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Quantitative Analysis:
Inferential Statistics
statistical procedures…
Quantitative Analysis:
Inferential Statistics
statistical procedures that are used to reach
conclusions about associations between variables; explicitly designed to test hypotheses
Basic Concepts
Karl Popper: theories can never be proven, only disproven
alternative hypothesis-we cannot
truly accept a hypothesis of interest we formulate a null hypothesis as the opposite of the alternative hypothesis, then use empirical evidence to reject the null hypothesis to demonstrate indirect, probabilistic support for our alternative hypothesis.
the dependent variable may be influenced by an infinite number of extraneous variables
and it is not plausible to measure and control for all of these extraneous effects
two variables may seem to be related in an observed sample, they may not be truly related in the population, and therefore inferential statistics are never certain or deterministic, but always
probabilistic
Sir Ronald A. Fisher: established the basic guidelines for significance testing; statistical result may be considered significant if it can be shown that the probability of it being
rejected due to chance is 5% or less (pv-value)
ignificance level is the maximum level of risk that we are
willing to accept as the price of our inference from the sample to the population
If p>0.05, we do not have enough evidence to reject
the null hypothesis or accept the alternative hypothesis.
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General Linear Model
general linear model (GLM): Most inferential statistical procedures in social science research are derived from a general family of statistical models
GLM is a system of equations that can be used to represent linear patterns of relationships in observed data.
A model is an estimated mathematical equation that can be used to represent a set of data; linear refers to a straight line. 
two-variable linear model that examines the relationship
between one independent variable (the cause or predictor) and one dependent variable (the effect or outcome)
straight lines can be represented using the mathematical equation y =
mx + c, where m is the slope of the straight line e (how much does y change for unit change in x)
and c is the intercept term (what is the value of y when x is zero); βo is the slope, β1 is the intercept term, and ε is the error term
Regression Coefficients: A line that describes the relationship between two or more variables is a regression line, (and other beta values) Regression Analysis: the process of estimating regression coefficients i
predictor variables xi may represent independent variables or
covariates (control variables).
Covariates are variables that are not of theoretical interest but
may have some impact on the dependent variable y and should be controlled so that the residual effects of the independent variables of interest are detected more precisely
captures systematic errors in a regression equation while the error term (ε ) captures random errors
dummy variables: predictor variables may even be nominal variables (e.g., gender: male or female); These are variables that can assume one of only two possible values: 0 or 1
A set of n nominal variables is represented using n-11 dummy variables
analysis of variance (ANOVA): If a dummy predictor variable, and we are comparing the effects of the two levels (0 and 1) of this dummy variable on the outcome variable
analysis of covariance (ANCOVA): doing ANOVA while controlling for the effects of one or more covariate
multivariate regression: multiple outcome variables
are modeled as being predicted by the same set of predictor variables
multivariate ANOVA (MANOVA) or multivariate ANCOVA (MANCOVA) respectively: doing ANOVA or ANCOVA analysis with multiple outcome variables, the resulting analysis
structural equation modeling: model the outcome in one regression equation as a predictor in another equation in an interrelated system of regression equations
model specification: most important
problem in GLM; should be based on theoretical considerations about the phenomenon being studied rather than what fits the
observed data best
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Factorial Designs
2 x 2 factorial design: the effect of the special curriculum
(treatment) relative to traditional curriculum (control) depends on the amount of instructional time (3 or 6 hours/week); the two factors being
curriculum type (special versus traditional) and instructional type (3 or 6 hours/week)
main effects: helps us estimate the independent effect of each factor
interaction effect: helps to estimate the joint effect of both factors
y=post treatment scores, x1=treatment, x2=instructional time
same factorial model can be analyzed using a two-way ANOVA analysis
Main effects are interpretable only when the interaction effect is non-significant.
Covariates can be included in factorial designs as new variables, with new regression coefficients; can be measured using interval or ratio scaled measures, even
when the predictors of interest are designated as dummy variables