Hockenbury Discovering Psychology 5th txtbk

A-10 APPENDIX A Statistics: Understanding DataFigure A.6 Scatter Plot of a PositiveCorrelation A correlation (or the lack ofone) can be clearly shown on a scatter diagram.This one shows a moderately strongpositive correlation between subjects’compliance with the yoga component ofthe alternative health-promotion programand their energy level. The positive directionof the correlation is indicated by theupward-sloping pattern of the dots, frombottom left to top right. This means that ifone variable is high, the other tends to behigh, too, and vice versa. That the strengthof the relationship is only moderate is indicatedby the fact that the data points(each indicating an individual subject’sscore) are not all positioned along astraight diagonal line.scatter diagram or scatter plotA graph that represents the relationshipbetween two variables.hours of study) tend to be multiplied bylow z scores (which are negative) on theother variable (fewer errors on exams),and vice versa, making negative crossproducts.When the cross-products aresummed and divided by the number ofcases, the result is a negative correlationcoefficient.An easy way to show different correlationsis with graphs. Plotting two variablestogether creates a scatter diagramCompliance with yoga routine or scatter plot, like the ones in FiguresA.6, A.7, and A.8. These figures showthe relationship between complying with some component of the alternative healthpromotionprogram and some other variable related to health. Although the figuresdescribe relationships actually found in the study, I have made up the specific correlationsto illustrate key points.Figure A.6 shows a moderately strong positive relationship between compliancewith the yoga part of the alternative program and a person’s energy level. You cansee this just by looking at the pattern of the data points. They generally form a linerunning from lower left to upper right. When calculated, this particular correlationcoefficient is .59, which indicates a correlation roughly in the middle between 0and 1.00. In other words, people who did more yoga tended to have higher energylevels. The “tended to” part is important. Some people who did not complywell with the yoga routine still had high energy levels, while the reverse was alsotrue. A 1.00 correlation, or a perfect positive correlation, would indicate that frequentyoga sessions were always accompanied by high levels of energy, and viceversa. What would a scatter diagram of a perfect 1.00 correlation look like? Itwould be a straight diagonal line starting in the lower left-hand corner of the graphand progressing to the upper right-hand corner.Several other positive correlations were found in this study. Compliance with thealternative diet was positively associated with increases in energy and positive healthCigarette smokingEnergy levelLevel of copingCompliance with meditation routineFigure A.7 Scatter Plot of a NegativeCorrelation In general, people who engagein meditation more often tend to smokeless. This negative correlation is indicatedby the downward-sloping pattern of dots,from upper left to lower right. Becausethese dots are clustered somewhat closertogether than those in Figure A.6, we cantell at a glance that the relationship here issomewhat stronger.Compliance withaerobic exercise programFigure A.8 Scatter Plot of No CorrelationYou may be surprised to learn that inthis study, compliance with the aerobic exerciseportion of the traditional programwas not related to level of coping. Thisscatter diagram shows that lack of relationship.The points fall randomly, revealingno general direction or trend and thusindicating the absence of a correlation.