Please enable JavaScript.
Coggle requires JavaScript to display documents.
QUANTITATIVE ANALYSIS INFERENTIAL STATISTICS, Chapter 15, Source:…
QUANTITATIVE ANALYSIS
INFERENTIAL STATISTICS
General Linear Model (GLM):
Most inferential statistical Procedure in social science derive from this model
GLM represents linear relationships using mathematical equations
Linear refers to straight-line relationships in data
Two-variable Linear Model:
Simplest GLM: One independent variable (predictor) and one dependent variable (outcome)
Example: Age (predictor) vs. Self-esteem (outcome)
Regression Analysis:
Regression line describes relationships between variables
Regression Coefficients estimated through regression analysis
GLM can include multiple predictors and outcomes
Dummy Variables:
Nominal variables like gender coded as number 0 or 1
Multiple categories represented by multiple dummy variables
Covariates and Errors:
Covariates: Control variables not of theoretical interest but influence the dependent variable
Covariates capture systematic error
GLM as a family of methods:
**
ANOVA:
Compare means across groups
ANCOVA
: ANOVA controlling for covariates
Multivariate Regression
: Multiple outcomes variables predicted by same predictors
MANOVA//MANCOVA:** ANOVA/ANCOVA with multiple outcomes
Structural Equation Modeling: Interrelated regression equations
Model Specification:
Most critical step in GLM
Should be based on theory, not just data fit
Data validates the model, not specifies it
Basic Concepts
Significance Testing (Sir Ronald Fisher)
A result is significant if the probability of it occurring by chance is less than or equal to 5%
p-value: probability of rejecting the null hypothesis by chance
Significance level (α): Maximum acceptable risk (0.05)
Key Statistical Concept:
Sampling Distribution: Theoretical distribution of infinite samples from the population
Standard Error: Inherent error in sample estimates
Confidence Interval (CI): Range around sample estimate
p-value and CI together indicate probability and precision of results
Karl Poppers Principle:
Theories can never be proven, only disproven
Example: The sun rising tomorrow can't be guaranteed, even if it has risen every day before.
Inductive theories are conjecture, not certainties
Challenges in Social Science Research
Dependent variables may be influenced by countless extraneous factors
Observed relationships in samples may not hold true in the population
nferential statistics are probabilistic, not deterministic
Two-group comparison
Basic Concept:
The simplest inferential analysis compares posttest outcomes of treatment groups vs. control groups in a randomized posttest-only design
Example: Do students in a special math program perform better than those in a traditional curriculum?
Variables:
Predictor variable: Dummy coded: Ex: 1=treatment group, 0=control group
Outcome variable: Ratio-scaled (e.g., math test score)
Analytic Techniques:
One-way ANOVA: Used because there is only one predictor variable
Student's t-test: Statistical test for comparing two group means
Student's t-test:
Introduced in 1908 by William Sealy Gosset
Examines if two group means differ significantly
Two-tailed test:
Non-directional (means differ)
One-tailed test:
Directional (one mean is greater)
Hypotheses:
Null hypothesis: Means are equal.
Goal: Reject the null hypothesis using sample data
Key Statistical Concepts:
Sample means differ from population due to sampling error
Confidence Interval: 95% CI sample mean plus or minus 2 standard errors
Statistical significance depends on: Difference in sample means and standard error
Significance Testing:
Compare computed t-statistic to critical value using the p-value or degree of freedom
If p < α (0.05); reject the null hypothesis
Effect Size (ES)
After significance, estimate magnitude of treatment effect
Use regression analysis
Regression coefficient (β)=effect size-difference between treatment and control means
Factorial Designs:
Design with two or more factors
Purpose
: Estimate main effects and interaction effect
Models
: Regression coefficients represent main effect and interaction effects and can also be analysis using two-way ANOVA
Interpretation
: If interaction effect is significant, main effects cannot be interpreted independently.
Covariates
: Can be added to factorial designs for better precision
Other Quantitative Techniques
Factor Analysis:
Data reduction technique
Aggregates observed measures into latent variables
Used for validity assessment in multi-item scales
Discriminant Analysis:
Classifies observations into nominal categories
Similar to regression but with a nominal dependent variable.
Common in marketing for customer/product classification
Logistic Regression (Logit Model):
Outcomes variable is binary (0 or 1)
Predicts probability of success using logistic curve
Popular in medical sciences
Probit Regression:
Outcome variable between 0 and 1 or binary.
Assumes standard normal distribution
Used in finance, insurance and credit scoring
Similar to logit but harder to compute
Path Analysis:
Multivariate GLM technique
Examines directional relationships among variables
Used for complex models in social science research
Time Series Analysis:
Analyzes data that changes over time
Applications: Forecasting stock prices, crime rates
Corrects for autocorrelation in time-dependent data
Chapter 15
Source: Bhattacherjee, A. (2019). Social science research: Principles, methods, and practices. Revised Edition. University of Southern Queensland.
https://usq.pressbooks.pub/socialscienceresearch