Midterm

Question 1

Correlation

Answer 1

The correlation between two features of the world is the extent to which they tend to occur together.

Question 2

Positively correlated:

Answer 2

When higher (lower) values of one variable tend to occur with higher (lower) values of another variable, we say that the two variables are positively correlated .

Question 3

Negatively correlated

Answer 3

When higher (lower) values of one variable tend to occur with lower (higher) values of another variable, we say that the two variables are negatively correlated

Question 4

Uncorrelated:

Answer 4

When there is no correlation between two variables, meaning that higher (lower) values of one variable do not systematically coincide with higher or lower values of the other variable, we say that they are uncorrelated .

Question 5

Line of best fit:

Answer 5

A line that minimizes how far data points are from the line on average, according to some measure of distance from data to the line

Question 6

Mean ( μ)

Answer 6

The average value of a variable

Question 7

Deviation from the mean:

Answer 7

the distance between an observation’s value for some variable and the mean of that variable

Question 8

Variance ( σ2)

Answer 8

A measure of how variable a variable is . It is the average of the square of the deviations from the mean

Question 9

Standard deviation ( σ)

Answer 9

Another measure of how variable a variable is. The standard deviation is the square root of the variance .t has the advantage of being measured on the same scale as the variable itself and roughly corresponds to how far the typical observation is from the mean (though, like the variance, it puts more weight on observations far from the mean)

Question 10

Covariance (cov)

Answer 10

measure of the correlation between two variables. It is calculated as the average of the product of the deviations from the mean

Covariance is a measure of how much two variables change together. It indicates whether an increase in one variable corresponds to an increase or decrease in another

However, it is not standardized and depends on the units of the variables involved, making it hard to interpret the strength of the relationship.

Question 11

Correlation coefficient (r)

Answer 11

Another measure of the correlation between two variables. It is calculated as the covariance divided by the product of the variances . The correlation coefficient takes a value between − 1 and 1, with − 1 reflecting perfect linear negative dependence, 0 reflecting no correlation, and 1 reflecting perfect linear dependence

Question 12

The square of the correlation coefficient (r^2)

Answer 12

It takes values between 0 and 1 and is often interpreted as the proportion of the variation in one variable explained by the other variable. But we have to pay careful attention to what we mean by “explained. ” Importantly, it doesn’t mean that variation in one variable causes variation in the other

It provides an indication of how well the regression equation fits the data. A higher r^2 indicates a better fit, suggesting that the independent variable is successful in explaining or predicting variations in the dependent variable.

Strength of Relationship: The closer
r^2 is to 1, the stronger the linear relationship between the two variables. If r^2 is close to 0, it suggests a weak or no linear relationship.

Interpretation: For example, if
r^2 is 0.75, it means that 75% of the variance in the dependent variable is explained by the independent variable.

Question 13

sum of squared errors

Answer 13

The sum of the square of the distance from each data point to a given line of best fit . This gives us one way of measuring how well the line fits/describes/explains the data .

Question 14

OLS regression Line

Answer 14

The line that best fits the data, where best fits means that it minimizes the sum of squared error .

Question 15

Slope of the regression line or regression coefficient:

Answer 15

The slope of the regression line describes how the value of one variable changes, on average, when the other variable changes . The slope of the regression line is the covariance of two variables divided by the variance of one of them, sometimes also called the regression coefficient .

Question 16

Causal Effect

Answer 16

Informally, the change in some feature of the world that would result from a change to some other feature of the world. Formally, the difference in the potential outcomes for some unit under two different treatment statuses

Question 17

Counterfactual comparison

Answer 17

A comparison of things in two different worlds or states of affairs, at least one of which does not actually exist.

Question 18

Treatment

Answer 18

Terminology we use to describe any intervention in the world. We usually use this terminology when we are thinking about the causal effect of the treatment, so we want to know what happens with and without the treatment. Importantly, although it sounds like medical terminology, treatment as we use it can refer to anything that happens in the world that might have an effect on something else

Question 19

Potential outcomes framework

Answer 19

framework for representing counterfactual EQUATION:

Question 20

Potential Outcome

Answer 20

The potential outcome for some unit under some treatment status is the outcome that unit would experience under that (possibly counterfactual) treatment status

Question 21

Fundamental problem of causal inference:

Answer 21

This refers to the fact that, since we only observe any given unit in one treatment status at any one time, we can never directly observe the causal effect of a treatment.

