Political Stats
Construct validity
degree to which a variable measures a concept
7. Christine wants to test her hypothesis that presidential popularity is related to the rate of bill passage, controlling for the partisan control of the US Senate. Which of the following would be the appropriate hypothesis test?
(a) Correlation coefficient. (b) Tabular analysis. (c) Difference of means. (d) None of the above. d
sampling distribution
the distribution of values taken by the statistic in all possible samples of the same size from the same population
10. Which of the following statements accurately describes theories?
(a) Theories are attempts to explain what causes what. and (b) Theories are attempts to explain variation in a dependent variable.
According the Chapter 3 of Kellstedt and Whitten, what is a confounding variable?
(c) A variable that changes the relationship between two other variables.
3. Which of the following accurately describes a continuous variable?
(a) A one-unit increase in the variable value always means the same thing. (b) Different values mean different things. (c) Both a and b are accurate.
1. Which of the following accurately describes a p-value?
(a) A p-value cannot equal zero.
In which of the following theoretical statements is it not at all likely that reverse causality would be problematic?
(a) A person's gender causes them to hold particular attitudes about abortion.
5. Which of the following is not true about a sampling distribution?
(a) A sampling distribution represents a hypothetical distribution, showing what the true population distribution would look like if our sample size were infinitely large.
5. From the example in Chapter 3 of Kellstedt and Whitten on the relationship between an individual's race (X) and the amount that the individual participates in politics (Y ), the answer to the second question on the causal hurdles scorecard is "yes" for which of the following reasons?
(a) An individual's participation in politics can not cause their race.
6. In the text, why did the authors argue that it is difficult to study whether or not participation in Head Start (X) affect educational outcomes (Y )?
(a) Because students in Head Start programs are likely to be systematically different from students who do not participate.
6. Nate wants to test his hypothesis that age is related to the dollar value of campaign contributions. Which of the following would be an appropriate hypothesis test?
(a) Correlation coefficient.
Which of the following best captures the difference between experimental and observational research designs?
(a) Experimental designs control for confounding variables through randomly assigning participants to different treatment groups, while observational designs accomplish this through statistical controls.
8. Which of the following is not an accurate statement about hypotheses according to Chapter 1 of Kellstedt & Whitten?
(a) For each causal theory there can be only one hypothesis.
11. Taylor randomly draws 10 beans from a giant bag of beans. If 4 of those 10 beans are blue, which of the following tells us what Laron can infer about all of the beans in the bag?
(a) Her best guess is that 40% of the beans are blue
8. In statistical hypothesis testing, which of the following accurately describes the role of the critical value?
(a) If the calculated value is greater than the critical value, we can conclude that there is a relationship between the two variables. (b) The critical value for a particular hypothesis test depends on the number of degrees of freedom. (c) If the calculated value is less than the critical value, we can not reject the null hypothesis. (d) All of the above. d
5. The value of a chi-squared statistic calculated for this table is 37.89 with a corresponding p-value below .001. Based on this information, what can we say about the relationship between these two variables?
(a) It is highly likely that this relationship would occur due to random chance. (b) It is highly likely that there is a causal relationship between these two variables. (c) It is highly unlikely that there is a causal relationship between these two variables. (d) None of the above. d
7. As described in the text, when studying political intolerance using surveys, why did Sullivan and his co-authors believe that it was so important to first ask survey respondents about what group they disliked the most?
(a) Sullivan and his colleagues thought that opposition was a critical component of the concept of tolerance, which made it necessary to find out what groups the respondent opposed.
10. According to K&W, why is probability theory relevant for scientific investigations?
(a) The rules of probability tell us how we can generalize from our sample to the broader population. (b) The rules of probability are key to identifying which relationships are statistically significant. (c) The rules of probability theory decide whether the patterns of relationships we observe in a sample could have occurred simply by chance. (d) All of the above.
9. Which of the following accurately describes a difference of means test?
(a) This is a test that is used when we want to test whether the value of a continuous dependent variable is different across values of a categorical independent variable.
1. What is the most important purpose of a research design?
(a) To most effectively control for as many confounding variables as possible, thus leaving the relationship between X and Y unpolluted by outside influences.
