Inferential Statistics Week 2 Solution

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Inferential StatisticsWeek 2 SolutionInferential Statistics2. Whatare degrees of freedom? How are they calculated?Answer: The degree of freedoms is equal to the number of independent observation or the number ofsubjects in the data, minus the parameters estimated. A parameter to be estimated is related to thevalue of an independent variableand included in a statistical equation. A researcher may estimateparameters using different amounts or pieces of information and the number of independent pieces ofinformation he or she used to estimate statistic or a parameter is called the degree of freedom.Calculation:Step 1Determine what type of statistical test I need to run. Both t-tests and chi-squared tests usedegrees of freedom and have distinct degrees of freedom tables. T-tests are used when thepopulation or sample has distinct variables. Chi-squared tests are usedwhen the population orsample has continuous variables. Both tests assume normal population or sample distribution.Step 2Identify how many independent variables I have in my population or sample. If I have a samplepopulation of N random values then the equation has N degrees of freedom. If my data setrequired me to subtract the mean from each data point--as in a chi-squared test--then I will haveN-1 degrees of freedom.Step 3Look up the critical values for my equation using a critical value table. Knowing the degrees offreedom for a population or sample does not give me much insight in of itself. Rather, the correctdegrees of freedom and my chosen alpha together give me a critical value. This value allows meto determine the statistical significance of my results.3. Whatdo inferential statistics allow you to infer?Answer:Inferential statistics is concerned with making predictions or inferences about apopulation from observations and analyses of a sample. That is, we can take the results of ananalysis using a sample and can generalize it to the larger population that the sample represents.In order to do this, however, it is imperative that the sample is representative of the group towhich it is being generalized.To address this issue of generalization, we have tests of significance. A Chi-square or T-test, forexample, can tell us the probability that the results of our analysis on the sample arerepresentative of the population that the sample represents. In other words, these tests of

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significance tell us the probability that the results of the analysis could have occurred by chancewhen there is no relationship at all between the variables we studied in the population westudied.4. Whatis the General Linear Model (GLM)? Why does it matter?Answer:The General Linear Model (GLM) underlies most of the statistical analyses that are used in applied andsocial research. It is the foundation for thet-test, Analysis of Variance (ANOVA),Analysis of Covariance(ANCOVA),regression analysis, and many of the multivariate methods including factor analysis, clusteranalysis, multidimensional scaling, discriminant function analysis, canonical correlation, and others.Because of its generality, the model is important for students of social research. Although a deepunderstanding of the GLM requires some advanced statistics training, I will attempt here to introducethe concept and provide a non-statistical description.When there is a relationship among the variables and then they can expressedby the general linearmodels.5. Compareand contrast parametric and nonparametric statistics. Why and in what types of cases wouldyou use one over the other?Answer:Nonparametric statistics (also called “distribution free statistics”) are those that can describesome attribute of a population, test hypotheses about that attribute, its relationship with some otherattribute, or differences on that attribute across populations, across time or across related constructs,that require no assumptions about the form of the population data distribution(s) nor require intervallevel measurement.In the literal meaning of the terms, aparametricstatistical test is one that makes assumptions about theparameters (defining properties) of the population distribution(s) from which one's data are drawn,while anon-parametrictest is one that makes no such assumptions. In this strict sense, "non-parametric" is essentially a null category, since virtually all statistical tests assume one thing or anotherabout the properties of the source population(s).We will use parametric statistics and non-parametric statistics in the following situation:

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