Question 22

Heterogeneous treatment effects

Answer 22

When the effect of a treatment is not the same for every unit of observation (as in the case of flu shots and virtually every other interesting example of a causal relationship), we say that the treatment effects are heterogeneous. Sometimes we’re still interested in the average effect even though we know the treatment effects are heterogeneous, and sometimes we want to explicitly study the nature of the heterogeneity. (In contrast, when discussing the unlikely possibility that treatment effects are the same for every unit, we would refer to homogeneous treatment effects.)

Question 23

Selecting on the dependent variable

Answer 23

Examining only instances when the phenomenon of interest occurred, rather than comparing cases where it occurred to cases where it did not occur.

Question 24

Dependent variable:

Answer 24

The variable associated with the outcome we are trying to describe, predict, or explain.

Question 25

Independent or Explanatory variable:

Answer 25

A variable we are using to try to describe, predict, or explain the dependent variable.

Question 26

Regression equation:

Answer 26

Regression equation: An equation linearly relating a dependent variable to some independent variables.

Question 27

Regression parameters

Answer 27

Regression parameters: The parameters (intercept and slopes) that relate a dependent variable to some independent variables in a regression equation. Alpha is the intercept, Beta is the slope

Question 28

Error

Answer 28

Error: The difference between the value of the outcome variable for an individual data point and the predicted value for that same data point. This is sometimes also referred to as the residual.

Question 29

Sum of squared errors (SSE):

Answer 29

For a given line, calculate the error for each data point by finding its vertical distance from the line. The sum of squared errors for that line is found by squaring each of the individual errors and adding them together.

Question 30

Ordinary least squares (OLS) regression:

Answer 30

The method for finding the line of best fit through data that minimizes the sum of squared errors.

Question 31

Regression line

Answer 31

The line of best fit through the data that one gets from OLS regression.

Question 32

Intercept (alpha)

Answer 32

Intercept: In the context of a regression, the intercept tells us the predicted value of the outcome when the values of all the explanatory variables are set to 0. This is also referred to as the constant term. Sometimes the intercept has a substantive interpretation, but sometimes it doesn’t because it doesn’t make sense to think about situations where all the explanatory variables are zero (for example, predicted voter turnout for people with an age of zero). In any case, we always include the intercept when we run a regression (except in very unusual circumstances where we know from theory that the intercept should be zero).

Question 33

Conditional mean function:

Answer 33

Conditional mean function: A function that tells you the mean (average) of some variable conditional on the value of some other variables.

Question 34

Out-of-sample prediction:

Answer 34

Using regression (or another statistical technique) to predict the outcome for observations that were not included in the original data you used to generate your predictions.

Question 35

Overfitting

Answer 35

Attempting to predict a dependent variable with too many independent variables, so that variables appear to predict the dependent variable in the data but have no actual relationship with it in the world.

Question 36

Estimand

Answer 36

The unobserved quantity we are trying to learn about with our data analysis.

Question 37

Estimator

Answer 37

The procedure applied to data to generate a numerical result

Question 38

Estimate

Answer 38

The numerical result arising from the application of our estimator to a specific set of data.

Question 39

Bias

Answer 39

Differences between our estimand and our estimate that arise for systematic reasons—that is, for reasons that will persist on average over many different samples of data.

Question 40

Noise

Answer 40

Differences between our estimand and our estimate that arise due to idiosyncratic facts about our sample.

Question 41

Unbiasedness:

Answer 41

An estimate/estimator is unbiased if by repeating our estimation procedure over and over again an infinite number of times, the average value of our estimates would equal the estimand.

Question 42

Expectation or Expected value:

Answer 42

Expectation or Expected value: The average value of an infinite number of draws of a variable is the variable’s expected value or its value in expectation.

Question 43

Precision

Answer 43

An estimate/estimator is precise if by repeating our estimation procedure over and over again, the various estimates would be close to each other. The more similar the hypothetical estimates from repeating the estimator, the more precise the estimate.

Question 44

Sampling Distribution

Answer 44

The distribution of estimates that we would get if we repeated our estimator an infinite number of times, each time with a new sample of data.

Question 45

Standard Error

Answer 45

The standard deviation of the sampling distribution. If the estimator is unbiased, the standard error gives us a sense of how far, on average, our estimate would be from the estimand if we repeated our procedure over and over with independent samples of data.