13. Abigail volunteers to help Congressman Bob's campaign. Along the way she notices that Congressman Bob, a Republican, is much more popular in the wealthier parts of his district. Which strategy should she use to turn what she has observed into a theory about politics?
(a) Try to move from the specific to the more general. (b) Try to drop the proper nouns. (c) Examine previous research. (d) All of the above.
8. The process of statistical inference is defined as:
(a) Trying to learn about a characteristic about a broader population based on observations of only a sample from that population.
9. Which of the following best fits the definition of independent outcomes?
(a) Two outcomes are independent if the realization of one of the outcomes does not affect the realization of the other outcomes.
2. A relationship between two variables is described as "statistically significant" under which of the following circumstances?
(a) When there is a sufficiently high p-value. (b) When there is a credible causal claim about the relationship between the two variables. (c) Both (a) and (b) are correct. (d) Neither (a) nor (b) are correct. d
6. If a mean age of a sample of 100 randomly chosen individuals is 48 and the standard deviation is 16, what is the standard error of the mean?
(b) 1.6
3. Which of the following is not true about normal distributions?
(b) As the name implies, they are quite common in everyday experience.
5. Suppose that a researcher finds that nations that have higher amounts of trade between them are less likely to go to war with one another. What should be your major concern with this finding?
(b) Did the researcher control for other possible causes of war? (c) Did the researcher control for other possible causes of trade? (d) Both (b) and (c).
1. Which of the following accurately describes a categorical variable?
(b) Different values mean different things.
2. Which of the following accurately describes an ordinal variable?
(b) Different values mean different things. (c) The categories are ordered from least to greatest. (d) Both b and c are accurate.
10. Which of the following accurately describes the relationship between a covariance and a correlation coefficient for the same two variables?
(b) If the covariance between two variables is positive, the correlation coefficient between the same two variables will also be positive.
From the example in Chapter 3 of Kellstedt and Whitten on the relationship between an individual's race (X) and the amount that the individual participates in politics (Y ), what is the Z variable that alters the relationship between X and Y ?
(b) Socioeconomic status.
3. Suppose Manuel wants to test the hypothesis that gender is related to vote choice in Uganda. Which of the following would be an appropriate bivariate hypothesis test?
(b) Tabular analysis.
11. What does it mean when we say that a variable has been "operationalized?"
(b) That the variable has been measured.
What does it mean to say that a relationship between two variables is spurious?
(b) The relationship that seems to be true in a bivariate examination is not, in fact, the true relationship.
2. If, for a sample in which the subjects are randomly chosen, the mean income is $45,000, the sample size is 1600, the standard deviation is $4,000, and the standard error of the mean is $10, what, approximately, is the 95% confidence interval for the population mean?
(c) $44,800 to $45,200.
7. Which of the following are useful for describing the values of a categorical variable?
(c) A bar graph.
4. Which of the following is true about the comparison between two randomly chosen samples, one with 1000 respondents, the other with 2000 respondents?
(c) Adding still another 1000 respondents, to make the sample size 3000, would further shrink the standard error of the mean, but by a smaller amount than the difference between 1000 and 2000 respondents.
12. Identify which one of the "Rules of the Road to Scientific Knowledge" has been violated. A researcher writing about the effects of military spending on public support for incumbent politicians writes "Since it is obvious that military spending hurts the economy and we have evidence that poor economic performance leads to lower incumbent support among voters, I conclude that military spending must hurt incumbent support."
(c) Consider only empirical evidence.
8. Which of the following is a potential weakness of the Polity IV measure of democracy, as described in the text?
(c) The concept includes both "contestation" and "participation," but the measure includes only indicators of "contestation," making it incomplete.
3. A competent researcher would be least likely to study which of the following using an experimental research design?
(c) The influence of personal ideology on candidate evaluations.
9. Which of the following is likely to be true if a researcher used a survey respondent's income (in dollars) in order to measure their political ideology?
(c) The measure would likely be reliable but invalid.
9. If a researcher finds results in the direction expected by his or her hypothesis, which of the following describes what has happened?
(c) Their theory has been supported.
7. Suppose a reputable pollster reports that, on the basis of a random sample of American adults, the President's approval rating is 50%, and that the margin of error is plus or minus 4%. What is the correct interpretation of this reported result?
