Hockenbury Discovering Psychology 5th txtbk

A-4 APPENDIX A Statistics: Understanding Datafrequency polygonA way of graphically representing afrequency distribution; frequency is markedabove each score category on the graph’shorizontal axis, and the marks are connectedby straight lines.skewed distributionAn asymmetrical distribution; more scoresoccur on one side of the distribution thanon the other. In a positively skewed distribution,most of the scores are low scores; in anegatively skewed distribution, most of thescores are high scores.symmetrical distributionA distribution in which scores fall equally onboth sides of the graph. The normal curve isan example of a symmetrical distribution.Another way of graphing the same data is with a frequency polygon, shown inFigure A.2. A mark is made above each category at the point representing its frequency.These marks are then connected by straight lines. In our example, the polygonbegins before the “0” category and ends at a category of “8,” even thoughboth of these categories have no cases in them. This is traditionally done so that thepolygon is a closed figure.Frequency polygons are good for showing the shape of a distribution. The polygonin Figure A.2 looks like a mountain, rising sharply over the first two categories,peaking at 2, and gradually diminishing from there. Such a distribution is asymmetrical,or a skewed distribution, meaning that if we drew a line through the middleof the x-axis (halfway between 3 and 4 hours), more scores would be piled up onone side of the line than on the other. More specifically, the polygon in Figure A.2represents a positively skewed distribution, indicating that most people had lowscores. A negatively skewed distribution would have mostly high scores, with fewerscores at the low end of the distribution. For example, if the traditional diet andexercise intervention worked, the 30 participants should, as a group, be exercisingmore at the end of the study than they had been at the beginning. Perhaps the distributionof hours of aerobic exercise per week at the end of the study would looksomething like Figure A.3—a distribution with a slight negative skew.In contrast to skewed distributions, a symmetrical distribution is one in whichscores fall equally on both halves of the graph. A special case of a symmetrical distribution,the normal curve, is discussed in a later section.A useful feature of frequency polygons is that more than one distribution canbe graphed on the same set of axes. For example, the end-of-study hours of aerobicexercise per week for the traditional and alternative groups could be compared ona single graph. Doing so would make it possible to see at a glance whether onegroup was exercising more than the other after a year of their respective programs.By the way, Figure A.3 is actually a figment of my imagination. According to thediaries kept by the traditional- and alternative-program participants, compliancewith the exercise portion of the program decreased over time. This does not necessarilymean that these subjects were exercising less at the end of the study than at thebeginning, but they certainly did not keep up the program as it was taught to them.Compliance with the prescribed diets was steadier than compliance with exercise;compliance by the alternative group dropped between three months and six months,and then rose steadily over time. There was, however, one major difference between998877Frequency6543Frequency6543221100 1 2 3 4 5 6 7Hours of aerobic exercise per week at start of study800 1 2 3 4 5 6 7Hours of aerobic exercise per week at end of study8Figure A.2 A Frequency Polygon (Positive Skew) Like TableA.1 and Figure A.1, this frequency polygon shows at a glancethat the number of hours of aerobic exercise weekly is notgreat for most people. The high points come at one and twohours, which doesn’t amount to much more than 10 or 15 minutesof exercise daily. An asymmetrical distribution like this one,which includes mostly low scores, is said to be positively skewed.Figure A.3 A Frequency Polygon (Negative Skew) Whenmore scores fall at the high end of a distribution than at thelow end, the distribution is said to be negatively skewed. Wewould expect a negatively skewed distribution if a healthpromotionprogram worked and encouraged more hours ofaerobic exercise. The more effective the program, the greaterthe skew.