Question 46

Margin of Error

Answer 46

Pollsters often multiply the standard error by 2 and report this as the margin of error. For example, if a survey reports a mean value of 50 with a margin of error of ±3 at a 95% confidence level, it means that we can be 95% confident that the true population mean falls within the range of 47 to 53. | For example, if a survey reports a mean value of 50 with a margin of err

Question 47

95% confidence interval:

Answer 47

If we applied the estimator an infinite number of times, each time on a new sample of data, the estimand would be contained in the 95% confidence interval (newly calculated each time) 95 percent of the time. Importantly, it is not true that we are 95 percent confident that the true estimand lies in the 95% confidence interval.

Question 48

Hypothesis Testing

Answer 48

Statistical techniques for assessing how confident we should be that some feature of the data reflects a real feature of the world rather than arising from noise.

Question 49

Null Hypothesis

Answer 49

The hypothesis that some feature of the data is entirely the result of noise.

Question 50

Statistical Significance

Answer 50

We say that we have statistically significant evidence for some hypothesis when we can reject the null hypothesis at some pre-specified level of confidence (typically, 95% confidence).

Question 51

p-value

Answer 51

The probability of finding a relationship as strong as or stronger than the relationship found in the data if the null hypothesis is true. We use p-values to assess statistical significance. For instance, if the p-value is less than.05, then we have statistically significant evidence (at the 95% confidence level) that the relationship is real. Importantly, the p-value is not equal to the probability that the null hypothesis is true.

Question 52

Publication Bias

Answer 52

The phenomenon whereby published results are systematically over-estimates because there is a bias toward publishing statistically significant results.

Question 53

p-hacking:

Answer 53

Searching over lots of different ways to run an experiment, make a comparison, or specify a statistical model until you find one that yields a statistically significant result and then only reporting that one.

Question 54

p-screening:

Answer 54

A social process whereby a community of researchers, through its publication standards, screens out studies with p-values above some threshold, giving rise to publication bias.

Question 55

Hawthorne effect

Answer 55

The phenomenon whereby subjects change their behavior because they know they are being studied.

Question 56

Demand Effect

Answer 56

A specific instance of a Hawthorne effect in which research subjects change their behavior to try to please the researcher.

Question 57

Signal

Answer 57

The systematic component of an outcome that is persistent across observations. For example: * genes of a plant is signal * amoung of sun it gets is noise *skill of a golf player is signal * luck in a particular

Question 58

Noise

Answer 58

Noise: Random components of an outcome that change from observation to observation.

Question 59

Reversion to the mean

Answer 59

The phenomenon whereby, if one observation of an outcome made up of signal and noise is particularly large (respectively, small) other observations will typically be smaller (respectively, larger).

Question 60

controlling

Answer 60

Using a statistical technique to find the correlation between two variables, holding the value of other variables constant.

Question 61

Dummy Variable

Answer 61

A variable that indicates whether a given unit has some particular characteristic, taking a value of 1 if the unit has that characteristic and 0 if the unit does not.

Question 62

Dependent or Outcome variable:

Answer 62

The variable in your data corresponding to the feature of the world that you are trying to understand or explain with your regression.

Question 63

Treatment Variable

Answer 63

The variable in your data corresponding to the feature of the world whose effect on the dependent variable you are trying to estimate.

Question 64

Control Variable

Answer 64

A variable in your data that you include in your statistical analysis in an attempt to reduce bias in your estimate of a causal effect

Question 65

Omitted variables bias

Answer 65

The bias resulting from failing to control for some confounder when attempting to estimate a causal effect.

Question 66

Local average treatment effect (LATE):

Answer 66

The average treatment effect for some specific subset of the population.

Question 67

Blocked/Stratified Random Assignment

Answer 67

The process of dividing experimental subjects into different groups (typically groups that you believe have similar potential outcomes) and then randomizing your treatment within each of those groups. This can significantly improve the precision of your estimates. If the probability of treatment varies across blocks or strata, you will have to account for this (e.g., by controlling for block-fixed effects) in order to obtain unbiased estimates.

Question 68

Noncompliance

Answer 68

When an experimental subject chooses a treatment status other than the one to which it was assigned

Question 69

Compliers

Answer 69

Units that take up the treatment status they are assigned

Question 70

Always Takers

Answer 70

Units that are always treated, regardless of whether they are assigned to be treated or untreated.

