Exploring Inferential Statistics And Their Discontents

2697 words - 11 pages

What are degrees of freedom?
The degrees of freedom (df) of an estimate is the number or function of sample size of information on which the estimate is based and are free to vary relating to the sample size (Jackson, 2012; Trochim & Donnelly, 2008).
How are the calculated?
The degrees of freedom for an estimate equals the number of values minus the number of factors expected en route to the approximation in question. Therefore, the degrees of freedom of an estimate of variance is equal to N - 1, where N is the number of observations (Jackson, 2012). Given a single set of six numbers (N) the df = 6 – 1 = 5.
What do inferential statistics allow you to infer?
Inferential statistics establish the methods for the analyses used for conclusions drawing conclusions beyond the immediate data alone concerning an experiment or study for a population built on general conditions or data collected from a sample (Jackson, 2012; Trochim & Donnelly, 2008). With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. A requisite for developing inferential statistics supports general linear models for sampling distribution of the outcome statistic; researchers use the related inferential statistics to determine confidence (Hopkins, Marshall, Batterham, & Hanin, 2009).
What is the General Linear Model (GLM)? Why does it matter?
The General Linear Model (GLM) is an important cornerstone that delivers a comprehensive and prevalent mathematical structure for statistical analyses in applied social research (Trochim & Donnelly, 2008; Zheng & Agresti, 2000). GLM is a system that measures the predictive power and significance of the predictors for comparison of contending GLM models with dissimilar linear predictors (Zheng & Agresti, 2000). GLM is the underpinning for the t-test, ANOVA, ANCOVA, regression analysis and various multivariate methods.
Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?
Parametric test make assumptions concerning estimates from population parameters with a normality of the distribution and commonly use interval or ratio data; nonparametric tests do not involve any population parameters and do not require a necessity for a normal distribution (Jackson, 2012; Qualls, Pallin, & Schuur, 2010). Qualls et at., (2010) discussed how parametric tests analyze data for inferential test, and one principal issue for applying parametric statistical tests towards nonnormally distributed data decreases power and escalate the probability of a type II error. Qualls et at., (2010) also mentioned an fitting use of nonparametric statistical analyses applies towards nonnormally distributed data thus improving the accuracy and validity of a nonparametric statistical inferential statistical test. Nonparametric tests do...

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