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Inferential Statistics Week 2 Solution

Solutions to inferential statistics problems from Week 2 coursework.

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    Inferential Statistics Week 2 Solution Inferential Statistics 2. What are degrees of freedom? How are they calculated? Answer: The degree of freedoms is equal to the number of independent observation or the number of subjects in the data, minus the parameters estimated. A parameter to be estimated is related to the value of an independent variable and included in a statistical equation. A researcher may estimate parameters using different amounts or pieces of information and the number of independent pieces of information he or she used to estimate statistic or a parameter is called the degree of fr eedom. Calculation: Step 1 Determine what type of statistical test I need to run. Both t - tests and chi - squared tests use degrees of freedom and have distinct degrees of freedom tables. T - tests are used when the population or sample has distinct variables. Chi - squared tests are used when the population or sample has continuous variables. Both tests assume normal population or sample distribution. Step 2 Identify how many independent variables I have in my population or sample. If I have a sample population of N random values then the equation has N degrees of freedom. If my data set required me to subtract the mean from each data point -- as in a chi - square d test -- then I will have N - 1 degrees of freedom. Step 3 Look up the critical values for my equation using a critical value table. Knowing the degrees of freedom for a population or sample does not give me much insight in of itself. Rather, the correct degrees of freedom and my chosen alpha together give me a cr itical value. This value allows me to determine the statistical significance of my results. 3. What do inferential statistics allow you to infer? Answer: Inferential statistics is concerned with making predictions or inferences about a population from observations and analyses of a sample. That is, we can take the results of an analysis using a sample and can generalize it to the larger population that th e sample represents. In order to do this, however, it is imperative that the sample is representative of the group to which it is being generalized. To address this issue of generalization, we have tests of significance. A Chi - square or T - test, for example, can tell us the probability that the results of our analysis on the sample are representative of the population that the sample represents. In othe r words, these tests of

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    significance tell us the probability that the results of the analysis could have occurred by chance when there is no relationship at all between the variables we studied in the population we studied. 4. What is 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 and social research. It is the foundation for the t - test , Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA) , regression analysis , and many of the multivariate methods including factor analysis, cluster analysis, multidimensional scaling, discriminant function analysis, canonical correlation, and others. Because of its generality, the model is important for students of social resear ch. Although a deep understanding of the GLM requires some advanced statistics training, I will attempt here to introduce the concept and provide a non - statistical description. When there is a relationship among the variables and then they can expressed by the general linear models. 5. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other? Answer: Nonparametric statistics (also called “distribution free statistics”) are those that can describe some attribute of a population, test hypotheses about that attribute, its relationship with some other attribute, or differences on that attribute across popu lations, across time or across related constructs, that require no assumptions about the form of the population data distribution(s) nor require interval level measurement. In the literal meaning of the terms, a parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one's data are drawn, while a non - parametric test 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 another about the properties of the source population(s). We will use parametric statistics and non - parametric statistics in the following situation:

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