Question 71

Never Takers

Answer 71

Units that are never treated, regardless of whether they are assigned to be treated or untreated.

Question 72

Defiers

Answer 72

Units that take up the opposite of the treatment status they are assigned

Question 73

Intent-to-treat (ITT) or reduced-form effect

Answer 73

The average effect on the outcome of being assigned to the treated rather than the untreated group. This need not be the average treatment effect because of noncompliance.

Question 74

First Stage effect

Answer 74

The average effect of being assigned to the treated group on take-up of the treatment. This corresponds to the fraction of compliers

Question 75

Complier average treatment effect (CATE):

Answer 75

The average treatment effect for the compliers—a special kind of LATE.

Question 76

Instrumental variables (IV):

Answer 76

nstrumental variables (IV): A set of procedures for estimating the CATE in the presence of noncompliance. The Wald Estimator is a special case of instrumental variables. All IV designs require that we can credibly estimate the effect of the instrument on the treatment and on the outcome (exogeneity), that the instrument affects the treatment (compliers), that the instrument only affects the outcome through its effect on the treatment (exclusion restriction), and that there is not a large number units who take-up treatment if and only if the instrument assigns them to the untreated group (defiers).

Question 77

Exogeneity:

Answer 77

An instrument is exogenous if it is randomly assigned or “as if” randomly assigned such that we can get an unbiased estimate of both the first-stage and reduced-form effects.

Question 78

Exclusion restriction:

Answer 78

An instrument satisfies the exclusion restriction if it affects the outcome only through its effect on the treatment, not through any other channel.

Question 79

Chance imbalance:

Answer 79

The situation where, despite random assignment, the treated and untreated groups differ in important ways because of noise

Question 80

Statistical power:

Answer 80

The statistical power of a study is technically defined as the probability of rejecting the null hypothesis of no effect if the true effect is of a certain non-zero magnitude. Colloquially, we say that a study has low statistical power if it was unlikely to produce a statistically significant result even if the effect being investigated is large. it is the likelihood that the study will detect an existing effect if it's present.

Question 81

Attrition:

Answer 81

The situation where experimental subjects drop out of the experiment, such that you do not observe outcomes for those subjects. Attrition is different from noncompliance.

Question 82

Interference:

Answer 82

The situation where the treatment status of one unit affects the outcome of another unit.

Question 83

Natural experiment:

Answer 83

When something was randomized not for research purposes, but careful analysts are nevertheless able to utilize this randomization to answer an interesting causal question.

Question 84

Running variable:

Answer 84

A variable for which units’ treatment status is determined by whether their value of that variable is on one or the other side of some threshold.

Question 85

Regression discontinuity design

Answer 85

A research design for estimating a causal effect that estimates the discontinuous jump in an outcome on either side of a threshold that determines treatment assignment.

Question 86

Continuity at the threshold

Answer 86

: The requirement that average potential outcomes do not change discontinuously at the threshold that determines treatment assignment. If continuity at the threshold doesn’t hold, then a regression discontinuity design does not provide an unbiased estimate of the local average treatment effect.

Question 87

Sharp RD:

Answer 87

An RD design in which treatment assignment is fully determined by which side of the threshold the running variable is on.

Question 88

Fuzzy RD:

Answer 88

A research design that combines RD and IV. The fuzzy RD is used when treatment assignment is only partially determined by which side of the threshold the running variable is on. The researcher, therefore, uses which side of the threshold the running variable is on as an instrument for treatment assignment. In this setting, continuity at the threshold guarantees that the exogeneity assumption of IV is satisfied. But we still have to worry about the exclusion restriction and the other IV assumptions.

Question 89

Difference-in-differences:

Answer 89

A research design for estimating causal effects when some units change treatment status over time but others do not.

Question 90

Parallel trends:

Answer 90

The condition that average potential outcomes without treatment follow the same trend in the units that do and do not change treatment status. This says that average outcomes would have followed the same trend had it not been for some unit’s changing treatment status. If parallel trends doesn’t hold, difference-in-differences does not provide an unbiased estimate of the ATT.

Question 91

First differences:

Answer 91

A statistical procedure for implementing difference-in-differences. It involves regressing the change in outcome for each unit on the change in treatment for each unit.

Question 92

Wide format:

Answer 92

A way to structure a data set in which each unit is observed multiple times, where each row corresponds to a unique unit.

