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Methods Final Exam
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Terms in this set (83)
Inferential Statistic
A 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
Population
The entirety of cases a researcher would like to (but can't possible) describe
Population Parameter
Quality in the population
Sample
The number of cases or observations drawn from a population
Sample Statistic
An estimate of a population parameter based on a sample from that population
Random Sampling Error
The extent to which a sample statistic differs BY CHANCE from a population parameter
Central Limit Theorem
Statistical rule that tells us that if we were to take an infinite amount of samples of size "n" from a population of "N" members, the means of these samples would form a normal distribution
Normal Distribution
Distribution used to describe interval-level intervals, forms a bell-like symmetry in a graph
Standardization
Occurs when the numbers in a distribution are transformed into standard units of deviation from the mean of the distribution
Z-Score
Standard value, the number of standard deviations a value is from the mean, converts raw deviations from μ into standard units, defines the tick marks of the normal distribution, 68% of the distribution lies between between Z=-1 and Z=1; 95% of the distribution lies between Z=-1.96 and Z=1.96
Probability
the likelihood of the occurrence of an event of set of events
95% Confidence Interval
Most common statistical standard, within 2 standard deviations of the population mean, the interval in which 95 percent of all possible values of the sample mean will fall by chance, defined by the sample means + or - 1.96 standard errors in normal estimation
Standard Error
A measure of statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates(sample standard deviation) / (square root of the sample size)
Student's t-distribution
A probability distribution that can be used to make inferences about a population mean when the sample size is small
Degrees of Freedom
The number of parameters being estimated (n-1)
Sample Proportions
The number of cases falling into one category of the variable divided by the number of cases in the sample
Chi-Square Test of Significance
Compares the observed frequencies to the expected frequencies (Df =
row-1*columns-1)
Sampling Frame
Method for defining the population you want to study
Selection Bias
Nonrandom processes create compositional differences between the population and the sample
Response Bias
Some types of cases are systematically more likely to respond to measurement (Voluntary Response)
Confidence Interval
The range of values in which we believe the population value exists with level of confidence
Confidence Interval Approach
Standard error to determine the smallest plausible mean difference in the population
Critical Value
Marks the upper plausible boundary of the random error and defines the null hypothesis limit
Null Hypothesis
The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error
P-Value Approach
Exact probability determined with the assumption that the null hypothesis is correct
Variance
the expectation of the squared deviation of a random variable from the mean (Total sum of the squares )
Standard Deviation
the extent to which the cases in an interval level distribution fall on or close to the mean of the distribution
Test of Statistical Significance
Helps you decide whether an observed relationship in an independent variable and a dependent variable really exist in the population or whether it could have happened by chance when the sample was drawn
Test Statistic
How many standard errors separate the sample difference from zero
Two Tailed Test Significance
The critical area of a distribution is 2 sided and test wether a sample is greater than or less than a certain range of values
Type I Error
Occurs when the researcher concludes that there is a relationship when one does not occur
Type II Error
Occurs when the researcher infers that there is no relationship in the population when one occurs
Adjusted R-Square
When you have multiple independent variables the value for R-square increases (counts for error in R square)
Correlation Analysis
Produces a measure of association known as Pearson's Correlation Coefficient, that gauges the direction and strength of a relationship between 2 interval level variables
Dummy Variable
Turning categorical variables into numerical values, cases falling into a specific category assume the value of 1 and all cases not falling into that category assume the value of 0
Error Sum of Squares
Prediction error, the component of the total sum of squares that is not explained by the regression equation.
Interaction Effect
When the effect of an independent variable cannot be fairly summarized by a single partial effect
Interaction Variable
The multipliccative product of 2 or more independent variables
Multicollinearity
When the independent variables are related to each other so strongly that it becomes difficult to estimate the partial effect of each independent variable on the dependent variable (2 variables are so strongly correlated you can predict the regression of one by looking at the regression of the other)
Multiple Regression
Gives the estimate of the effects of multiple variables, Able to isolate the effect of one independent variable on the dependent variable while controlling for the effects of the other independent variables
Partial Regression Coefficient
Estimates the mean change in the dependent variable for each unit change in the independent variable, controlling for the other independent variable
Pearson's Correlation Coefficient
Determines the direction and strength of an interval-level relationship (measures the linear interdependence between 2 variables)
Prediction Error
The difference between the estimates and the case's actual value of y. The actual value of the dependent variable minus the estimated value of the dependent variable.
