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Chapter 15 - Coggle Diagram
Chapter 15
Interested readers are referred to advanced text books or
statistics courses for more information on these techniques:
Factor analysis is a data reduction technique that is used to statistically aggregate a large number of observed measures (items) into a smaller set of unobserved (latent)variables called factors based on their underlying bivariate correlation patterns.
Discriminant analysis is a classificatory technique that aims to place a given observation in one of several nominal categories based on a linear combination of predictor
variables.
Logistic regression (or logit model) is a GLM in which the outcome variable is binary (0 or 1) and is presumed to follow a logistic distribution, and the goal of the regression analysis is to predict the probability of the successful outcome by fitting data into a
logistic curve.
Probit regression (or probit model) is a GLM in which the outcome variable can vary between 0 and 1 (or can assume discrete values 0 and 1) and is presumed to follow a standard normal distribution, and the goal of the regression is to predict the probability
of each outcome.
Path analysis is a multivariate GLM technique for analyzing directional relationships
among a set of variables.
Time series analysis is a technique for analyzing time series data, or variables that
continually changes with time.
Inferential statistics are the statistical procedures that are used to reach conclusions
about associations between variables
we can only reject
hypotheses based on contrary evidence but can never truly accept them ecause presence of
evidence does not mean that we may not observe contrary evidence later.
A second problem with testing hypothesized relationships in social science research is that 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.
The significance 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.
A sampling distribution is the theoretical
distribution of an infinite number of samples from the population of interest in your study.
However, because a sample is never identical to the population, every sample always has some inherent level of error, called the standard error.
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Most inferential statistical procedures in social science research are derived from a
general family of statistical models called the general linear model
One of the simplest inferential analyses is comparing the post-test outcomes of treatment and control group subjects in a randomized post-test only control group design, such as whether students enrolled to a special program in mathematics perform better than those in a traditional math curriculum.
The t-test examines whether the means of two groups are statistically different from each other (non-directional or two-tailed test), or whether one group has a statistically larger (or smaller) mean than the other (directional or one-tailed test).
Extending from the previous example, let us say that the effect of the special curriculum (treatment) relative to traditional curriculum (control) depends on the amount of instructional time (3 or 6 hours/week).
Regression analysis
involving multiple predictor variables is sometimes called multiple regression, which is
different from multivariate regression that uses multiple outcome variables.
Covariates can be included in factorial designs as new variables, with new regression
coefficients
Covariates can be measured using interval or ratio scaled measures, even
when the predictors of interest are designated as dummy variables.