(c) We can be approximately 95% confident that the true level of approval in the population as a whole is somewhere between 46% and 54%.
11. According to Chapter 5 of the text, why is conceptual clarity an important first step in the measurement process?
(d) Because, without clear definitions of the concepts we intend to measure, it is impossible to know whether the measures accurately capture what we intend to measure.
4. What is the most significant benefit of randomly assigning participants to different treatment groups?
(d) It controls for other possible causes of the dependent variable.
1. What is the key insight of the Central Limit Theorem?
(d) Regardless of the shape of a frequency distribution of a randomly chosen sample, a hypothetical distribution of an infinite number of sample means will be normally distributed, with a knowable variance.
12. What is operationalization?
(d) The specific ways in which a theoretical concept is measured using real-world observations.
10. Which of the following hypothetical survey questions would most likely suffer from poor measurement as a result of a lack of conceptual clarity?
10. Which of the following hypothetical survey questions would most likely suffer from poor measurement as a result of a lack of conceptual clarity? b
Variable
: A dimension that describes an observation
degrees of freedom in X^2 caculation
=(r-1)(c-1)
Casual inference
A statement about cause and effect that claims that a change in one variable is the cause of a change in another variable. (asks why)
Theory
A tentative conjecture about the causes of some phenomenon of interest that involves an Outcome or dependent variable, to be explained Explanatory, independent, or causal variable(s) thought to affect the outcome A mechanism ("how") that links the two
Reliable
Applying the same measurement rules to the same case or observation will produce identical results.
Coding
Assigning a score for a variable to an observation
3 levels of measurement
Categorical, Ordinal, Continuous
Descriptive Inference
Lesser type of inference
2 types of casual inference
Reverse and Forward
3 bivariate hypothesis tests
Tabular analysis, Difference of means, Correlation coefficient
alternative hypothesis
The hypothesis that states there is a difference between two or more sets of data.
p-value
The probability level which forms basis for deciding if results are statistically significant (not due to chance). The lower the p-value, the greater confidence we have that there is a systematic relationship between the two variables for which we estimated the particular p-value (most of the time is .05)
difference of means test
comparing real-world data with what we would expect to find if there were no relationship b/w our IV and DV. Use the sample means and standard deviations to make inferences about the unobserved population.
Central Limit Theorem
The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.
Acceptable standard of statistical significance
When the X^2 value is greater the degree of freedom value found by looking at the chart.
Inference
a belief based on evidence and rules for processing that evidence
standard deviation
a computed measure of how much scores vary around the mean score
null hypothesis
a statement or idea that can be falsified, or proved wrong
tabular analysis
a type of bivariate analysis that is appropriate for two categorical variables (usually dealing with rows and columns of the table)
Valid
accurately represents the concept that it is supposed to measure
Regression
addressing confounding through conditioning on observable variables
Conceptual clarity
knowing what we want to measure
Degrees of freedom (difference of mean test)
n1 + n2 -2 reflect the basic idea that we will gain confidence in an observed pattern as the amount of data on which that pattern is based increases.
Hypothesis
observable implications; testable propositions entailed by the logic of the theory
standard error of the difference between two means
se (Mean of Y1 - Mean of Y2) =
Experimentation
solving confounding and ordering through randomized intervention
t-statistic for difference of means test
t =(Mean of Y1 - Mean of Y2) / se(Mean of Y1 - Mean of Y2)
Correlation
the non-independence of two variables for a set of observations
Operationalization
the process of deciding on measures for concepts
confidence interval
the range of values within which a population parameter is estimated to lie (t is confidence interval (most of the time it is 95%))
Standard error of the mean
the standard deviation of a sampling distribution (numerator is standard deviation)
p value (difference of means test)
to have a p-value of .10 (meaning there's a 10% (= 1 in 10) chance that we would see this relationship randomly in our sample if there was no relationship between X and Y in the underlying population)
methodology
tools for gathering and analyzing data to try to make valid inferences
independent outcomes
two or more outcomes such that the realization of one of the outcomes does not affect the realization of the other outcomes
laws of probability
useful for taking particular information about a characteristic of an observed sample of data & attempting to generalize that information to the underlying and unobserved population
X^2 statistic for tabular association
x^2 = sum ((observation-expected)^2/expexted)