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104 Cards in this Set
- Front
- Back
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What are Research Questions? |
Conceptual and Concrete |
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Distinguish Conceptual and Concrete Questions |
Conceptual questions: abstracts and difficult to answer Concrete questions: Expressed using tangible/empirical properties |
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Conceptual Definitions |
Describes a concepts measurable properties and specified the unit of analysis to which the concept applies. 1. Identifies a measurable characteristics that varies in a population 2. Specifies the subject or gross to which the concept applies ( the unit of analysis) 3. offer a way of measuring the variation |
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Operational Definitions |
- Describes the instrument to be sued in measuring the concept and putting a conceptual definition into operation. -"An operation defintion describes explicitly how the concept is to be measured empirically" -Measurable properties must be concrete and must vary - How much the measurement very spend on how we measure the property |
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Properties of good measurement |
1. Reliability - The extent to which a measurement is consistent, not subject to much random variation 2. Valid - The extent to which a measurement records the true, intended value of a characteristic, not subject to bias or systematic error |
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Random error |
introduces haphazard, chaotic distortion into measurement process. This kinds of error decreases the reliability of measurement |
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systematic error |
introduces consistent, chronic distortions into measurement process. This kind of error decreases the validity of measurement |
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Reliability: How to Assess |
- Test retest method: apply the measurement to the same group again. Do you get the same values? - Alternative form method: use a different form of the same measurement strategy to subject in a retest - are the alternative forms of the measurement highly correlated? -Split half method: use different forms of the same measurement strategy at one time. Is one half of the question correlated to the other half question. -Conbrach's Alpha: Use different forms of the same measurement strategy at one time. Are the various questions correlated to each other? This is a statistic that gives an overall of the item reliability, |
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Validity: How to Assess |
Face validity: Informed, expert judgement, widely accepted in academic literature Construct validity: Does measurement explains the things (other then the concept or characteristic) that it should present and explain. |
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Levels of Measurement |
Nominal, Ordinal, Interval |
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Nominal Level Variable |
Records differences that can't be compared with math; may have many possible values (categorical) or just yes/no (Binary) |
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Ordinal level variable |
Records relative differences in value; can be compared with inequalities; can't be compared with arithmetic |
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Interval level variable |
most precise measurement; can be compared with math; many possible values |
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Additive Indexes |
- Definition: An addictive index is a additive combination of ordinal level variables, each of which is coded identically, and all of which measures of the same concept -Why? Addictive indexes generally provided more precise and reliable measures of characteristics than does a single ordinal-level measure. |
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Measures of Central Tendency |
mode, median, mean |
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Measures of Dispersion |
Common examples of measures of statistical dispersion are the variance, standard deviation and interquartile range. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.
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Terms to Describe Distributions |
Biomodal Distribution Positive Skew Negative Skew |
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Elements of Good Explanations |
-Specify the unit of analysis -Tell us why something interesting varies -Identify what causes something to vary -Asset the direction or tendency of the difference -Avoid circular logic or truism -Falsifiable -Can help us answer more than one question -Dont have to be right |
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Dependent Variable |
The variable that represents the effect in a causal explanation |
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Independent variable |
The variable that represents a casual factor in an explanation |
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Template for Writing Hypothesis |
In a comparison of (unit of analysis), those having (one value of the independent variable) will be more likely to have (one value of the depending variable) than will those having (a different value of the independent variable). |
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Intervening Variables: |
- A variable that acts as a go-between or mediator between the IV and DV |
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If the dependent variable is measured at nominal or ordinal level, we make comparison using what? |
Cross tabulation analysis |
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If the dependent variables is measured at interval level we making comparisons using what? |
Mean comparison analysis. |
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Cross Tabulations |
Definition: A table that shows the distribution of cases across the value of a DV at the different levels of the IV Frequency: number of times observed in sample |
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Rules of setting up Cross-Tabulations |
1. values of the IV defines columns, values of the DV define the rows 2. Calculate the % with in the values of the IV. Should sum to 100% 3. Interpret a cross-tabulation by comparing percentages across columns at the same value if the DV. |
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Mean Comparison Tables |
You can use mean comparison table when the dependent variable is measured at the Interval level and the independent ordinal or nominal level. Organized in two columns: values of the IV listed in the first column. Means and Frequencies reported in the second column Can be represented graphically as a line chart |
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Direct Relationship between variables |
More IV equals to more DV |
