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# General Statistics and Sample Size Applicability

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1)If you have a population that has a small sample, but does not meet all of the criteria for the nonparametric test how can you tell what test to use?

2)How might one know if a samples follow a normal distribution?

https://brainmass.com/statistics/nonparametric-tests/235180

#### Solution Summary

This solution of 429 words discusses the effect of size on a sample and population and looks at the differences between with the standard normal distribution and the student's t-distribution. It also explains the concept of degrees of freedom (df) and test statistic.

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## 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.

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.

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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