# Exploring Inferential Statistics and Their Discontents

This is a two part assignment that will be submitted within one document.

Part I

Part I checks your understanding of key concepts from Jackson and Trochim, Donnelly, and Arora.

Answer the following questions:

1.

2. What are degrees of freedom? How are the calculated?

3. What do inferential statistics allow you to infer?

4. What is the General Linear Model (GLM)? Why does it matter?

5. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would you use one over the other?

6. 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, Donnelly, and Arora (2016) 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:

1. 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?

2. Compare and contrast the concepts of effect size and statistical significance.

3. What is the difference between a statistically significant result and a clinically or "real world" significant result? Give examples of both.

4. What is NHST? Describe the assumptions of the model.

5. Describe and explain three criticisms of NHST.

6. Describe and explain two alternatives to NHST. What do their proponents consider to be their advantages?

References: At least five (5) resources. In addition to these specified resources, other appropriate scholarly resources, including older articles, may be included.

Length: 5- 7 pages

Use current APA standards.

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#### Solution Preview

Part 1

2.

Degrees of freedom are the number of values in the final calculation of a statistic that are free to vary. This is the number of values involved in a calculation have the freedom to vary. To calculate the degrees of freedom we minus one from the number of values in a data set. Df = N-1 where N is the number of values in the sample size. This applies to 1-sample t test.

3.

Inferential statistics allow me to infer conclusions that extend beyond the immediate data. Inferential statistics is used to infer from the sample data what the population might be. Inferential statistics allow me to infer information about the whole population even though I have access only to limited number of data (1). Inferential statistics enable me to make inferences about the population. These statistics are required because it is not possible or convenient to measure information about the entire population.

4.

The general linear model is a statistical linear model. From a narrow perspective the general linear model is an ANOVA procedure in which the calculations are done using a least squares regression approach to show the statistical relationship between one or more predictors and a continuous response variable. The general linear model is a generalization of multiple linear regression model to the case of more than one dependent variable It matters because it underlies most statistical analyses that are used in social research. It provides the foundation for Analysis of variance, t-test, analysis of covariance, and regression analysis (2). In addition it also provides the foundation for multivariate statistical analysis methods such as factors analysis, cluster analysis, multidimensional scaling, discriminant analysis, and canonical correlation.

5.

A parametric statistic is one obtained from a test in which specific assumptions are made about the population parameter. A nonparametric statistic is one obtained from a test in which non-metric independent variables are used. The basis of parametric statistic is a distribution. In case of nonparametric statistic the basis is arbitrary. In case of parametric statistic, the measurement level is interval or ratio, whereas in case of nonparametric statistic the measurement level is nominal or ordinal. In case of parametric statistics, the measure of central tendency is mean, whereas in case of nonparametric statistics, the measure of central tendency is the median. For parametric statistic, the information about the population is completely known, however, in case of nonparametric statistic, the information about the population is unavailable. The correlation test for parametric statistics is Pearson's test, whereas the correlation test for nonparametric statistics is Spearman's test. The parametric statistic and ...

#### Solution Summary

The response provides you a structured explanation of inferential statistics and its concepts . It also gives you the relevant references.