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Inverse Relationship between variables |
More IV equals to less DV |
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Linear relationship between variables |
effect of the IV on the DV stays the same |
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Curvilinear relationship between variables |
effect of IV on DV depends on the value of the IV. |
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Negative relationship between variables
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The lower value of the IV is associated with a higher value of the DV |
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Positive relationship between variables
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The lower value of the IV is associated with lower value of the DV |
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The purpose of Research Design |
-Research design is the different between political journalism an political science -We design research to test our theories about politics and government. We propose specific hypotheses to test our explanation of how things work |
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Elements of Causal Relationships |
Correlation Time Order No other Explanation |
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Importance of Rival Explanations |
- For every explanation we propose, and fore every hypothesis we test, there are alternative uses, rival explanations, for the phenomena. - Rival explanations undermine our ability to evaluate the effect of the indecent variable on the dependent variable. -Does vacation of x explain variation in y? -Could variation in z be the real cause of the variation in y? |
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Compositional Differences |
-Is any characteristic that varies across categories of an IV. -If a compositional difference is a cause of the DP, then changes in the DP may be plausibly attributed to the compositional difference, NOT the IV. |
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Random Assignment in Experiments: |
-Random Assignment prevents selection bias |
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Statistical Controls in Controlled Comparisons |
- many interesting questions about politics cannot be answered using experimental research. -Political scientist generally work with observational data which makes them need statistical control |
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Field Experiment |
Researcher manipulates subjects in the real world |
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Laboratory Experiment |
Researcher manipulates subject in controlled environment |
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Advantages and Disadvantages of Experiments |
-Internal validity: Effect of treatment of precisely measured - Laboratory experiments have relatively high interval validity - External Validity: Results generalize to real world - Filed experiments have relatively high external validity. |
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Internal validity |
within the conditions created artificially by the researcher, the effect of the IV on the DV is isolated from other plausible expiations. |
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External validity |
The results of a study can be generalized - that is, its finding can be applied to situations in the non artificial, natural world. |
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Control Variables |
A variable that is held constant in order to assess or clarify the relationship between two other variables. Control variable should not be confused with controlled variable, which is an alternative term for independent variable. |
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Spurious Relationship |
- x does does not effect y. Its explained by z - The control variable Z, defines a large compositional difference across values of the IV, X. Further, this compositional difference is a cute of the DV, Y. After holding Z constant, the empirical association between X and Y turns to be completely coincidental. NOT casual at all. |
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Additive Relationship |
- x does explain y and so does z - The control variable isa cute of the DV but defines a small compositional difference across the value of the IV. Because the relationship between x and z is wet, x retains a causal relationship with y after controlling for z. -In the additive scenario, the control variable , z, also helps explain the DV |
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Interaction relationship |
- the effect of x on y depends on the value of z - The relationship between the IV and the DP depends on the value of the control variable. - For one value of Z, the X-Y relationship might be stronger than for another value of Z. |
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Visualizing controlled comparison for Spurious Relationship |
the slop of the line relating x and y for each group will be zero/flat lines |
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Visualizing controlled comparison for Additive relationship |
the slop of the line relating x and y for each group will be parallel and not zero |
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Visualizing controlled comparison for Interactive relationship |
the slop of the line relating x and y for each group will be different |
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Purpose of a literature review |
-establish a theoretical framework for your topic subject area
-define key terms, definitions and terminology -identify studies, models, case studies etc supporting your topic -define / establish your area of study, ie your research topic. |
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Purpose of Controlled Comparisons |
Help account for rival explanation |
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Zero ordered relationship |
also known as gross relationship or an uncontrolled relationship, it is an overall association between two variables that does not take into account other possible differences between cases being studied |
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Control Comparison Table |
is used to account for the influence of a control variable. |
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Controlled Cross Tabulation |
- A controlled comparison table between an IV and DV for each value of the control variable. Cases are divided into groups according to their values on the control variable. - It reveals the controlled effects of the IV on the DV. |
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Controlled Mean Comparison Tables |
condense relationship to a single, easy-to-interpret measure of central tendency and are illustrated as additive relationships and interactions. |
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Identifying Patterns, Graphing Controlled Comparisons |
look at notes and textbook |
