M4-223

OVERVIEW

In an exhibit at Museum of Science in Boston, Massachusetts, balls several inches thick are dropped at regular time intervals into a vertical pegboard bounded by Plexiglas. The balls dribble down, obeying the law of gravity, coming to rest in columns at the bottom. Interestingly the balls do not end up evenly distributed among the columns. Instead, they come to rest in a roughly bell-shaped configuration. This exhibit shows the normal distribution—a concept that ties back to visual displays, studied in Module Two.

The normal distribution is defined as a frequency diagram symmetric about a line through the mean value, which has a shape more or less like a bell (Tapson, 1996). It connects to histograms taught in the second unit of this course because a natural thing for a psychologist to do after creating a histogram is to judge if it has the normal distribution shape. Remember a histogram visually represents measurements taken on a number of people in a psychological study. Although the term “normal” might seem to imply a distribution describing only “normal people’s behavior,” normal in this context is not used in that sense. A normal distribution describes common behavior but also unusual or extremely unusual behavior.

The normal distribution pertains to the analysis of psychological data for a simple reason: In psychology, it is common for a data set placed into a histogram to have a normal shape. As indicated by the definition, the shape need not fit exactly that of a bell to be considered normal. There is a range of shapes one may describe as normal. Statisticians say the normal distribution describes a family of distributions. That is a formal way of stating that, for a distribution to be normal, it can be any of a number of shapes as long as they fit essential criteria (Bennett, Briggs, & Triola, 2014, pp. 161–166; Huck, 2009; “The Normal Distribution,” n.d.).

The normal distribution remains the most widely used statistical model (Ruxton, Wilkinson, & Neuhäuser, 2015). Examples of behaviors described by the normal distribution include self-ratings for mood, anxiety, and energy (Ortiz, Bradler, Garnham, Slaney, & Alda, 2015), scores on a test of emotional intelligence (Martskvishvili, Arutinov, & Mestvirishvili, 2013), scores on a test where individuals describe music in words (Music Description Test; Zimmerman, 1971), and scores on a measure of well-being (Spittlehouse, Vierck, Pearson, & Joyce, 2014).

In a similar way, many physical behaviors follow a normal distribution and objects sometimes record evidence of this distribution. For example, on the carpeting on each step of a staircase in an old home, you may observe a pattern of wear. You see a decreasing amount of wear in either direction from a concentration of wear in the center. In other words, you see a normal distribution imprinted in the carpet. People have tended to walk in the middle but have sometimes strayed from this pattern. At Wells Cathedral in Wells, England, one sees a similar pattern of wear in stone steps of the Prior’s Staircase. As persons have trodden up and down it since the cathedral opened in the year 1239, they have mainly stepped around the middle and less often to the left and right. The stairs have recorded this normal-distribution behavior in a normally distributed pattern of wear.

What does the normal distribution imply about behavior on a deeper level? The normal distribution reflects the operation of chance. If nature had a logo for the operation of chance, nature would use the normal distribution. You can interpret this distribution as a variable in the real world where many factors influenced this variable. A common expression can clarify this statement. When you get very busy, you may say, “I was being pulled in all different directions.” You are expressing that many different demands were placed on you. A variable normally distributed reflects that the variable was recorded in real life, where many other things affected it or pulled it in different directions. When the variable is placed in a diagram, a distribution emerges that looks as if the middle/anchor point was pulled in different directions, resulting in the stretched out display you know as the normal distribution.

A psychologist finds data falling into a normal distribution valuable from a practical standpoint. The properties of the normal distribution and mathematical probabilities associated with any particular region of it located along the horizontal axis (x-axis) are known (Bennett et al., 2014), so a psychologist can determine probabilities associated with any points along the x-axis of the distribution. The significance of this point will make more sense later; here it is simply important to note the normal distribution helps to pave the way for inferential statistics, studied later in this course.

A theme developed throughout this course needs to be sounded once again. Information in this overview and in the textbook allows a psychologist to make careful, educated, informed assessments and decisions about the structure of data. The information does not permit a researcher to go on autopilot. A number of data sets follow a normal distribution. One needs, however, to evaluate every data set case by case. Sometimes distributions emerge besides normal (Swartout, Thompson, Koss, & Su, 2015). Even when a distribution emerges as within the realm of normality, “normal” is a general term; details about how closely (or not) a distribution looks like a perfect bell-shaped curve are still going to help a psychologist understand the data. The tools learned in Module Two—the histogram, the line chart (Bennett et al., 2014), together with knowledge about the normal distribution—permit a student or researcher in every emerging instance of research to tabulate and to express data in a visual display. This analysis might furnish immediate and peremptory answers about structure of data. But perhaps more frequently, this analysis provides direction about which additional analyses to conduct, as well as background knowledge necessary for interpreting results of other procedures.

References

Bennett, J., Briggs, W. L., & Triola, M. F. (2014). Statistical reasoning for everyday life (4th ed.). New York, NY: Pearson.

Huck, S. W. (2009). Statistical misconceptions. New York, NY: Taylor & Francis Group, LLC.

Martskvishvili, K., Arutinov, L., & Mestvirishvili, M. (2013). A psychometric investigation of the Georgian version of the Trait Emotional Intelligence Questionnaire. European Journal of Psychological Assessment, 29(2), 84-88.

Museum of Science, Boston. (2015). Retrieved from http://www.mos.org

The normal distribution. (n.d.). Retrieved from http://www.stat.yale.edu/Courses/1997-98/101/normal.htm

Ortiz, A., Bradler, K., Garnham, J., Slaney, C., & Alda, M. (2015). Nonlinear dynamics of mood regulation in bipolar disorder. Bipolar Disorders, 17,139-149.

Ruxton, G. D., Wilkinson, D. M., & Neuhäuser, M. (2015). Advice on testing the null hypothesis that a sample is drawn from a normal distribution. Animal Behaviour, 107, 249-252.

Spittlehouse, J. K., Vierck, E., Pearson, J. F., & Joyce, P. R. (2014).Temperament and character as determinants of well-being. Comprehensive Psychiatry,55, 1679-1687.

Swartout, K. M., Thompson, M. P., Koss, M. P., & Su, N. (2015). What is the best way to analyze less frequent forms of violence? The case of sexual aggression. Psychology of Violence, 5, 305-313.

Tapson, F. (1996). Barron’s mathematics study dictionary. Hauppauge, NY: Barron’s Educational Series, Inc.

Zimmerman, W. W. (1971). Verbal description of aural musical stimuli. Journal of Research in Music Education. 19(4), 422-432.

4-1 Discussion: What Is Cool About the Normal Distribution?

 

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The normal distribution is notable for its ubiquity and its usefulness. Psychology data sets, when graphed in a histogram, commonly have a normal shape. After reading chapter 5 of your textbook, post something you find interesting about the normal distribution and state why you find it interesting. (RESPONSE SHOULD BE A PARAGRAPH OR TWO)

Complete Milestone Two of the attachments.