Histograms and Descriptive Statistics – due in 48 hours

 
Preparation
This assessment has three parts, each of which is described below. Submit all three parts as Word documents.
Note: All the course documents you will need for the assessment are linked in the Resources section.
Read Assessment 1 Context to learn about the concepts used in this assessment.
This assessment uses the grades.sav file, found in the Resources for this assessment. 
The fictional data in the grades.sav file represent a teacher’s recording of student demographics and performance on quizzes and a final exam across three sections of the course. Each section consists of about 35 students (N = 105).
There are 21 variables in grades.sav. To prepare for this assessment, complete the following:

Open your grades.sav file and navigate to the “Variable View” tab.
Read the Data Set Instructions, and make sure you have the correct Values and Scales of Measurement assigned.

Part 1: Histograms and Descriptive Statistics
Your first IBM SSPS assessment includes two sections:

Create two histograms and provide interpretations.
Calculate measures of central tendency and dispersion and provide interpretations.

Key Details and Instructions

Submit your assessment as an attached Word document.
Begin your assessment by creating a properly formatted APA title page. Include a reference list at the end of the document if necessary. On page 2, begin Section 1.
Organize the narrative report with your SPSS output charts and tables integrated along with your responses to the specific requirements listed for that assessment. (See the Copy/Export Output Instructions in the Resources for instructions on how to do this.)
Label all tables and graphs in a manner consistent with APA style and formatting guidelines. Citations, if needed, should be included in the text as well as a reference section at the end of the report.
For additional help in completing this assessment, refer to IBM SPSS Step-By-Step Instructions: Histograms and Descriptive Statistics, linked in the Resources.

Section 1: Histograms and Visual Interpretation
Section 1 will include one histogram of “total” scores for all the males in the data set, and one histogram of “total” scores for all the females in the data set.
Create two histograms using the total and gender variables in your grades.sav data set:

A histogram for male students.
A histogram for female students.

Below the histograms, provide an interpretation based on your visual inspection. Correctly use all of the following terms in your discussion:

Skew.
Kurtosis.
Outlier.
Symmetry.
Modality.

Comment on any differences between males and females regarding their total scores. Analyze the strengths and limitations of visually interpreting histograms.
Section 2: Calculate and Interpret Measures of Central Tendency and Dispersion
Using the grades.sav file, compute descriptive statistics, including mean, standard deviation, skewness, and kurtosis for the following variables:

id.
gender.
ethnicity.
gpa.
quiz3.
total.

Below the Descriptives table, complete the following:

Indicate which variable or variables are meaningless to interpret in terms of mean, standard deviation, skewness, and kurtosis. Justify your decision.
Next, indicate which variable or variables are meaningful to interpret. Justify your decision. For meaningful variables, specify any variables that are in the ideal range for both skewness and kurtosis.
Specify any variables that are acceptable but not excellent.
Specify any variables that are unacceptable. Explain your decisions.
For all meaningful variables, report and interpret the descriptive statistics (mean, standard deviation, skewness, and kurtosis).

Part 2: Data Screening
For this part of the assessment, respond to the following questions:
What are the goals of data screening? How can you identify and remedy the following?

Errors in data entry.
Outliers.
Missing data.

Part 3: z Scores, Type I and II Error, Null Hypothesis Testing
This IBM SPSS assessment includes three sections:

Generate z scores for a variable in grades.sav and report/interpret them.
Analyze cases of Type I and Type II error.
Analyze cases to either reject or not reject a null hypothesis.

The format of this assessment should be narrative with supporting statistical output (table and graphs) integrated into the narrative in the appropriate place (not all at the end of the document). See the Copy/Export Output Instructions for instructions on how to do this.
Download the z Scores, Type I and Type II Error, Null Hypothesis Testing Answer Template from the Required Resources, 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 Error.
Section 3: Case Studies of Null Hypothesis Testing.

 
Histograms
The following resources provide information about how to create and interpret histograms.

