Week

5: Quantitative Methods: t Tests and ANOVA

Last week, you examined and applied the principles of descriptive statistics, which, as you may have noted, are only used to make conclusions about the data and sample in a particular study. Descriptive statistics are not useful in making generalizations or broad conclusions beyond the scope of the immediate components of the study. In order for researchers to apply the findings of a study to the outside population or world, they employ what is known as inferential statistics.

This week explores the concepts and uses of inferential statistics and introduces two useful parametric tests: ttests and analysis of variance (ANOVA). These tests are used to inspect the differences in the means of two or more data sets in a study. Through the material and assignments, you familiarize yourself with t tests and ANOVA and their relationships to dependent and independent variables, hypotheses, and power analysis. You continue to use SPSS to apply the weekly concepts by calculating, presenting, and drawing conclusions based on a t test and ANOVA.

Learning Objectives

Students will:

Analyze the purpose and value of t tests and ANOVA in research and evidence-based practice

Differentiate between the independent and dependent t test

Interpret and report results of t tests and ANOVA

Learning Resources

Required Media

Research By Design. (2017, December 7). 05 SPSS for beginners – One sample t Test [Video File]. Retrieved from https://www.youtube.com/watch?v=C2Qa5d9ij0Y

Laureate Education (Producer). (2016). The t test for independent samples [Video File]. Baltimore, MD: Author. Retrieved from http://studyhall.laureate.net/research/quantitative-reasoning-and-analysis-resources-rsch-8210/

Accessible player

Laureate Education (Producer). (2016). The t test for related samples [Video File]. Baltimore, MD: Author. Retrieved from http://studyhall.laureate.net/research/quantitative-reasoning-and-analysis-resources-rsch-8210/

Accessible player

Laureate Education (Producer). (2016h). One-way ANOVA demonstration [Video File]. Baltimore, MD: Author. Retrieved from http://studyhall.laureate.net/research/quantitative-reasoning-and-analysis-resources-rsch-8210/

Accessible player

Required Readings

Gray, J.R., Grove, S.K., & Sutherland, S. (2017). Burns and Grove’s the practice of nursing research: Appraisal, synthesis, and generation of evidence (8th ed.). St. Louis, MO: Saunders Elsevier.

Chapter 25, “Using Statistics to Determine Differences”

This excerpt elaborates on how statistics are used to examine causality using procedures such as contingency tables, chi-squares, ttests, and analysis of variance (ANOVA).

Statistics and Data Analysis for Nursing Research

Chapter 5, “Statistical Inference”

This chapter discusses inferential statistics, sampling error, sampling distributions, and the laws of probability. The chapter also introduces key terms such as standard error of mean, hypothesis testing, and parametric test.

Chapter 6, “t Tests: Testing Two Mean Differences”

This chapter considers the various forms of the t test, including the two-sample t test, Kolmogrov-Smirnov test, independent groups t test, and dependent groups t test. The chapter also discusses the many variables involved in these tests such as effect size, meta-analysis, and Cohen’s d.

Chapter 7, “Analysis of Variance” (pp. 137–146 and 155–158)

The first part of this chapter introduces the basic assumptions, requirements, general logic, and terminology surrounding analysis of variance (ANOVA). The second excerpt focuses on sampling distribution of the F ratio and the null and alternative hypotheses.

Jadcherla, S. R., Wang, M., Vijayapal, A. S., & Leuthner, S. R. (2010). Impact of prematurity and co-morbidities on feeding milestones in neonates: A retrospective study. Journal of Perinatology, 30(3), 201-208. doi:10.1038/jp.2009.149

This article outlines the procedures and results of a retrospective study of how perinatal and comorbidity factors affect the rate at which infants meet feeding milestones. The article also includes an application of inferential statistics to the results of the study.

Optional Resources

Shin, J. H. (2009). Application of repeated-measures analysis of variance and hierarchical linear model in nursing research. Nursing Research, 58(3), 211–217. doi:10.1097/NNR.0b013e318199b5ae

Note: You will access this article from the Walden Library databases.

Walden University. (n.d.). Analysis of variance. Retrieved August 1, 2011, from http://streaming.waldenu.edu/hdp/researchtutorials/educ8106_player/educ8106_analysis_of_variance_anova.html

Walden University. (n.d.). Inferential statistics. Retrieved August 1, 2011, from http://streaming.waldenu.edu/hdp/researchtutorials/educ8106_player/educ8106_inferential_stats_and_hypothesis_testing.html

Walden University. (n.d.). t-Tests. Retrieved August 1, 2011, from http://streaming.waldenu.edu/hdp/researchtutorials/educ8106_player/educ8106_ttests.html

Discussion: t Tests and ANOVA in Clinical Practice

Inferential statistics enable researchers to apply the data they gather and the conclusions they draw from a particular sample to a larger population. As the name implies, inferential statistics focus on inferring whether there is a relationship between two or more variables. These statistical analyses include t tests and analysis of variance (ANOVA). t Tests are part of a group of statistical tests that test hypotheses; in fact, it is necessary to formulate a hypothesis in order to use a t test, because the results of the test can only be interpreted in the context of a scientific hypothesis.

Inferential statistics such as t tests work well for comparing two groups. Although mathematically equivalent to the t test, ANOVA allows for the comparison of more than two groups. Therefore, when three or more groups are involved, the ANOVA should be used.

In this week’s Discussion, you are asked to locate a current research article that utilizes either a ttest or ANOVA analysis. You provide a summary of the research study and of the study’s application to evidence-based practice. You also examine the article’s use of a t test or ANOVA and how either of those statistical analysis tools helped to inform the article’s conclusions and recommendations.

To prepare:

Consider some of the important issues in health care delivery or nursing practice today. Bring to mind the topics to which you have been exposed through previous courses in your program of study, as well as any news items that have caught your attention recently. Select one topic to consider for this Discussion.

Next, review journal, newspaper, and Internet articles that provide credible information on your topic. Then, select one research article on which to focus that used inferential statistical analysis (either a t test or ANOVA) to study the topic.

Assignment 3: t Tests and ANOVA

This week, you explore key statistical concepts related to data and problem solving through the completion of the following exercises using SPSS and the information found in your Statistics and Data Analysis for Nursing Research textbook. The focus of this assignment is to become familiar with the SPSS data analysis software, and to develop an understanding of how to calculate and summarize inferential statistics using t tests and ANOVA.

To prepare:

Review the Statistics and Data Analysis for Nursing Research chapters that you read as a part of the Week 5 Learning Resources. As you do so, pay close attention to the examples presented—they provide information that will be useful for you to recall when completing the software exercises. You may also wish to review the Research Methods for Evidence-Based Practice video resources.

Refer to the Week 5 t Test Exercises and follow the directions to perform a t test.

Download and save the Polit2SetC.sav data set. You will open the data file in SPSS.

Compare your data output against the tables presented in the Week 5 t Test Exercises SPSS Output.

Formulate an initial interpretation of the meaning or implication of your calculations.

Refer to the Week 5 ANOVA Exercises and follow the directions to perform an ANOVA using the Polit2SetA.sav data set.

Compare your data output against the tables presented in the Week 5 ANOVA Exercises SPSS Output.

Formulate an initial interpretation of the meaning or implication of your calculations.

To complete:

Complete the Part I, Part II, and Part III steps and Assignments as outlined in the Week 5 t Test Exercises page.

Complete the steps and Assignment as outlined in the Week 5 ANOVA Exercises page.

Create one document with your responses to the t test exercises and the ANOVA exercises.

Submit this Assignment.

Submit your Week 5 Assignment draft and review the originality report.