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Part I Part I checks your understanding of key concepts from Jackson and Trochim & Donnelly.
Answer the following questions:
Jackson even-numbered Chapter exercises (pp. 220-221; 273-275)
What are degrees of freedom? How are the calculated?
What do inferential statistics allow you to infer?
What is the General Linear Model (GLM)? Why does it matter?
Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?
Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?
Part II Part II introduces you to a debate in the field of education between those who support Null Hypothesis Significance Testing (NHST) and those who argue that NHST is poorly suited to most of the questions educators are interested in. Jackson (2012) and Trochim and Donnelly (2006) pretty much follow this model. Northcentral follows it. But, as the authors of the readings for Part II argue, using statistical analyses based on this model may yield very misleading results. You may or may not propose a study that uses alternative models of data analysis and presentation of findings (e.g., confidence intervals and effect sizes) or supplements NHST with another model. In any case, by learning about alternatives to NHST, you will better understand it and the culture of the field of education.
Answer the following questions:
What does p = .05 mean? What are some misconceptions about the meaning of p =.05? Why are they wrong? Should all research adhere to the p = .05 standard for significance? Why or why not?
Compare and contrast the concepts of effect size and statistical significance.
What is the difference between a statistically significant result and a clinically or “real world” significant result? Give examples of both.
What is NHST? Describe the assumptions of the model.
Describe and explain three criticisms of NHST.
Describe and explain two alternatives to NHST. What do their proponents consider to be their advantages?
Which type of analysis would best answer the research question you stated in Activity 1? Justify your answer.
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Inferential Statistics
Part1:
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 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 research. Although a deep understanding of t...
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