Probability and Hypothesis Testing .

Introduction

In Unit 4, we begin the transition from descriptive statistics to inferential statistics that are studied in the remainder of the course, including correlation, t tests, and analysis of variance. The interpretation of inferential statistics requires an understanding of probability and the logic of null hypothesis testing. The logic and interpretative skills addressed in this unit are vital to your success in interpreting data in this course as well as to the success of learners who take advanced courses in statistics.

Studies

Readings

Use your Warner text, Applied Statistics: From Bivariate Through Multivariate Techniques, to complete the following: Read Chapter 3, Statistical Significance Testing, pages 81124. This reading addresses the following topics: ?The logic of null hypothesis testing. ?Type I and Type II errors. ?The z test. ?Null hypothesis and alternative hypothesis. ?Limiting Type I error. ?Effect size. ?Statistical power. .

. [u04a1] Unit 4 Assignment 1? .

z Scores, Type I and II Errors, Hypothesis Testing

This is your second IBM SPSS assignment. It includes three sections in which you will: 1.Generate z scores for a variable in grades.sav and report and interpret them. 2.Analyze cases of Type I and Type II errors. 3.Analyze cases to either reject or not reject a null hypothesis.

Download the Unit 4 Assignment 1 Answer Template from the Resources area and use the template to complete the following sections: Section 1: z Scores in SPSS. Section 2: Case Studies of Type I and Type II Errors. Section 3: Case Studies of Null Hypothesis Testing.

Format your answers in narrative style, integrating supporting statistical output (table and graphs) into the narrative in the appropriate places (not all at the end of the document). See the Copy/Export Output Instructions in the Resources area for assistance.

Submit your answer template as an attached Word document in the assignment area.

Unit 4 Assignment 1 Answer Template

Student Name

Unit 4 Assignment 1 Answer Template

The following assignment includes three sections consisting of:

1. z scores in SPSS.
2. Case studies of Type I and Type II errors.
3. Case studies of null hypothesis testing.

Additional notes:

• Answer in complete sentences.
• Follow APA rules for scholarly writing.
• Include a reference list if necessary.
• Save your answers and upload this template to the assignment area for grading.

Section 1: z Scores in SPSS

A z score is typically analyzed when population mean () and population standard deviation (s) are known. However, in SPSS, we can still calculate z scores with the grades.sav data using the sample mean (M) and sample standard deviation (s). To do this, open grades.sav in SPSS. On the Analyze menu, point to Descriptive Statistics, and then click Descriptives

You will be calculating and interpreting z scores for the total variable. In the Descriptives dialog box, move the total variable into the Variable(s) box. Select the Save standardized values as variables option and click OK.

SPSS provides descriptive statistics for total in the Output window. SPSS also creates a new variable in the far right column, labeled Ztotal, in the Data Editor area. Ztotal provides a z score for each case on the total variable. You are now prepared to answer the following Section 1 questions.

Question 1

What is the sample mean (M) and sample standard deviation (s) for total? You will use these values in Question 2 below.

[Answer here in complete sentences. Also insert the output from SPSS here. Replace this prompt and the prompts below, using as much space as necessary to answer questions.]

Question 2

A z score for this sample is calculated as [(X M) s]. Locate Case #53s unstandardized total score (X) in the Data Editor. In the formula below, replace X, M, s, and ? to show how the z score in Ztotal is derived for Case #53.

(X M ) s = ?

Question 3

Run Descriptives on Ztotal. What are the mean and standard deviation of Ztotal? (Hint: 0E7 in SPSS is scientific notation for 0). Are the mean and standard deviation what you would expect? Justify your answer.

[Answer here in complete sentences. Also place the SPSS output here.]

Question 4

Case number 6 has a Ztotal score of 1.56. What does a z value of 1.56 represent?

[Answer here in complete sentences.]

Question 5

Identify the case with the lowest z score. Refer to Appendix A in the Warner (2013) text. Interpret the percentile rank of this z score rounded to whole numbers.

[Answer here in complete sentences.]

Question 6

Identify the case with the highest z score. Refer to Appendix A in the Warner (2013) text. Interpret the percentile rank of this z score rounded to whole numbers.

[Answer here in complete sentences.]

Section 2: Cases Studies of Type I and Type II Errors Question 7

A jury must determine the guilt of a criminal defendant (not guilty, guilty). Identify how the jury would make a correct decision. Analyze how the jury would commit a Type I error versus a Type II error.

[Answer here in complete sentences.]

Question 8

An I/O psychologist asks employees to complete surveys measuring job satisfaction and organizational citizenship behavior. She intends to measure the strength of association between these two variables. The researcher is concerned that she will commit a Type I error. What research decision influences the magnitude of risk of a Type I error in her study?

[Answer here in complete sentences]

Question 9

A clinical psychologist is studying the efficacy of a new drug medication for depression. The study includes a placebo group (no medication) versus a treatment group (new medication). He then measures the differences in depressive symptoms across the two groups.

What would a Type I error represent within the context of his study? How can he reduce the risk of committing a Type I error? How does this decision affect the risk of committing a Type II error?

[Answer here in complete sentences.]

Section 3: Case Studies of Null Hypothesis Testing Question 10

You are running a series of statistical tests in SPSS using the standard criterion for rejecting a null hypothesis. You obtain the following p values.

Test 1 calculates group differences with a p value = .07.

Test 2 calculates the strength of association between two variables with a p value = .50.

Test 3 calculates group differences with a p value = .001.

For each test below, state whether or not you reject the null hypothesis. For each test, also explain what your decision implies in terms of group differences (Test 1 and Test 3) and in terms of the strength of association between two variables (Test 2).

Test 1 (group differences) =

Test 2 (strength of association) =

Test 3 (group differences) =

Question 11

A researcher calculates a statistical test and obtains a p value of .86. He decides to reject the null hypothesis. Is this decision correct, or has he committed a Type I or Type II error? Explain your answer.

[Answer here in complete sentences]

Question 12

You are proposing a research study that you would like to conduct while attending the University. During the proposal, a committee member asks you to explain in your own words what you meant by saying p less than .05. Provide an explanation.

[Answer here in complete sentences]

References

Provide references if necessary. This concludes Unit 4 Assignment 1. Save your answers and upload this template to the assignment area.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage.