M5-223
Article: One Hour of Extra Screen Time Drags Down Teenagers’ Grades The reading provides information and perspective crucial for success on the short paper assignment in this module. This resource supports the short paper activity in this module.
Video: Writing Null and Alternative Hypotheses (6:14) This video explains null and alternative hypotheses. This resource supports the milestone activity in this module.
The captioned version of this video can be found here.
Video: How to Calculate Pearson’s Correlation Coefficient (8:46) (Optional) This video shows how to calculate the Pearson’s correlation coefficient by hand.
Website: How Ice Cream Kills: Understanding Correlation and Causation (Optional) This website explains correlation and causation in easy-to-understand analogies.
Correlation is one of the most important procedures in psychology. Literally thousands of studies have used correlation to analyze data (Adebowale, 2015; Brodsky, Elmore, & Naffziger, 1976; Caryk & Walker, 1986; Cherian & Cherian, 1998; Hsiao, Lu, & Tsai, 2015; Huddleston, 2015; Khodarahmi & Zarrinabadi, 2015). Correlation technically is a general term referring to several procedures; the term for the type of correlation this course considers is Pearson product-moment correlation. This course does not cover correlation procedures beyond the Pearson product-moment correlation, which was invented by the statistician Charles Pearson in the nineteenth century and is the oldest and most commonly used.
The correlation connects to Module Two because it measures linear relation between variables in a scatterplot. A scatterplot is a graph in which a psychologist plots two variables: one variable on an x-axis and one on a y-axis. Each point the psychologist plots is determined by x-axis and y-axis values. A scatterplot for unassociated variables is a jumble. A scatterplot for two associated variables shows a linear formation. This formation may range from slight and barely perceptible to strong and visually obvious. A formation of points whose upper part points roughly northeast (or in the direction of a clock’s minute hand that points between roughly 5 and 10 minutes after the hour) is positive. A formation whose upper portion points roughly northwest is negative.
A correlation can quantitatively express any of these trends. Its output is a value r. This value indicates direction and degree of linear relation between two variables. A positive sign (+) is a signpost for a positive relation. A negative sign (-) is a signpost for a negative relation. An r with the (unsigned) value of zero signifies an absence of linear relation. Correlation relates to “regression analysis,” studied in MAT 240. Regression analysis is more fundamental than correlation; however, correlation is a piece of the regression concept, the latter of which applies information about an association between two variables. The correlation focuses on expressing the linear relation.
The correlation procedure is popular for a number of reasons. Psychologists sometimes cannot conduct experiments to answer their questions because experiments would not be practical, would not be ethical, or both. For instance, a psychologist would not think of deliberately exposing individuals to cruel psychological harm in an experiment. The psychologist might still be interested in learning about something like prejudice in everyday life. To do this the psychologist could collect data and run a correlation. The result could tell the psychologist if a variable of interest relates to prejudice.
Recall that a correlation is concerned with linear relation between variables. This point is important. Two variables can be highly related; however, a psychologist who applies correlation to these data may find a low r. The resolution between these seemingly contradictory facts is that variables can relate in a curvilinear way; and because correlation detects only linear (straight-line) relations, a correlation misses detection of a curvy relation. In a scatterplot of the variables, the pattern of points would look like a rainbow shape (or an inverted rainbow shape). Psychologists occasionally proclaim that variables they studied are unrelated because a correlation procedure yielded a low r, when the variables unbeknownst to the psychologists relate in a curvy way. This misinterpretation is bound to arise if psychologists do not view their data in a display, which is why one should graph the data. If you look for whether variables relate, you should draw a scatterplot in particular. By drawing a scatterplot, you will not miss a nonlinear relationship that a correlation is unable to reveal.
Graphing a scatterplot is necessary, but it is not sufficient to prevent misinterpretation of correlation. Other misinterpretations may arise. For example, a psychologist who does an experiment and finds one variable caused the other is justified to assume the variables have a correlation (variables that experimentally relate also correlate). However, this does not imply the reverse, where correlated variables show cause and effect. Consider the logic in asserting, “I am married to this individual so I must know this individual” (which makes sense), versus the logic in asserting, “I know this individual therefore I am married to him/her.” Just reversing the order of these statements does not make it automatically true at all.
