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# Exam 4 study Guide POS 3713

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This 3 page Study Guide was uploaded by Leah Burkett on Monday May 2, 2016. The Study Guide belongs to POS 3713 at Florida State University taught by Dr. Matthew Pietryka in Spring 2016. Since its upload, it has received 16 views. For similar materials see Political Science Research Methods in Political Science at Florida State University.

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Date Created: 05/02/16

Political Science Study Guide: Exam VI 1. What is the difference between a sample and a population and why do we care about each? Population: data for every possible case Sample: subset of cases that are drawn from an underlying population. The vast majority of all analysis undertaken by social scientists is done on sample data and NOT populations. 2. What is a P-value? P-value: which ranges between 1 and 0; the probability that we would see the relationship that we are finding because of random chance. The probability we would see the observed relationship between the 2 variables in our sample data if there were truly no relationship between them in the unobserved population. 3. What is a Null Hypothesis and how does it relates to the p-value? What is the alternative hypothesis? Null Hypothesis: a theory-based statement but it is about what we would expect to observe if our theory was incorrect. The p-value relates to the null hypothesis because it helps to convey the level of confidence with which we can reject the null. Alternative hypothesis: the alternative hypothesis to the Null. 4. What is Statistical Significance, in the context of OLS? By merely increasing our sample size, we can affect the statistically significance of those coefficients. Statistical significance is determined by a t-test in which the standard error is the denominator of that quotient. 5. What does it mean if a relationship is not statically significant? When a relationship is not statistically significant it means that the p-value is greater than .05. 6. What does OLS do? Why do we use OLS? OLS is a method for estimating the unknown parameters in a linear regression model, with the goal of minimizing the differences between the observed response in some arbitrary dataset and the responses predicted by the linear approximation of the data. 7. The two components of a regression model are systematic component and the stochastic component. What are these, exactly? Systematic component: Y (not random) Stochastic component: ui (random component) 8. How do we interpret the results from an OLS regression? What information do we need before we can interpret the alpha and betas? What does it mean to say a beta is statiscally significant? Alpha: Example 50 When all other variables are equal to 0, the Y value will be 50. Beta: Example- 8 for education With every one unit increase in education, we will see an 8 unit increase un support for president Bush. R-squared: Example 44 44% of the variation in Bush’s support can be explained by ___, ___, and____. To say beta is statistically significant means that whatever the beta is, has influence on the Y value due to more than just chance alone. 9. What is the formula for an OLS Model? How do we calculate predicted values of Y if we know the values of the independent variable? Β=∑=(xi-x)(yi-y)/ (xi-x)^2 α = y- Βx 10. How can we tell if a beta is statically significant? How can you calculate a 95% confidence interval around a beta coefficient? How are these two calculations related and how can you use each to asses statistically significance? We can tell a Beta is statically significant if after calculated , the t-statistic is greater than the values of 2 or less than the value of -2. To calculate the confidence interval, we take the beta value +/- (critical value * Standard error of the beta) They are related because they utilize the beta variable in the OLS equation. 11. What are Dummy variables? How can we interpret betas associated with dummy variables? How do we recognize the reference category for a series of dummy variables? Dummy variable: a numerical variable used in a regression Analysis to represent subgroups of the sample in your study. In research designs, dummy variables are of the ten used to distinguish different treatment groups. For bivariate regression betas represents the relationship between x and y. For multi0ple regression betas represent the relationship x and after controlling for Z; or the relationship between y and z after controlling for the x. Typically the reference category chosen from a series of dummy variables id the most common or largest category. 12. What are Residuals? Another name for the estimated stochastic (ui) is the residual. “residual” is another name for the “leftover”, and this is appropriate because ui is the leftover part of yi after we have drawn the line defined by y= α+Bxi. 13. What is leverage? What is influence over a regression line? How do we know if a case will have influence? What do we do when we think we have influential cases? Leverages is a measure of how far away the independent variables values of an observation are from those of the other observations. A data point is influential if it unduly influences any part of a regression analysis: such as predicted responses, the estimates slope coefficients, or the hypothesis test results. We know a case will have influence when it does not follow the general trend of the rest of the data and the presence of the data point significantly increases or reduces the slope of the regression line. large residual and leverage= high influence 1) double check the values of all variables for such a case 2) we report such findings about such cases along with other findings 3) Dummying out influential cases in rode to isolate and identify. 14. How and to what extent does OLD help us establish causality? Regression does NOT assume causality. Regression is imply about establishing a relationship between the variations of two (or more) variables. 15. What are logit and probit models? Why do we need them? The difference between logit and probit models lies in this assumption about the distribution of the errors. Probit: type of regression where the dependent variable can only take 2 values, for example married/not married. Logit: is a regression model where the dependent variable is categorical. Used to estimate the probability of a binary response based on one or more predictions. Calculations: Know how to calculate and interpret 1. Predictions of y given the values of the independent variables and OLS parameter values. 2. 95% confidence intervals of an OLS alpha or beta. For this exam, always use 2 as the critical value. 3. A t-ratio of an OLS alpha and beta to determine the statistical significance. For this exam, always use 2 as the critical value for t-tests and preform two- tailed tests.

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