Review of Statistical Concepts

Review of Statistical Concepts

Introduction

It is important to understand statistical concepts in order to understand test development and interpretation. In previous statistics classes, you explored many of the basic statistical concepts that you will need to know.

This week, you review some of these concepts—such as mean, variance, standard deviation, standard score, and correlation—and examine how they relate to psychometrics by using SPSS to compute them from a dataset provided to you. You also submit specifications for your proposed Final Project test.

Objectives

Students will:

· Calculate mean, correlation, variance, and standard deviation

· Analyze the relationship between correlation and causation

· Analyze constructs to develop test specifications for psychological testing instruments

Readings

· Anastasi, A., & Urbina, S. (1997). Psychological testing (7th ed.). Upper Saddle River, NJ: Prentice Hall.

. Chapter 3, “Norms and the Meaning of Test Scores” (pp. 49–54)

· Cohen, J. (1990). Things I have learned (so far). American Psychologist, 45(12), 1304–1312. Retrieved from the Walden Library databases.

· Document: Test Specifications Template Note: You will use this template to complete this week’s Assignment.

· Document: Test Specifications Example (for reference) Note: You will use this template to complete this week’s Assignment.

Media

· Laureate Education, Inc. (Executive Producer). (2010).  Normal curve interactive . Baltimore, MD: Author. Note: If you are unable to view the above media piece due to a visual impairment, please contact the Director of Disability Services at Walden University. The concepts presented in this media piece are also described on page 50-52 of your text.

· Laureate Education, Inc. (Executive Producer). (2010).  Two tailed curve . Baltimore, MD: Author. Note: If you are unable to view the above media piece due to a visual impairment, please contact the Director of Disability Services at Walden University. The concepts presented in this media piece are also described on page 50-52 of your text

Knowledge Assessment

One common way to understand test scores is to compare them to the scores from a sample of people representing the larger population. For instance, if you administered a test of math skills to a large random sample of adults in the United States, you could find the average, or mean, score. This would make your test more useful, because any individual who completed it could see whether his or her score was above average, average, or below average with respect to math ability as measured by the mean score from the overall population sample.

You could also compute the standard deviation of scores in your sample. This would tell you how far, on average, the scores are (or deviate) from the mean (i.e., how spread out they are). Standard deviation scores are used to create standardized scores, which can be used to show exactly how far above or below the mean any person’s score is in standard deviation units (i.e., a score that is 1 standard deviation above the mean has a standard score of 1). For example, standard deviation can be used to provide a precise location of any one individual’s math score compared to the overall population.

Closely related to standard deviation is variance, which is the squared standard deviation or, more accurately, the mean of the squared deviation scores. Although not an intuitively useful number on its own, variance is used in many statistical procedures.

Correlation is another statistical concept that is crucial in psychometrics. Correlation tells you the strength and direction of the relationship between two variables, such as IQ and academic performance. This strength, or degree, can range from –1.00 to +1.00, with 0 indicating no relationship.

For this Knowledge Assessment, you use SPSS to calculate the mean, standard deviation, and variance of two variables, and also to compute the correlation coefficient between the two variables in this week’s dataset in the Learning Resources. To begin, open SPSS, click File>Open>Data and open the dataset.

The data file, which was collected over the Internet, shows the responses of 1,146 U.S. residents who answered questions about themselves and their spouse or romantic partner. You complete calculations using the variables INC1, the participant’s annual income, and INC2, the partner or spouse’s annual income.

QUESTION 1

1. Find the mean partner's income. Click ANALYZE>DESCRIPTIVE STATISTICS>DESCRIPTIVES. Move INC2 into the variable box and click “OK.” The mean participant income is:

	a.	$36,475
	b.	$52,418
	c.	$45,486
	d.	$38,602

QUESTION 2

1. Find the standard deviation of income for participants. You will see it as part of the output for question 1. The standard deviation of the participant’s partner’s income is:

	a.	$45,415
	b.	$35,218
	c.	$50,112
	d.	$5,112

QUESTION 3

1. 3. The variance of the participant’s partner’s income is:

	a.	1 Billion
	b.	2.1 Billion
	c.	201
	d.	172

QUESTION 4

1. Find the correlation between participant income and spouse income. Click ANALYZE>CORRELATE>BIVARIATE. Move INC1 and INC2 into the variable box and click “OK.” The correlation is:

	a.	.017
	b.	.344
	c.	.450
	d.	.687

Discussion

Correlation

Correlation is important for measuring test validity, or the ability of a test to measure what it is intended to measure. It is intuitive that the scores on the test and the construct need to be correlated, or related. Correlation also is used to measure test reliability. Test reliability includes the degree to which a test is consistent over time and the degree to which the test items are consistent with each other. Thus, different administrations of the same test to the same individual should produce similar or related (correlated) scores. Correlation also has important implications for causality, but it is critical to understand that just because two things are correlated, there is no implication that one of them causes the other.

Keeping correlation in mind, think about SAT scores. These scores are frequently used to select students for admission to college and to predict college success. Consider the advantages and disadvantages of using test scores as part of an admissions selection process. Then consider whether this method would work equally well for all students, regardless of their background (e.g., cultural or socioeconomic). Similarly, a student’s choice of major, such as art, might affect the predictive ability of the SAT. Under such circumstances, would the correlation coefficient between two sets of scores still be relevant to the specific context? Can the test scores still be predictors of success in college? Do specific scores cause success in college?

To prepare for this Discussion, think of examples of misleading correlations and meaningful correlations. Also consider how you would explain the relationship between correlation and causation.

With these thoughts in mind:

Post an example of a misleading correlation and an example of a meaningful correlation. Then explain the relationship between correlation and causation. Be specific and provide examples. Support your response using the Learning Resources and the current literature.

Be sure to support your postings and responses with specific references to the Learning Resources.

Assignment 

Test Specifications

Test specifications provide a descriptive outline of a test and can include information about the construct measured, the format and structure of a test, the number of items, and other information as needed. In this week’s Learning Resources, there is a Test Specifications Template that you should now complete for your proposed Final Project. This template will help guide you through determining the specifications for your test. There is also a completed template that you may look at as a reference.

The Assignment (1–2 pages)

Submit completed test specifications for your Final Project test using the Test Specifications Template provided in this week’s Resources.

Support your Application Assignment with specific references to all resources used in its preparation. You are to provide a reference list for all resources, including those in the Learning Resources for this course.