Question 93

Long format:

Answer 93

A way to structure a data set in which each unit is observed multiple times, where there is a row for each unit in each time period.

Question 94

Fixed effects regression:

Answer 94

A statistical procedure for implementing difference-in-differences. It involves regressing the outcome on the treatment while also including dummy variables (fixed effects) for each time period and for each unit.

Question 95

Pre-trends:

Answer 95

The trend in average outcomes before any unit changes treatment status. If pre-trends are not parallel, it is harder to make the case that the parallel trends condition is plausible.

Question 96

Lead treatment variable:

Answer 96

A dummy variable indicating that treatment status in a unit will change in the next time period.

Question 97

Mediator:

Answer 97

A feature of the world that is affected by the treatment and affects the outcome.

Question 98

Causal mediation analysis:

Answer 98

Techniques for trying to estimate how much of the effect of a treatment on an outcome is the result of the treatment’s effect on a mediator and the mediator’s effect on the outcome.

Question 99

Percentage point change:

Answer 99

The simple numerical difference between two percentages.

Question 100

Percent change:

Answer 100

A way of measuring the degree of change. It is the difference between the initial value and the new value divided by the original value (multiplied by 100). Unlike percentage point change, percent change is highly sensitive to the original value.

Question 101

Conditional probability:

Answer 101

The probability of an event conditional on some other information. We write the probability of C conditional on E as Pr(C|E).

Question 102

Prior belief:

Answer 102

Your belief about some thing before learning new evidence.

Question 103

Posterior belief:

Answer 103

Your belief about some thing after incorporating new evidence.

Question 104

Bayes’ rule:

Answer 104

A formula for calculating your posterior belief conditional on new evidence and your prior belief.

Question 105

Statistical power:

Answer 105

The probability of finding a statistically significant result in the data given that the relationship really exists in the world.

Question 106

Internal validity

Answer 106

: An estimate is internally valid if it is a credible estimate of the estimand (e.g., the estimator is unbiased).

Question 107

External validity:

Answer 107

An estimate is externally valid if there is good reason to think the relationship will hold in a context other than the one from which the data is drawn.

Question 108

Strategic adaptation:

Answer 108

Changes in behavior that result from an attempt to avoid the effects of a change in someone else’s behavior. efforts to imporve outcomes on some dimesntions lead people to adjust their behavior to get around those efforts.

Question 109

Selected sample:

Answer 109

A sample of data that wasn’t drawn at random from the population of interest but rather was selected to be studied because it possessed some particular set of characteristics.

Question 110

Causal effect:

Answer 110

The change in some feature of the world that would result from a change to some other feature of the world.

Question 111

Average Treatment Effect (ATE):

Answer 111

The difference in average outcome comparing two counterfactual scenarios—one where everyone in the population is treated and one where everyone in the population is untreated.

Question 112

Average Treatment Effect on the Treated (ATT):

Answer 112

The difference in average outcome comparing the scenario where everyone in the subgroup of people who in fact received treatment is treated and the counterfactual scenario where everyone in that subgroup is untreated.

Question 113

Average Treatment Effect on the Untreated (ATU):

Answer 113

The difference in average outcome comparing the counterfactual scenario where everyone in the subgroup of people who did not receive treatment is treated and the scenario where everyone in that subgroup is untreated.

Question 114

Difference in means:

Answer 114

The difference in average outcome comparing the subgroup of people who in fact received treatment to the subgroup of people who in fact did not receive treatment.

Question 115

Baseline differences:

Answer 115

Differences in the average potential outcome between two groups (e.g., the treated and untreated groups), even when those two groups have the same treatment status.

Question 116

Confounder:

Answer 116

A feature of the world that (1) has an effect on treatment status and (2) has an effect on the potential outcome over and above the effect it has through its effect on treatment status.

Question 117

Reverse causality:

Answer 117

When the outcome affects treatment status.

Question 118

Over-estimate:

Answer 118

When the bias is positive, so that the estimate is larger than the true effect in expectation.

Question 119

Under-estimate:

Answer 119

When the bias is negative, so that the estimate is smaller than the true effect in expectation.

Question 120

Mechanism (or mediator):

Answer 120

A feature of the world that the treatment affects, which then, in turn, affects the outcome

Question 121

Pre-treatment covariate:

Answer 121

A variable that is correlated with treatment and outcome before the treatment occurs.

Question 122

whos a bad bitch

Answer 122

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