Foundations of Inferential Statistics: Key Concepts and Applications

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Inferential Statistics2. 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 ofsubjects in the data, minus the parameters estimated. A parameter to beestimated is related to thevalue of an independent variable and 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 used when 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. What do 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 ofsignificance tell us the probability that the results of the analysis could have occurred by chance

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