves an intervening variable, where the causal order would be Income -> Education -> Vote.
- This outcome, where the nature of the relationship between two variables changes depending on the value of a third variable, is an example of what?
Answer: Specification
This is a textbook example of specification, also known as an interaction effect. The initial relationship is not uniform across all subgroups. Instead, the control variable specifies the conditions under which the original relationship holds true (or is stronger/weaker). Replication would mean the relationship was the same in both subgroups. Explanation would mean the relationship vanished in both subgroups. Suppression is when a relationship appears only after controlling for a third variable.
- An analyst is studying political polarization. The table below shows the ideological self-placement of partisans in a survey. Which statement best summarizes the key finding in this table?
Answer: The relationship demonstrates strong political sorting, with a vast majority of cases falling along the main diagonal.
The table shows a powerful association where most Democrats identify as Liberal (180/200 = 90%) and most Republicans identify as Conservative (180/200 = 90%), with very few 'cross-pressured' individuals. This pattern, where cases cluster on the diagonal of a table linking party and ideology, is a classic indicator of political sorting or polarization. Choice A is incorrect because the association is extremely strong. Choice B overstates the case; the relationship is probabilistic, not deterministic, as some off-diagonal cases exist. Choice D is incorrect because Moderates are a small minority in both parties according to the table.
- An analyst examining the table below concludes that independents who are gun owners are extremely likely to oppose gun control, noting that 100% of them do. Why should this specific conclusion be treated with caution?
Answer: The percentage for that subgroup is based on an extremely small number of cases, making it unreliable.
While the percentage (4 out of 4) is technically 100%, drawing a strong conclusion from such a small subgroup (N=4) is a major error. Percentages based on very small cell sizes are highly unstable and likely to be the result of random chance. A different sample of just a few people could dramatically alter the percentage. Choices A and B are valid general points about crosstabs, but C points to the most immediate and severe flaw in this specific interpretation. Choice D refers to the marginal distribution, which doesn't invalidate the internal comparison.
- A political analyst examines the relationship between a citizen's age and their primary source of news. The results are displayed in the table. Which statement best characterizes the relationship shown?
Answer: Reliance on online news sources is highest for the youngest group and declines with age, while reliance on television is highest for the oldest group.
This requires interpreting the pattern across multiple categories. For 'Online', the column percentages are 120/200=60% (18-29), 80/200=40% (30-49), and 40/200=20% (50+), showing a clear decline. For 'Television', the percentages are 60/200=30% (18-29), 80/200=40% (30-49), and 120/200=60% (50+), showing a clear increase. Choice C accurately captures both of these monotonic trends. Choice A is incorrect because reliance on television does not consistently increase from the first to second group. Choice D incorrectly describes the television trend as curvilinear. Choice B incorrectly dismisses the very strong and clear patterns.
- The table shows support for an environmental regulation by geographic region. What is the percentage-point difference in support for the regulation between respondents in the South and those in the West?
Answer: 15
The independent variable is Region, so we must use column percentages. Support in the South: (120 / (120 + 80)) 100 = 60%. Support in the West: (90 / (90 + 30)) 100 = 75%. The difference is 75% - 60% = 15.0 percentage points. A common error would be to calculate the difference in row percentages: %South among Supporters (120/300 = 40%) vs. %West among Supporters (90/300 = 30%), which yields 10.0 (Distractor A). Another error is to subtract raw counts (120-90=30). Distractor C comes from subtracting the number of 'Oppose' respondents in the two regions (80-30=50) and misinterpreting that as a percentage or from an off-by-one calculation. Distractor D (33.3) is the difference between % Oppose for West (25%) and % Oppose for South (40%).
- A researcher studies the relationship between party identification and opinion on a new trade agreement. The data is presented in the table below. Which of the following statements most accurately describes the relationship shown?
Answer: As party identification shifts from Democrat to Republican, support for the agreement tends to increase.
To describe the relationship, one must compare the percentage of support/opposition across party lines (column percentages). For Democrats, 60/200 = 30% support. For Independents, 100/200 = 50% support. For Republicans, 150/200 = 75% support. This shows a clear positive relationship: as one moves from Democrat to Republican, support increases. Choice A is incorrect because a majority of Democrats and half of Independents do not support it. Choice B makes a causal claim, which a cross-tabulation cannot prove. Choice D uses row percentages, which describe the composition of opinion groups, not the opinions of party groups.
- While this conclusion may be true, the analyst's reasoning from the county-level data to an individual-level conclusion is a potential instance of which logical error?
Answer: The ecological fallacy
The ecological fallacy occurs when a researcher draws inferences about individuals based on data from aggregate groups. It is possible, for instance, that in counties with many college graduates, it is the non-graduates who are mobilized to vote at higher rates, even while the overall county turnout is high. The aggregate correlation does not guarantee the individual-level correlation.
- A political scientist hypothesizes that higher levels of education are associated with higher rates of voter turnout. The following table displays data from a recent survey. What is the percentage-point difference in voter turnout between respondents with a college degree and those with a high school diploma or less? (Assume education is the independent variable).
