# Histograms And Descriptive Statistics

For this three-part assessment, you will create and interpret histograms and compute descriptive statistics for given variables; analyze the goals of data screening; and generate *z *scores for variables, analyze types of error, and analyze cases to either reject or not reject a null hypothesis. You will use SPSS software and several Capella course files to complete this assessment.

A solid understanding of descriptive statistics is foundational to grasping the concepts presented in inferential statistics. This assessment measures your understanding of key elements of descriptive statistics.

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

- Competency 1: Analyze the computation, application, strengths, and limitations of various statistical tests.
- Analyze the strengths and limitations of examining a distribution of scores with a histogram.
- Analyze the relevant data from the computation, interpretation, and application of
*z*-scores. - Analyze real-world application of Type I and Type II errors and the research decisions that influence the relative risk of each.

- Competency 2: Analyze the decision-making process of data analysis.
- Analyze meaningful versus meaningless variables reported in descriptive statistics.
- Apply the logic of null hypothesis testing to cases.

- Competency 4: Interpret the results of statistical analyses.
- Interpret histogram results, including concepts of skew, kurtosis, outliers, symmetry, and modality.
- Interpret descriptive statistics for meaningful variables.

- Competency 5: Apply a statistical program’s procedure to data.
- Apply the appropriate SPSS procedures for creating histograms to generate relevant output.
- Apply the appropriate SPSS procedure for generating descriptive statistics to generate relevant output.
- Apply the appropriate SPSS procedures for creating
*z*-scores and descriptive statistics to generate relevant output.

- Competency 7: Communicate in a manner that is scholarly, professional, and consistent with expectations for members of the identified field of study.
- Communicate in a manner that is scholarly, professional, and consistent with expectations for members of the identified field of study.

Read Assessment 1 Context [DOC] for important information on the following topics:

- The standard normal distribution and
*z*scores. - Hypothesis testing.
- Null and alternative hypotheses.
- Type I and Type II errors.
- Probability values and the null hypothesis.

#### APA Resources

Because this is a psychology course, you need to format this assessment according to APA guidelines. Additional resources about APA can be found in the Research Resources in the courseroom navigation menu. Use the resources to guide your work.

- American Psychological Association. (2010).
*Publication manual of the American Psychological Association*(6th ed.). Washington, DC: Author.- This resource is available from the Capella University Bookstore.

#### Required Resources

The following resources are required to complete the assessment.

##### SPSS Software

The following statistical analysis software is required to complete your assessments in this course:

- IBM SPSS Statistics Standard or Premium GradPack (recent version for Windows or Mac).
- As a Capella learner, you have access to the more robust IBM SPSS Statistics
**Premium**GradPack arranged at an academic discount through a contracted vendor. - Please refer to the Statistical Software page on Campus for general information on SPSS software, including the most recent version made available to Capella learners.

- As a Capella learner, you have access to the more robust IBM SPSS Statistics

##### Data Set and Software Procedure

- Data Set Instructions [DOCX].
- These instructions explain how to access the data needed for this assessment.

- grades.sav.
- This file contains the data set used with SPSS to complete the assessment.

##### Assessment Template and Output Instructions

- Copy/Export Output Instructions [DOCX].
- This document provides instructions for extracting output from SPSS. You will insert your output into the assessment answer template as indicated.

*z*Scores, Type I and Type II Error, Null Hypothesis Testing Answer Template [DOCX].- Use this template to complete your assessment.

#### 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.Print

## Copy/Export Output Instructions

SPSS output can be selectively copied and pasted into Word by using the Copy command:

1. Click on the SPSS output in the Viewer window.

2. Right-click for options.

3. Click the Copy command.

4. Paste the output into a Microsoft Word document.

The Copy command will preserve the formatting of the SPSS tables and charts when pasting into Microsoft Word.

An alternative method is to use the Export command:

1. Click on the SPSS output in the Viewer window.

2. Right-click for options.

3. Click the Export command.

4. Save the file as Word/RTF (.doc) to your computer.

5. Open the .doc file.