Abstract
Measurement is at the heart of all psychological testing and assessment. A number of statistical tests and procedures can be used to help evaluate how well a test measures what it is supposed to measure. The information presented in this chapter provides a solid foundation of basic statistical methods and concepts used in measurement. Rules for assigning numbers to represent objects and concepts are presented, involving four types of scales: nominal, ordinal, interval, and ratio. This chapter also describes how numbers are used to represent scores from individuals or groups of people, forming a distribution of scores. Various descriptive statistics are presented, such as measures of central tendency and measures of variability. Correlation coefficients are discussed in depth, along with an introduction to linear regression.
One does not need to be a statistical wizard to grasp the basic mathematical concepts needed to understand major measurement issues.
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References
Gray, P. (1999). Psychology. New York, NY: Worth.
Hays, W. (1994). Statistics (5th ed.). New York, NY: Harcourt Brace.
Hopkins, K. D. (1998). Educational and psychological measurement and evaluation (8th ed.). Boston, MA: Allyn & Bacon.
Kubiszyn, T., & Borich, G. (2003). Educational testing and measurement: Classroom application and practice (7th ed.). New York, NY: Wiley.
Latané, B. (1981). The psychology of social impact. American Psychologist, 36(4), 343–356.
Osterlind, S. J. (2006). Modern measurement: Theory, principles, and applications of mental appraisal. Upper Saddle River, NJ: Pearson.
Reynolds, C. R. (1999). Inferring causality from relational data and design: Historical and contemporary lessons for research and clinical practice. The Clinical Neuropsychologist, 13, 386–395.
Sattler, J. M. (1992). Assessment of children. In rev (3rd ed.). San Diego, CA: Author.
Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680.
Recommended Reading
Hays, W. (1994). Statistics (5th ed.). New York, NY: Harcourt Brace. This is an excellent advanced statistics text. It covers the information covered in this chapter in greater detail and provides comprehensive coverage of statistics in general.
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill. An excellent advanced psychometric text. Chapters 2 and 4 are particularly relevant to students wanting a more detailed discussion of issues introduced in this chapter.
Reynolds, C. R. (1999). Inferring causality from relational data and designs: Historical and contemporary lessons for research and clinical practice. The Clinical Neuropsychologist, 13, 386–395. An entertaining and enlightening discussion of the need for caution when inferring causality from relational data. Contains both historical and contemporary examples, including a lawsuit where hundreds of billions of dollars changed hands.
Internet Sites of Interest
http://data.gov. This site provides easy access to all open data from the United States federal government.
http://nces.ed.gov/. This is the site for the National Center for Education Statistics, the primary federal agency responsible for collecting and analyzing data related to education.
http://unstats.un.org/. This is the United Nations Statistics Division Homepage. It contains information on the population and demographics of regions, countries, and cities.
http://www.ncaa.org. This site is great for the sports enthusiasts! It provides access to sports statistics compiled by the National Collegiate Athletic Association for sports ranging from baseball to lacrosse.
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2.1 Electronic Supplementary Material
Supplementary File 2.1
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Practice Items
Practice Items
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Calculate the mean, variance, and standard deviation for the following score distributions. For these exercises, use the formulas listed in Table 2.5 for calculating variance and standard deviation.
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Calculate the Pearson correlation coefficient for the following pairs of scores
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Reynolds, C.R., Altmann, R.A., Allen, D.N. (2021). The Basic Statistics of Measurement. In: Mastering Modern Psychological Testing. Springer, Cham. https://doi.org/10.1007/978-3-030-59455-8_2
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DOI: https://doi.org/10.1007/978-3-030-59455-8_2
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