Hockenbury Discovering Psychology 5th txtbk

A-8 APPENDIX A Statistics: Understanding Datastandard normal curve or standardnormal distributionA symmetrical distribution forming a bellshapedcurve in which the mean, median,and mode are all equal and fall in the exactmiddle.Let’s take an example from the distribution found in Table A.2. What is thez score of a weight of 149 pounds? To find out, you simply subtract the mean from149 and divide by the standard deviation.z 149 12417.10 1.46A z score of 1.46 tells us that a person weighing 149 pounds falls about one and ahalf standard deviations above the mean. In contrast, a person weighing 115 poundshas a weight below the mean and would have a negative z score. If you calculate thisz score, you will find it is .53. This means that a weight of 115 is a little more thanone-half a standard deviation below the mean.Some variables, such as height, weight, and IQ, if graphed for large numbers ofpeople, fall into a characteristic pattern. Figure A.5 shows this pattern, which iscalled the standard normal curve or the standard normal distribution. The normalcurve is symmetrical (that is, if a line is drawn down its center, one side of thecurve is a mirror image of the other side), and the mean, median, and mode fallexactly in the middle. The x-axis of Figure A.5 is marked off in standard deviationunits, which, conveniently, are also z scores. Notice that most of the cases fallbetween 1 and 1 SDs, with the number of cases sharply tapering off at eitherend. This pattern is the reason the normal curve is often described as “bell shaped.”The great thing about the normal curve is that we know exactly what percentageof the distribution falls between any two points on the curve. Figure A.5 shows thepercentages of cases between major standard deviation units. For example, 34.13percent of the distribution falls between 0 and 1. That means that 84.13 percentof the distribution falls below one standard deviation (the 34.13 percent that isbetween 0 and 1, plus the 50 percent that falls below 0). A person who obtains az score of 1 on some normally distributed variable has scored better than 84 percentof the other people in the distribution. If a variable is normally distributed (thatis, if it has the standard bell-shaped pattern), a person’s z score can tell us exactlywhere that person stands relative to everyone else in the distribution.CorrelationSo far, the statistical techniques we’ve looked at focus on one variable at a time, suchas hours of aerobic exercise weekly or pounds of weight. Other techniques allow usto look at the relationship, or correlation, between two variables. Statistically, themagnitude and direction of the relationship between two variables can be expressedby a single number called a correlation coefficient.To compute a correlation coefficient, we need two sets of measurements fromthe same individuals or from pairs of people who are similar in some way. To take aFigure A.5 The Standard Normal CurveThe standard normal curve has severalcharacteristics. Most apparent is its symmetricalbell shape. On such a curve, themean, the median, and the mode all fall atthe same point. But not every curve that isshaped roughly like a bell is a standardnormal curve. With a normal curve, specificpercentages of the distribution fallwithin each standard deviation unit fromthe mean. These percentages are shownon the graph.