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Foundations of Inferential Statistics: Key Concepts and Applications

Solved assignment on inferential statistics, covering key concepts and practical applications.

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    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 freedom. 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 - squared 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 critical 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 the 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 other words, these tests of significance tell us the probability that the results of the analysis could have occurred by chance

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