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

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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
  1. Used to describe random processes
  2. Describing data
  3. 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
  1. Location (mean, median & mode).
  2. Variation (range, standard deviation & variance)
  3. 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
Definition
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.