# Shared Flashcard Set

## Details

Quantitative Analysis
Probability/Statistics
75
Political Studies
04/26/2013

Term
 Random Events
Definition
 Events that we cannot predict wirh certainty. "Unpredictable" Example is flipping a coin.
Term
 Fair
Definition
 Processes in which all outcomes have the same probability.  Example: fair coin, fair dice
Term
 Independent Events
Definition
 If two events are independent, it means that knowing one outcome does not allow you to predict the other outcome.  Example: Just because you got 5 heads in a row during a coin toss does not mean you are "due" for a tails. There is still a 50-50 chance of getting either a heads or tails.
Term
 Binomial Process
Definition
 A random process with only two outcomes.  Can have the feature of equal probability or not.
Term
 Binomial Distribution
Definition
 The plot of the two outcomes (discrete). N= number of trials, p= probability of success and each event is independent.
Term
 Multinomial Process
Definition
 When a process has a countable number of possible outcomes (more than 2). Can have equal probabilities for each outcome or not.
Term
 Uniform Distribution
Definition
 Every number in a given range has an equal chance of showing up.
Term
 Probability Distribution
Definition
 Shows the likelihood that various values of the variable will occur. Shows us what kinds of outcomes are common and what kinds are rare.
Term
 Discrete Distributions
Definition
 Knowing all the possible results and there are a countable number of them.
Term
 Probability Distribution
Definition
 Used to describe random processes Describing data Help us to understand how large the random component is in the things we observe
Term
 Normal (Gaussian) Distribution
Definition
 Is a continuous probability distribution. A frequency distribution in which there are many possible values with a probability of occurring. *data tends to be around a central value with no bias left or right, creates what we know as the "bell curve"
Term
 Mean
Definition
 Avergage. The sum of a set of numbers divided by how many numbers there are. 2+4+8+10=22 24/4=6 (mean) Equation: EXi/N
Term
 Sample Error
Definition
 The extent to which the sample does not reflect the population. The sample may no be representing a certain portion of the population accurately.
Term
 Sample Average
Definition
 Sample average=population mean + sampling error
Term
 Randomization Error
Definition
 During an experiment, the random assignment of subjects to experimental control groups may randomly produce differences between the two groups (control and experimental), resulting in an error
Term
 Measurement Error
Definition
 Difference between the actual value of a quantity and the value obtained by a measurement. Repeating the measurement will reduce the random error.
Term
 Y = f(X) + E
Definition
 E= the effects of every variable, (the random component) on the outcome.  X= the independent vairable Y= outcome or the dependent variable (the thing we are trying to explain)
Term
 Expected Value
Definition
 The mean of the sampling distribution
Term
 Sampling Distribution
Definition
 A probability distribution that shows what happens when we repeat the smapling process many times.
Term
 Standard Deviation
Definition
 Number used to describe the variation in a variable's distribution  *the square root of the variance
Term
 Standard Error
Definition
 The standard deviation of the sampling distribution.
Term
 Z Score
Definition
 When values are transformed in a way that allows for comparisons between variables measured on different scales.
Term
 Law of Large Numbers
Definition
 When the sum or the mean of large random smaples are plotted, the shape is of a bell (normal distribution). Tells us what is a good guess of the mean.
Term
 Variance Equation
Definition
 E(X1-X)2/N-1 X1= each number in the sample X=mean N= number of samples Ex: E(1, 6, 8, 9) Mean = 1 + 6 + 8 + 9/4 = 6 (1-6)2+ (6-1)2 +(8-1)2+(9-1)2/4-1 = 163/3 =54.33
Term
 T Distribution
Definition
 Is a normal distribution but with longer tails. Sample size is small and the sample falls further away from the mean.
Term
 Unbiased
Definition
 Occurs if the mean of the sampling distribution for the estimator (expected value) is equal to the population value being estimated.  Bias = population value - expected value of estimator
Term
 Statistics
Definition
 The field of studey that involves the collection and analysis of numerical facts or data.
Term
 Variation
Definition
 Things differ from person to person
Term
 Representative Sample
Definition
 Every member of the population we are studying has the same chance of appearing in the sample.
Term
 Experimental Group
Definition
 Set of participants who receive the "manipulation"
Term
 Control Group
Definition
 Set of participants in an experiment who do not receive the "manipulation"
Term
 Nominal
Definition
 Observations are assigned to categories with no ordering among categories. Can only be assigned to one category. Ex: Married, widow, divorced, single, seperated.
Term
 Binary Variables
Definition
 A nomial measurement with only two possible categories. Ex: male or female.
Term
 Ordinal
Definition
