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# Statistical Significance

In Week 4, you explored how the confidence interval helps to estimate a population mean. Hypothesis testing is an approach that allows us to make some determination about whether a hypothesis should be rejected, based upon sample statistics. This approach is integral to the scientific method and provides us with a measureable level of certainty when making inferences back to the population.

Consider the following:

A researcher is conducting work on social inequality and wants to know whether there are marked differences between socioeconomic status of Caucasians and Non-Caucasians. Since the researcher cannot measure the entire population, a sample is drawn and a hypothesis can be constructed and evaluated as to whether any noticeable differences in the sample also likely appear in the population.

As a scholar-practitioner, it will be important for you to develop your knowledge and skillset in hypothesis testing. As evident in the scenario provided, hypothesis testing establishes a process to determine the probability of observing similar scores noted in the sample under the null hypothesis.

For this week, you will examine hypothesis testing and determine the statistical significance and meaningfulness in the data. You also will explore the results of data to determine implications for social change.

Learning Objectives

Students will:

• Evaluate statements related to null hypothesis
• Evaluate p-values
• Evaluate type I and type II errors
• Evaluate for meaningfulness
• Evaluate statistical significance
• Evaluate sample size
• Analyze implications for social change

Learning Resources

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 8, “Testing Hypothesis: Assumptions of Statistical Hypothesis Testing” (pp. 241-242)

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 6, “Testing Hypotheses Using Means and Cross-Tabulation”

Warner, R. M. (2012). Applied statistics from bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage Publications.

Applied Statistics From Bivariate Through Multivariate Techniques, 2nd Edition by Warner, R.M. Copyright 2012 by Sage College. Reprinted by permission of Sage College via the Copyright Clearance Center.

• Chapter 3, “Statistical Significance Testing” (pp. 81–124)

Applied Statistics From Bivariate Through Multivariate Techniques, 2nd Edition by Warner, R.M. Copyright 2012 by Sage College. Reprinted by permission of Sage College via the Copyright Clearance Center.

Magnusson, K. (n.d.). Welcome to Kristoffer Magnusson’s blog about R, Statistics, Psychology, Open Science, Data Visualization [blog]. Retrieved from http://rpsychologist.com/index.html

As you review this web blog, select [Updated] Statistical Power and Significance Testing Visualization link, once you select the link, follow the instructions to view the interactive for statistical power. This interactive website will help you to visualize and understand statistical power and significance testing.

Note: This is Kristoffer Magnusson’s personal blog and his views may not necessarily reflect the views of Walden University faculty.

American Statistical Association (2016). American Statistical Association Releases Statement on Statistical Significance and P-Values. Retrieved from https://www.amstat.org/asa/files/pdfs/p-valuestatement.pdf

As you review this press release, consider the misconceptions and the misuse of p-values in quantitative research.

Document: Week 5 Scenarios (PDF)

Use these scenarios to complete this week’s Assignment.

Datasets

Your instructor will post the datasets for the course in the Doc Sharing section and in an Announcement. Your instructor may also recommend using a different dataset from the ones provided here.

Required Media

Walden University, LLC. (Producer). (2016f). Meaningfulness vs. statistical significance [Video file]. Baltimore, MD: Author.

Note: The approximate length of this media piece is 4 minutes.

In this media program, Dr. Matt Jones discusses the differences in meaningfulness and statistical significance. Focus on how this information will inform your Discussion and Assignment for this week.

Walden University, LLC. (Producer). (2016n). Halfway point [Video file]. Baltimore, MD: Author.

Note: The approximate length of this media piece is 2 minutes.

In this media program, Dr. Annie Pezalla, Associate Director of Curriculum and Assessment with the Office of Research and Doctoral Studies at Walden University, discusses what you have learned so far in the course. She also discusses what you have to look forward to as well as things to look out for in the remainder of the course.

Optional Resources

Skill Builders:

• Evaluating P Values
• Statistical Power

To access these Skill Builders, navigate back to your Blackboard Course Home page, and locate “Skill Builders” in the left navigation pane. From there, click on the relevant Skill Builder link for this week.

You are encouraged to click through these and all Skill Builders to gain additional practice with these concepts. Doing so will bolster your knowledge of the concepts you’re learning this week and throughout the course.

Week Five: Statistical Significance

When do results reveal information upon which you can act upon or recommend to others with a degree of certainty [“significance”]. In week five you will learn significance is not as subjective as some would believe. When working with students including quantitative data within proposed studies, I require proposed and defended levels of significance upon which to responsibly assert study findings under a section entitled: anticipated outcomes. The contracted significance then removes bias or susceptibility to declare without substantive proof or evidence.

In the week’s work, yo will read: “Once you start to understand how exciting the world of statistics can be, it is tempting to fall into the trap of chasing statistical significance. That is, you may be tempted always to look for relationships that are statistically significant and believe they are valuable solely because of their significance. Although statistical hypothesis testing does help you evaluate claims, it is important to understand the limitations of statistical significance and to interpret the results within the context of the research and its pragmatic, “real world” application.”

NOTE: APA 7.0 Style and Format: we are entering week five and a constructive focus, by now, should be a scoring rubric  which requires and evaluation of your work for consistency to APA 7.0 publication standards . Prior editorial feedback shall have been considered and now incorporated into subsequent assignments. Increased accuracy, through the engagement if instructor feedback, should be automatic points. There have been several course announcements [including focused assignment tutorials] and, within each and every discussion thread, I have read and constructively responded to peers about APA 7.0 style and format mistakes. So, for example, there would be an expectation no student would include a ‘case summary’ or ‘descriptive statistics’ display within product as neither informs or orients a passive audience. Graphs, tables and figures need to be formally labeled and entitled [as described in APA 7.0 and through instructor modeling within threads]. No visual display of data should appear within a work without  a dedicated preceding explanatory text fore naming the visual display and orienting a passive audience to content and application

Discussion: Statistical Significance and Meaningfulness

Once you start to understand how exciting the world of statistics can be, it is tempting to fall into the trap of chasing statistical significance. That is, you may be tempted always to look for relationships that are statistically significant and believe they are valuable solely because of their significance. Although statistical hypothesis testing does help you evaluate claims, it is important to understand the limitations of statistical significance and to interpret the results within the context of the research and its pragmatic, “real world” application.

As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relationship exists between an intervention and an outcome, there is a difference between groups, or there is a correlation between two constructs, it does not always provide a default measure for its importance. Although relationships are significant, they can be very minute relationships, very small differences, or very weak correlations. In the end, we need to ask whether the relationships or differences observed are large enough that we should make some practical change in policy or practice.

For this Discussion, you will explore statistical significance and meaningfulness.

To prepare for this Discussion:

• Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance.
• Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of statistical power and significance testing.
• Review the American Statistical Association’s press release and consider the misconceptions and misuse of p-values.
• Consider the scenario:
• A research paper claims a meaningful contribution to the literature based on finding statistically significant relationships between predictor and response variables. In the footnotes, you see the following statement, “given this research was exploratory in nature, traditional levels of significance to reject the null hypotheses were relaxed to the .10 level.”

By Day 3

Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style

references

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 8, “Testing Hypothesis: Assumptions of Statistical Hypothesis Testing” (pp. 241-242)

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 6, “Testing Hypotheses Using Means and Cross-Tabulation”

Last Updated on June 28, 2022

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