News articles will often report studies based on correlation but stating takeaways appropriate for an experiment (Elias, 2004). For example, on his widely broadcasted radio show “Intelligence for Your Life,” John Tesh might say a study indicates two things are associated, and then he will tell his listeners to conclude doing the one thing (variable x) will lead to the other thing (variable y), even though the study was based on correlation. Correlation gives no evidence for a cause and effect statement allowing the conclusion that one variable leads to occurrence of the other; therefore, this conclusion is not valid. These lapses do not necessarily invalidate the entire quality of the show; some information is accurate, and Tesh’s dissemination of information on a variety of topics is useful.
Correlation and its interpretation constitute a complex area. This overview is a guideline of some of the most fundamental concepts and applications. A reader interested in types of correlation in addition to Pearson product-moment correlation may consult a book on nonparametric statistics (Kraska-Miller, 2014). A reader can find further information about correlation and causation in a book written on the topic by Kenny (1979), and a reader can locate further discussion about the intricate topic of “when to and when not to assign causation” in Bennett, Briggs, and Triola (2014), Huck (2009), and Mosteller and Tukey (1977). A reader may see Brodsky and Gutheil (2016) for a discussion of illusory correlation, which is an instance in which an individual thinks there is a correlation when there is none (something pertinent to the matter of prejudice and to situations that occur in the legal field in particular).
References
Adebowale, T. A. (2015). Counseling intervention in the provision of psycho-social support for widows: Empirical evidence from Nigeria. Gender and Behaviour, 13(1), 6540-6546.
Bennett, J., Briggs, W. L., & Triola, M. F. (2014). Statistical reasoning for everyday life (4th ed.). New York, NY: Pearson.
Brodsky, A. M., Elmore, P. B., & Naffziger, N. (1976). Development of the attitudes toward feminist issues scale. Measurement and Evaluation in Guidance, 9(3), 140-145.
Brodsky, S. L., & Gutheil, T. G. (2016). Traps of common sense. In S. L. Brodsky & T. G. Gutheil (Eds.), The expert expert witness: More maxims and guidelines for testifying in court (2nd ed.) (pp. 190–193). Washington, DC: American Psychological Association.
Campbell, S. (1999). Statistics you can’t trust: A friendly guide to clear thinking about statistics in everyday life. Parker, CO: Think Twice Publishing.
Caryk, C. J., & Walker, J. L. (1986). Optimism and irrational beliefs. Psychological Reports, 59, 457-458.
Cherian, L., & Cherian, V. I. (1998). Early science experiences of Northern Sotho-speaking South African pupils and their attitude toward science. Psychological Reports, 83, 1238.
Elias, M. (2004, April 5). Frequent TV watching shortens kids’ attention spans. USA Today. Retrieved from http://usatoday30.usatoday.com /news/ health/ 2004-04-05-tv-kids-attention-usat_x.htm
Hsiao, C.-Y., Lu, H.-L., & Tsai, Y.-F. (2015). Factors influencing mental health nurses’ attitudes towards people with mental illness. International Journal of Mental Health Nursing, 24, 272-280.
Huck, S. W. (2009). Statistical misconceptions. New York, NY: Taylor & Francis Group, LLC.
Huddleston, C. A. (2015). Development of an instrument to measure student attitudes toward science fairs (Doctoral Dissertation, Liberty University, 2014). Dissertation Abstracts International, 76.
Kenny, D. A. (1979). Correlation and causality. New York, NY: John Wiley & Sons, Inc.
Khodarahmi, E., & Zarrinabadi, N. (2015). Self-regulation and academic optimism in a sample of Iranian language learners: Variations across achievement group and gender. Current Psychology: A Journal for Diverse Perspectives on Diverse Psychological Issues, 34, 1-18.
Kraska-Miller, M. (2014). Nonparametric statistics for social and behavioral sciences. Boca Raton, FL: Taylor & Francis Group, LLC.
Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression: A second course in statistics. Reading, MA: Addison-Wesley Publishing Company.