Sociology 106:
Intermediate Social Statistics
Class Outline
Information about this course
What is Social Statistics?
Review of Basic Concepts
descriptive vs. inferential statistics
population vs. sample
parameter vs. statistic
What is data? variables a
10/6/13
Class Outline
Hypothesis testing
Significance tests for large samples
Steps of a significance test
Means
Proportions
Significance tests for small samples
t statistic
Hypothesis Testing
In hypothesis testing, a hypothesis about the value of
the
Class Outline
Inferential statistics parameter estimation
Point estimation
Interval estimation
Confidence intervals for means
Confidence intervals for proportions
Parameter Estimation
In parameter estimation a sample is drawn from a
population, a statis
Class Outline
Causality
3 criteria for causality
Multivariate relationships
Statistical control
Multivariate regression
Estimation
Interpretation
Comparing nested models
What do we mean by causality?
Causality refers to a relationship between two
Class Outline
Multivariate regression
Testing causal models
Model goodness-of-fit
Comparing nested models, F
Testing causal models
Suppose we are interested in understanding the causal relationship
between sex, education, and income.
We hypothesize th
Class Outline
Bivariate Regression
Statistical Inference and hypothesis testing
Predicted value of y, y
Using the data on SAT and GPA scores, we estimated a regression
equation:
y = 0 .198 + 0 .533 x
This estimated regression equation (prediction equatio
Class Outline
Correlation
What is correlation?
Scatterplots
Covariance
Pearson correlation coefficient, r
properties
significance test
factors affecting r
intercorrelation matrix
Variable types and Statistical methods
Dependent
Independent
Discrete
Contin
Class Outline
Bivariate Regression
What is regression?
Linear function: deterministic relationships
Linear regression function: stochastic
relationships
Assumptions
Estimating the linear regression function
Interpreting the estimated regression para
11/4/13
Class Outline
One-Way ANOVA Part 2
Conceptual explanation again
Examples
The logic of One-Way ANOVA
H0: 1 = 2 = = g
That is: the populations from which the samples are drawn all
have the same mean.
Say that we want to study whether a familys so
Class Outline
Contingency tables
Bivariate probability distributions
joint
conditional
Associations
statistical independence and dependence
Chi-square test of independence
chi-square test statistic and distribution
Contingency tables
Contingency ta
Class Outline
Probability distributions
Normal distributions and standardized
scores
Standard normal distributions
Sampling distributions
Interpretations of Probability
Two primary interpretations of probability
1) Analytical view of probability
- the
Class Outline
Chi-square test of independence (contd)
Measuring Association using Odds Ratio
Simpsons paradox the missing 3rd variable
2 test statistic
IJ
( f o f e )2
ij =1
fe
=
2
2 test of independence example
Sex
Female
Male
Total
Degree attainment
<
Class Outline
Significance tests for two groups
Significance tests for dependent (paired) samples
Type I and Type II Errors
Dependent, or Paired, Samples
Dependent samples:
- if there is some sort of matching or linking that
occurs between the members
Class Outline
Significance tests for two groups
Hypothesis tests comparing two groups
Significance tests for independent samples
Comparing two means
Comparing two proportions
Bivariate analysis
Bivariate analysis involves two variables:
- response va
Class Outline
Descriptive statistics
Central tendency
mode
mean
median
Variability
variance
standard deviation
Summary measures as estimators of
population parameters
Mode
The mode of a frequency distribution is the value that occurs most
often,
Class Outline
One-Way ANOVA
Explanation
Examples
One-Way ANOVA
ANOVA: Analysis of Variance
One-Way ANOVA is a statistical tool used to
draw inferences about differences in the means of
two or more groups by testing the null hypothesis
that the groups