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Role of Inferential Statistic |
-Definition: Set of procedures for deciding how closely a relationship we observe in a sample corresponds to the unobserved relationship in the population from which the sample was drawn -Purpose: To help the investigator make the correct interpretation about empirical relationship -Example: How often a random sample will produce a 9-percentage point difference between veterans and non-veterans if, in fact, no difference exist in the population |
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Type I and Type II error |
Every researcher whites to make the correct inferno about the data, rejecting the null hypothesis when it is false and not rejecting it when it true. But there two ways to get it wrong. Type I error and type II error. |
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Type I error |
- Occurs when the researcher concludes that there is a relationship in the population when, in fact, there none - Occurs when you reject a null hypothesis that is actually true |
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Type II error |
- Occurs when the researcher infers that there is no relationship in the population when, in fact, there is. - Occurs when you fail to reject a null hypothesis thats actually true |
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Significance level |
Is the probability of making a type I error. For example, if we use the conventional .05 significance level, that means there is a 5% chance that we will mistakenly reject a null hypothesis that is actually true |
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The Logic of Null Hypothesis Testing |
- Our inferences are based on null hypothesis testing - If the null hypothesis is true, what is the probability of observing our statistic by chance (from random sampling error)? - Inferential statistic help us quantify these probabilities and test hypothesis about population |
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Central Limit Theorem |
Is an established statistical rule that tells us that, if we were to take an infinite number os sample size from a population of N members, the mean of these sales would be normally distributed. This distribution of sample means, furthermore, would have a mean equal to the true population mean and have random sampling error equal to ó, the population standard deviation, divided by the square root of n. |
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Sample v. Population |
- Population is very large, parameters, greek letters, generally unknown. Everybody/everything we want to make an inference about us. - Sample is small or medium size, statistics, Ordinary letters, known. The data we actually have available. |
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Statistic |
Estimate of a population parameter based on a sample drawn from a population |
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A test of Statistical significance |
Helps you decide whether an observed relationship between an IV and a DV really exist in the population or whether it could have happened by chance when the sample was drawn |
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Standard Error: Variance |
-The average of the squared deviation is known by a statistical name, the variance. The population variance is equal to the sum of the squared deviation decided by N. - Divide the sum of the squared deviation by n-1 - As Variation goes up, random sampling error increase in direct relation to the population's standard deviation |
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Standard Error: Sample Size Components |
- As the sample size goes up, random sampling error declines as a function of the square root of the sample size |
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Standard error of proportion |
formula |
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standard error of means |
formula |
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Probability Distributions |
- Mathematically defined expected value. The normal distribution is the most importance in relation. - The likelihood of the occurrence of an event or set of events. - What is the probability that your randomly chosen mean will have a value between 55.5 and 6.5? Use the standard error, 2.5, to covert each raw value into Z score. The lower value has a Z score equal toL (55.5 - 58) / 2.5 = -1. The higher value has a Z score equal to: (60.5 - 58) - 2.5 = +1. The normal distribution says that 68 percent of all the cases fall in this interval. |
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Random Sampling |
- Definition: Every member of population has equal chances of being selected fro the sample - Purpose: Controls for selection bias, make reliable inference about population - Researcher must define the sam;ing frame |
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Random Sampling Error |
- Definition: Amount of variation in a statistic that occurs from random chance, white noise, inherent error in sampling - Distinguish distribution of statistics (like means and proportion) from the distribution of variables (like points scored and gender) - Sampling errors have known statistical properties |
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Issues in Random Sampling |
- Selection Bias: Researcher more likely to select some in population than others - Response Bias: Occurs when some cases in the sample are more likely then others to be measures -Population Parameter: Sample statistic random sampling error |
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Coefficient |
A number used to multiply a variable Ex: 4x - 7 = 5 (4 is the coefficient) |
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Standard Error |
- a yardstick for judging random error - In a gender selection example, if null hypothesis is true, the mean (of means) of girls born is 50 and standard error (of the means) is 5. |
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Test Statistic |
-Tells how many standard errors separate the sample difference from zero, the difference claimed by Ho. - (Ha - Ho) / standard error of the difference - (observed - expected) / SE |
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Normal Distribution |
- The normal distribution with mean ,ū = 0 and standard deviation ó = 1 - used to describe interval-level variables. |
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T-Distribution |
- a probability distribution that can be used for making inferences about about a population mean when the sample size is small - The shape depends on the sample (not like the bell) looks like normal distribution but has lower peak, thicker tails, it makes null hypothesis testing more conservative |
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Steps in Null Hypothesis Testing |
1. State Ha, Ho 2. Estimate Statistic of Interest 3. Sample Statistic - Ho / Standard error = test statistic 4. Determine probability of test statistic. If Ho is True (p-value) 5. Reject or fail to reject the null hypothesis. |