Regression Analysis
Produces a statistic (the regression coefficient) that estimates the size of the effect of the independent variable on the dependent variable
Regression Line
Y= a + bX, the line of best fit
Regression Sum of Squares
The component of the total sum of squares that we pick up by knowing the independent variable, how well a model represents the data being modeled
R-Square
A measure of how close the data are to the fitted regression line
Scatterplot
Graphically shows he relationship between 2 variables
Binary Variable
Variable than can assume only 2 values, identical to dummy variables
Common Log
Log to the base of 10
Natural Log
Log of the base e
Likelihood Function
A number that summarizes how well a model's predictions fit the observed data
Logits
Natural log transformation of odds
Maximum Likelihood Estimation
Takes the sample wide probability observing a specific value of a binary dependent variable and sees how well this probability predicts that outcome for each individual case in the sample
Odds
The number of occurrences of one outcome divided by the number of occurrences of the other outcome
Odds Ratio
The relationship between the odds at one value of the independent variable compared with the odds at the next lower value of the independent variable
Factor Analysis
Allows researchers to uncover patterns across related measures to create summary variables that represent different dimensions of the same concept
External Validity
Extent to which the results of an experiment can be generalized across populations, time and settings
Regression Coefficient
The slope of a line obtained using linear least squares fitting
Census
Survey conducted on the full set of observation objects belonging to a given population or universe
Random Selection
Occurs when every member of the population has an equal chance on being included in the sample
Measure of Association
Tells the researcher how well the independent variable works in explaining the dependent variable
Standard Error of the Sample Mean
Measures how much x̄ departs, by chance, from μ
Random sampling error
Equal to σ/√n, if σ is known
Equal to s/√n, if σ is unknown
Standard Error of a Sample Proportion
Measures how much p departs, by chance, from a population proportion
Defined by √pq/√n
Ordinarily can be applied in finding the 95% confidence interval of p, using normal estimation
Random Sample
A sample that has randomly been drawn from the population
Range
The maximum actual value mines the minimum actual value
Total Sum of Squares
An overall summary of the variation in the dependent variable
Represents all the errors in guessing the value of the dependent variable for each case, using the mean of the dependent variable as a predictive instrument
Percent Change in the Odds
The percent that the odds change with each change in a unit of the independent variable
Marginal Effects at the Means
A way to report changes in probability of the dependent variable by examining the effect of one independent variable on the probability of the dependent variable, while holding the other independent variables constant at their sample averages
Marginal Effects at Representative Values
A way to report changes in the probability of the dependent variable across the range of an interesting independent variable- and do to so separately, for discrete categories of another independent variable
Average Marginal Effects
A way to report changes in the probability of the dependent variable by holding all other controls constant at their means and looking at the impact the independent variable has on the dependent variable
05 Level of Significance
The lowest level of significance
A P-value must have a value of less that .05 to reject the null hypothesis
Concordant Pair
A pair of observations that is consistent with a positive relationship
Discordant Pair
A pair of observations that is consistent with a negative relationship
Tied Pair
A pair of observations that has different values on the independent variable but the same value on the dependent variable
T-Ratio
Calculated just like a Z-score and used to figure out significance
At a .05 level of significance, the T-Ratio must be higher than 1.96 or lower than -1.96 to reject the null hypothesis
Standard Error of the Difference
What the P-value approach is based on
Eyeball Test of Statistical Significance
Asking if the mean difference is at least twice its standard error
If the answer is no, accept the null hypothesis
Error Bar Chart
Graphing means and their errors in a box-and-whiskey plot setup
If the two bars do not touch, reject the null hypothesis
Cramer's V
Examining Controlled Comparisons, based on Chi-square, takes a value between 0, no relationship, and 1, perfect relationship.
Lambda
Designed to measure the strength of a relationship between two categorical variables, at least one of which is a nominal-level relationship
Somers's D
Is appropriate for gauging the strength of ordinal level relationships
Proportional Reduction in Error (PRE)
A prediction based metric that varies in magnitude between 1 and 0. How much better you can predict the dependent variable knowing the Ind v.
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