Lane, D. M. (2013). HyperStat online: An introductory statistics textbook and online tutorial for help in statistics courses. Retrieved from http://davidmlane.com/hyperstat

Introduction to Statistics.
Describing Univariate Data.

StatSoft, Inc. (2013). Electronic statistics textbook. Tulsa, OK: StatSoft. Retrieved from http://www.statsoft.com/textbook

Review the following parts of the Elementary Statistics section to learn about the normal distribution:

Why the normal distribution is important.
Illustration of how the normal distribution is used in statistical reasoning (induction).

Skillsoft. (2017). Descriptive statistics and graphical methods [Video].

In this section of Using Basic Statistics and Graphical Methods in Six Sigma, watch the sections on histograms and normal probability plots.

Descriptive Statistics
These resources provide information on creating and interpreting descriptive statistics. 

StatSoft, Inc. (2013). Electronic statistics textbook. Tulsa, OK: StatSoft. Retrieved from http://www.statsoft.com/textbook

Review the following parts of the Elementary Statistics section of the book:

What are variables?
Measurement Scales.

Proceed to the section Basic Statistics and review the subtopics under Descriptive Statistics. 

Crabtree, R. (2018). Basic six sigma statistics [Video]. Skillsoft.

Open the table of contents and click the segment Measures of Central Tendency. The video segments explain calculating and interpreting these statistics.
Running time: 23 minutes.

Z Scores

z score table. Retrieved from http://www.z-table.com/

This table provides the information needed to answer questions 5 and 6 of the assessment. 

Skillsoft. (n.d.). Basic probability and statistical distributions in six sigma [Video].

Navigate to this course’s table of contents, choose “Statistical Distributions,” and watch the Probability Distributions and Normal Distribution videos. 
Running time: 7 minutes.

Type I and Type II Errors

Skillsoft. (2017). Key concepts in hypothesis testing [Video].

In this section of Basics of Hypothesis Testing and Tests for Means in Six Sigma, watch the segment “Hypothesis Testing Terminology” for information about Type I and Type II errors.
Running time: 23 minutes.

Null Hypothesis

Lane, D. M. (2013). HyperStat online: An introductory statistics textbook and online tutorial for help in statistics courses. Retrieved from http://davidmlane.com/hyperstat

The Logic of Hypothesis Testing.

This section explains hypothesis testing and details the meaning of Type I and Type II errors. 

StatSoft, Inc. (2013). Electronic statistics textbook. Tulsa, OK: StatSoft. Retrieved from http://www.statsoft.com/textbook

Review these two parts of the Elementary Concepts section, which explain statistical significance:

What is “statistical significance” (p value)?
How to determine that a result is “really” significant.

Skillsoft. (n.d.). Introduction to hypothesis testing and tests for means in six sigma [Video].

?Navigate to the “Key Concepts in Hypothesis Testing” section of the course.
Running time: 19 minutes. 

Program-Specific Resources
These programs have opted to provide program-specific content designed to help you better understand how the subject matter is incorporated into your particular field of study.
School of Psychology Learners

Harraway, J. A., & Barker, R. J. (2005). Statistics in the workplace: A survey of use by recent graduates with higher degrees. Statistics Education Research Journal, 4(2), 43–58.

School of Education Learners

Young, J. R., Young, J. L., & Hamilton, C. (2014). The use of confidence intervals as a meta-analytic lens to summarize the effects of teacher education technology courses on preservice teacher TPACK. Journal of Research on Technology in Education, 46(2), 149–172.
Harrison, J., Thompson, B., & Vannest, K. J. (2009). Interpreting the evidence for effective interventions to increase the academic performance of students with ADHD: Relevance of the statistical significance controversy. Review of Educational Research, 79(2), 740–775.

Additional Resources for Further Exploration

Khan Academy. (2013). Retrieved from https://www.khanacademy.org

This website offers resources covering a range of subjects, including statistics.