 Number represent rank ordering but we do not know how far aprt the ranks are. Ex: strongly agree, agree; neither agree or disagree; disagree; and strongly disagree.
Term
 Interval
Definition
 Have regular numbers that indicate how far apart observations are.  Ex: number of years of education, income.
Term
 Ratio
Definition
 Level of measurement in which observations are assigned numbers and the numbers indicate how far apart observations are. Different form interval because have a natural zero point.
Term
 Qualitative vs. Quantitative
Definition
 Qualitative: nominal variables (discrete) Quantitative: ordinal and interval measurements (continuous vairables)
Term
 Ecological Fallacy
Definition
 Studying one kind of thing and making conclusions about another unit of analysis.
Term
 Event History Analysis
Definition
 Used to study the occurrence of events.
Term
 Time Series Analysis
Definition
 Analysis of data over time. Can help us solve the problem of casual ordering.
Term
 Cross-Sectional Analysis
Definition
 The collection of data on many examples at one point in time. Cannot determine causation.
Term
 Panel Study
Definition
 Observe untis at several points in time. Provides a large sample size and time odering to help determine causation.
Term
 Sample
Definition
 Is a subset of all the units (population) on which we would like to have data.
Term
 Measures of Central Tendency
Definition
 What is typical in a data set and the extent to which observations differ from one another (mean, median & mode). Is an attempt to summarize the data set with one number that is "typical" of all numbers in the data set.
Term
 Measures of Variability
Definition
 How different observations are from one another.
Term
 Univariate
Definition
 One variable
Term
 Bivariate
Definition
 Two vairables
Term
 Multivariate
Definition
 More than two variables
Term
 Median
Definition
 The middle. Order numbers from highest to lowest and it is the number found in the middle. If there is an even number, take the two numbers in the middle and divide by two.
Term
 Mode
Definition
 The score that occurs most frequently in the data. Ex: 1, 3, 4, 3, 6, 7, 4, 3, 9, 3 Mode: 3
Term
 Outliers
Definition
 Exceptional data points. Impacts the mean the most.  Ex: 1, 2, 3, 4, 26 26 is the outlier.
Term
 Confidence Interval
Definition
 Allows us to make estimates of values in the population while taking into account that our estimates are never accurate (idicates reliability).  Mean + Z(S.e/standard error)
Term
 Z Table
Definition
 +/- 1 --> 68% +/-2 --> 95% +/-3 --> 99%
Term
 Kurtosis
Definition
 A measure of whether the data are peaked or flat relative to a normal distribution
Term
 Skewness
Definition
 Is a measure of symmetry or the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.
Term
 High Kurtosis
Definition
 Have a distinct peak near the mean, decline rather rapidly, and have heavy tails
Term
 Low Kurtosis
Definition
 Have a flat top near the mean rather than a sharp peak and little/thin tails. A uniform distribution would be the extreme case.
Term
 Histogram
Definition
 A graphical technique for showing both the skewness and kurtosis of data set.
Term
 3 Moment Generating Functions
Definition
 Location (mean, median & mode). Variation (range, standard deviation & variance) Symmetry (skewness, kurtosis)
Term
 Unit of Analysis
Definition
 The thing on which data was collected (organizations, countries, people)
Term
 Independent Vairable
Definition
 Variable that is used to try to explain/predict a dependent variable. Known as "X" in the equation.
Term
 Dependent Variable
Definition
 The variable that we are tring to explain/predict. Known as "Y" in the equation.
Term
 Gauss-Markov Theorem
Definition
 In a linear regression model in which that errors have the expectation of zero and are uncorrelated, and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator
Term
 Causation
Definition
 One factor (X) leads to another factor (Y) to occur
Term
 Probability
Definition
 Tells us where the numbers are coming from. Likelihood of an event occurring.
Term
 Statistics
Definition
 The collection and analysis of data so that we are able to infer to a population. Interested in the causal realtionship as politcial scientists.
Term
 Data
Definition
 Information that we break into categories (gender, race, religion, etc) then assign it a number (nominal).
Term
 Cumulative Distribution Function (CDF)
Definition
 The proportion of population with value less than X The probability of having a value less than x
Term
 Probability Density Function
Definition
 Describes the relative likelihood for this random variable to take on a given value. The probability for the random variable to fall within a particular region is given by the integral of this variable’s density over the region
Term
 Poisson Process
Definition
 Counts the number of event and the number of times these events occurred in a given interval of time.
Term
 Classical
Definition
 Based on theory.
Term
 Empirical
Definition
 Based on practice.
Term
 Discrete
Definition
 Whole numbers (0, 1, 2)
Term
 Continuous
Definition
 Any number on the number line.
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