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POLS 306 - Final Exam

Terms in this set (66)

What is statistical significance?
The practice of using data from a sample and the rules of probability to make careful statements about the population from which the sample was drawn that
quantify our uncertainty about the statements.
Population data
A set of all possible relevant cases (researchers rarely get to see this kind of data)
Sample data
A subset of the underlying population (ideally randomly drawn)
Sample size
Larger samples are better, but beyond a certain point, the marginal improvement is minimal (the key is understanding how the MOE accompanies the sample size)
Why do we want a greater sample size?
Statistics are typically guaranteed to get very close to the parameters they estimate (and it ensures outliers are not overrepresented)
Probability theory
Allows us to quantify our uncertainty about our statements
Simple Random Sample
A sample in which every possible sample has an equal chance of being chosen
Why do we want a random sample?
The sample should reasonably look like the population, and non-random samples allow for bias in the sample
Central Limit Theorem
The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.
Selection bias
A polling error in which the sample is not representative of the population being studied, so that some opinions are overor underrepresented
Response bias
The likelihood of not responding
Random sampling error
The extent to which a sample statistic varies by chance from a population parameter. In other words, it's the expected sampling error of a sample statistic (AKA Standard Error)
Random sampling error formula
Expected sampling error = variation component divided by the square root of "n"
If the variable on which a statistic is based has high variability, spread, dispersion what does this mean for sampling error?
It increases it.
Interval-level variables random sampling error formula
Expected sampling error = standard deviation divided by the square root of n
95% Confidence Interval Definition
The range within which the true population mean lies, with 95% certainty
99% confidence interval
+/- 2.57 SDs
95% confidence interval
+/- 1.96 SDs
90% confidence interval
+/- 1.65 SDs
If I want more confidence that my interval contains the true parameter value within it, what can I do?
Accept a wider interval
If I want more precision, what can I do?
Increase the sample size
Confidence Interval Approach Steps
Identify a parameter to estimate
Use sample to derive an estimate
Calculate an interval around the statistic to represent precision/uncertainty
Make comparisons to test differences
Hypothesis Testing Approach Steps
Devise a hypothesis
Similar to setting a confidence level, set a significance level, meaning a tolerance for incorrectly embracing the research hypothesis as correct
Determine whether the data support the hypothesis or not
Hypothesis testing
Null hypothesis is assumed to be true until sufficient evidence is produced to reject it in favor of the alternative
Ho
Null hypothesis
When is something statistically significant?
When the p value is less than .05
Type I error
false positive (rejecting the null hypothesis when it is true)
Type II error
false negative (failing to reject a false null hypothesis)
Three levels of significance
.10 (10% probability of Type I error in H0 is true)
.05 (5% probability of Type I error in H0 is true)
.01 (1% probability of Type I error in H0 is true)
What is a p-value
Probability that the null hypothesis is true
Significant difference
T-statistic under .05
No significant difference
T-statistic above .05
When to use a two tailed test
If theory leads one to expect the parameter to be difference from a null value, but not in a particular direction
When to use a one tailed test
If theory leads one to expect a particular direction
Two-tailed test
A test of a statistical hypothesis, where the region of rejection is on both sides of the sampling distribution
What does it mean for two variables to be associated?
The two variables are not independent of each other
Chi-square
Involves categorical variables. Looks at 2 distributions of categorical data to see if they differ from each other.
Correlation
A relationship between two or more things
Model
A set of conceptual relationships that explain the variation in a dependent variable
Regression
A measure of the correlation between the mean value of one variable and corresponding values of other variables
Bivariate analysis
Given a degree of uncertainty, what can we say about the relationship between a IV and a DV?
Correlation coefficient
Represented as "r"
Positive correlation
Means larger values of X tend to go with larger values of Y, and smaller values of X go with smaller values of Y
Negative correlation
Means larger values of X tend to go with smaller values of Y, and smaller values of X go with larger values of Y
What is a strong correlation?
-/+ 1 is perfect
Ordinary Least Squares (OLS) Regression
A form of regression that fits the best line to the relationship between variables
What is OLS used for?
Only on continuous dependent variables
What does regression tell us?
For each unit change in X, how Y changes on average
Basic idea of bivariate regression
Find the best-fit line through a scatter plot
Best fit line
The weaker the correlation, the wider selection of lines will look reasonable since the scatterplot is messier. The best fitting line is thus the one that minimizes the sum of squared residuals
Ordinary least squares
a statistical procedure that estimates regression equation coefficients that produce the lowest sum of squared differences between the actual and predicted values of the dependent variable
Common ways to asses goodness of fit
- Root mean-squared error, or standard error of the residuals (Root MSE)
- R-squared statistic
Root MSE
Estimates how far the observed values of Y tend to fall from the regression line (predicted Y). This is the average accuracy of the model
R-squared
Measures how much of the variation in Y is accounted for by the variation in X
What does OLS form?
It forms a line - the best fit line that reduces squared residuals
What can we do with nominal variables?
Create dichotomous/dummy variables
What do we do with moderated relationships?
Create interactions
Dummy variable
A variable for which all cases falling into a specific category assume the value of 1, and all cases not falling into that category assume a value of 0.
Multicollinearity
The term used to describe the correlation among the independent variables. OLS assumes no multicollinearity, referring to the correlation between variables.
For a probability of .5
Odds will be 1
Log odds will be 0
For probability between 0 and <.5
Odds will be between 0 and almost 1
Log odds will be negative
Maximum likelihood estimation (MLE)
Summarizes how well a model's predictions fit the observed data
How to determine likelihood (MLE)
Multiply all the individual likelihoods together
Marginal effects at the means (MEMs)
Report changes in the probabilities of the DV across the values of one IV, holding all other IVs constant at their sample means
Marginal effects at representative values (MERs)
Report changes in the probabilities of the DV across the values of one IV — and do so at two or more discrete values of another IV
Residual
The vertical distance between a data point and the regression line
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