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Confidence Intervals |
- Formula - Definition: The interval within which 95% of samples estimated will fall by chance - Doesn't have to be 95% but thats the most common - Based on standard error and desired significance level: lower boundary = observed state - (1.96 x SE) upper boundary = observe state + (1.96 x SE) |
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P-Values |
In this approach, the researcher determines the exact probability of obtaining the observed sample different, under the assumption that the null hypothesis is correct. - If the p-value is greater than .05, then the null hypothesis cannot be rejected. - If the p-value is less than or equal to .05, then the null hypothesis can be rejected. - This approach is based on the standard error of the difference between two sample means |
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Conclusion about Null Hypothesis |
- based on confidence level - confidence intervals for statistic |
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Standard Error of Difference of Means |
1. Calculate standard error of each mean estimate 2. Square each SE 3. Add them together 4. Take the square root |
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Standard Error of Difference of Proportions |
1. Calculate p and q for each group (q = 1-p) 2. For each group, multiply p by (1 - p) and divide by n 3. add results for each group together 4. take the square root |
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Chi-Squared Test of Significance |
- Similar Idea: Classic method of testing relationship in a table - Test null hypothesis that variables based on a test statistic and probability distribution -When to use it: When DV and IV are both measure at the nominal or ordinal level - it determines whether the observe dispersal of cases departs significantly from what we would expect to find if the null hypothesis were correct. |
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How to calculate Chi-squared Test Statistic |
1. Calculate expected frequency for each cell 2. Subtract expected frequency from observed frequency in each cell 3. Square number in each cell 4. Divide by expected 5. add up all the cell-by-cell calculations |
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Test Statistics |
z scores t-statistics Chi-Squared |
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Correlation and the Correlation Coefficient |
- Pearsons Correlation Coefficient (r) - Definition: a statistic that ranges between -1 and 1 that indicates strength and direction of relationship between two interval-level variables |
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Purpose of Bivariate Regression |
- Definition: linear regression with one explanatory variable - When it's used: The DV is a measure at interval-level, you're focused on one IV - How it works: Minimizes sum of squared errors. This is the total amount of variance; we've looked average variance from mean for interval-level variance |
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Scatterplots |
In a scatterplot, the independent variable is measured along the horizontal axis and the dependent variable is measured along the vertical axis. |
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Sum of Squared Errors |
- is an overall summary of the variation in the dependent variable in the dependent variable. - It also represents all our errors in guessing the value of the dependent variable for each case, using the mean of the dependent variable as a predictive instrument. |
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Interpreting Regression Coefficients |
- Intercept: expected value of DV with the value of the IV is zero - Slope: Average effect of one-unit increases in the IV - Can make informed prediction: you're given the value of the IV and predict the value of the DV - to do this, you enter value for x in the line equation and solve for y |
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Making prediction for Regression Results |
- Regression coefficients are means of sample statistics - They are the difference of means which we know follows a normal distribution in repeating sample - We apply familiar tests of statistical significance: Regression coefficient is a difference of means, so it has SE. WE can divide coefficient by SE to get a t-statistic. Then compare t-statsitic to t-distribution to judge significance |
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Rules for interpreting Regressing Coefficients |
- Be clear about units of measurement: Make sure you know that a 1 unite of measure is - Regression Coefficient in units of the DV - Sometimes the intercept term is practically meaningless (but statistically necessary) |
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R-Squared |
- Defintion: A statistic that ranges between 0 & 1 that tells us how much variation in DV our IV explains -Formula: R^2 = RSS/TSS TSS = total sum of squared errors ESS = error of sum Squares RSS = TSS - ESS (RSS is Regression Sum of Squares) |
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Adjusted R-Squared |
- Definition: Like R2, but it takes into account how many IV sued by linear regression model |
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Purpose of Multiple Regression |
- Defintion: Statistical method to estimate average effect of IV on DV controlling for other IV - When its used: Used with interval-level DV and multiple explanatory variables -Precise estimates: can forecast expected value of DV given value of IV - Independent variables measured at different levels: very flexible, can use interval, ordinal and nominal-level DV |
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Interpreting Partial Regression Coefficients |
- partial regression coefficients express how the DV changes with a one unit increase in the IV with all other IV held constant |
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Dummy Variable Regression |
- They are IV for which cases coded either 1 and 0, where 1's falling into the category and O's not in it - other names for dummy variables: nominal, indicators, binary - When it's used: To test or control for difference between groups |
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Making prediction from multiple regression results |
- it is linear and additive - It estimates the partial effect of one indent variable by controlling for the effect of all other independent variable in the model. Ex: regression estimated the partial effect of education level on turnout, controlling for battleground. A multiple regression will ferret out this spurious effect if any. |
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Interaction Term |
Multicollinearity: when the IV are related to each other so strongly that it becomes difficult to estimated the partial effect of each IV on the DV |
