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Quantitative Analysis: Inferential Statistics - Coggle Diagram
Quantitative Analysis:
Inferential Statistics
Basic Concepts
In inferential statistics, this probability is called the p-value
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
The precision of our sample estimates is defined in terms of a confidence interval
General Linear Model
Most inferential statistical procedures in social science research are derived from a
general family of statistical models called the general linear model
the process of estimating regression coefficients is called regression analysis
Two-Group Comparison
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
The t-test was introduced in 1908 by William Sealy Gosset, a chemist working for the
Guiness Brewery in Dublin
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)
To conduct the t-test, we must first compute a t-statistic of the difference is sample
means between the two groups
Factorial Designs
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
Interpretation of
covariates also follows the same rules as that of any other predictor variable.
Other Quantitative Analysis
Factor analysis is a data reduction technique that is used to statistically aggregate a
large number of observed measures into a smaller set of unobserved 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
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.