Answer: 25
To find the effect of the independent variable (Education) on the dependent variable (Voter Turnout), we must calculate column percentages. First, find the turnout rate for each education group: For 'High School or Less', the turnout is (150/(150+100))∗100=60.0%. For 'College Degree', the turnout is (340/(340+60))∗100=85.0%. The percentage-point difference is 85.0−60.0=25.0. - A researcher posits the following hypothesis: 'As citizens' level of formal education increases, they become less likely to identify with a political party and more likely to identify as Independent.' Using the table below, which conclusion about this hypothesis is most justified?
Answer: The hypothesis is not supported, because the percentage of partisans (Democrat or Republican) increases with education level.
The hypothesis predicts that as education rises, the proportion of partisans should fall and the proportion of independents should rise. Let's calculate the percentage of partisans for each education level (column percentages). High School: (80+80)/200 = 80% partisan. College: (100+90)/250 = 76% partisan. Graduate Degree: (120+60)/200 = 90% partisan. The percentage of partisans actually increases from college to graduate degree, and the percentage of independents is lowest for the highest education group (10%). This contradicts the hypothesis.
- For the table showing the relationship between media consumption and political knowledge, a researcher calculates Goodman and Kruskal's lambda (λ) to be 0.20. What is the correct interpretation of this value?
Answer: Knowing a respondent's level of media consumption reduces the error in predicting their political knowledge by 20%.
Lambda is a Proportional Reduction in Error (PRE) measure of association. A value of 0.20 means that knowledge of the independent variable (Media Consumption) reduces the error in predicting the value of the dependent variable (Political Knowledge) by 20% compared to simply guessing the modal category of the dependent variable.
- In the following table, the independent variable (Income Level) is on the rows and the dependent variable (Trust in Government) is on the columns. Which statement is the most accurate interpretation of the data?
Answer: As income level increases, the likelihood of having high trust in government increases.
Because the independent variable is in the rows, we must calculate row percentages and compare them down the columns. For Low Income, 50/200 = 25% have High Trust. For Middle Income, 100/250 = 40% have High Trust. For High Income, 75/150 = 50% have High Trust. The percentage of people with High Trust clearly increases as income rises. Choice B correctly states this. Choices A and D are based on column percentages (e.g., of those with high trust, 75/225 or 33.3% are high income), which answers a different question. Choice C makes an incorrect comparison by looking at raw numbers within each row instead of percentages across rows.
- This scenario, where a relationship is invisible until a control variable is introduced, is a classic example of:
Answer: A suppressor variable effect
A suppressor variable is a control variable that, when introduced, reveals a relationship that was not apparent in the initial bivariate analysis. In this case, job position was suppressing the underlying relationship between gender and income. Spuriousness is when a relationship disappears after a control. Specification is when the relationship differs across categories of the control. Replication is when it stays the same.
- A campaign manager wants to determine if a 'gender gap' exists, meaning that men and women differ in their support for the campaign's candidate. Using the survey data in the table, which of the following calculations is the necessary first step to address this question?
Answer: Calculate the percentage of women who support the candidate and compare it to the percentage of men who support the candidate.
The research question asks how the dependent variable (vote choice) differs across categories of the independent variable (gender). To answer this, one must calculate percentages within each category of the independent variable. This means calculating column percentages: what percentage of women support the candidate, and what percentage of men support the candidate? Choice A calculates row percentages, which would describe the gender composition of the candidate's supporters, a different question. Choice B examines only the marginal distribution of gender. Choice D uses raw counts inappropriately.
- The table below shows voting preferences for a proposition by ideology. According to the data, the difference in the percentage of 'Yes' votes is greatest between which two ideological groups?
Answer: Liberals and Conservatives
This requires calculating the percentage of 'Yes' votes for each group and comparing differences. Liberal 'Yes' vote: 150/200 = 75%. Moderate 'Yes' vote: 120/200 = 60%. Conservative 'Yes' vote: 40/200 = 20%. The differences are: Liberals vs Moderates = |75% - 60%| = 15 percentage points. Moderates vs Conservatives = |60% - 20%| = 40 percentage points. Liberals vs Conservatives = |75% - 20%| = 55 percentage points. The greatest difference is between Liberals and Conservatives at 55 percentage points.
- A political pollster investigates whether a respondent's area of residence is related to their position on a zoning law. The results are in the table. What is the most appropriate conclusion?
Answer: There is essentially no association between area of residence and opinion on the zoning law.
To assess the relationship, we calculate column percentages. Support among Urban residents: 102/200 = 51%. Support among Rural residents: 50/100 = 50%. The one-percentage-point difference is negligible and likely due to random sampling noise. Therefore, the most appropriate conclusion is that there is no meaningful association. Choice A exaggerates the tiny difference. Choice B calculates row percentages (102/152 = 67% of supporters are urban), which is misleading because the sample has twice as many urban residents. Choice D incorrectly claims significance for what is almost certainly a null finding.
