Contents

CHAPTER 11: Data Analysis and Interpretation: Part I. Describing Data, Confidence Intervals, Correlation 371to inform readers what is presented. When bars are presented, it is important toinform readers what they represent and how they were calculated (Estes, 1997).ILLUSTRATION: DATA ANALYSIS FOR A CORRELATIONAL STUDY• A correlation exists when two different measures of the same people,events, or things vary together—that is, when scores on one variable covarywith scores on another variable.Prediction, as you saw in Chapter 2, is an important goal of the scientificmethod. Correlational research frequently provides the basis for this prediction.A correlation exists when two different measures of the same people, events, orthings vary together—that is, when scores on one variable covary with scoreson another variable. For example, a widely known relationship exists betweensmoking and lung disease. The more individuals smoke (e.g., measured byduration of smoking), the greater their likelihood of contracting lung disease.Thus, smoking and lung disease covary, or go together. This correlation alsocan be expressed in these terms: the less people smoke, the lower their chancesfor contracting lung disease. Based on this correlation we can make predictionsabout lung disease. For example, if we know how long an individual hassmoked, we can predict (to some degree) his or her likelihood of developinglung disease. The nature of our predictions and the confidence we have in makingthem depend on the direction and the strength of the correlation.Correlational analyses are frequently associated with survey research(see Chapter 5). Respondents complete questionnaires asking about demographicvariables (e.g., age, income), as well as their attitudes, opinions,STRETCHING EXERCISEA TEST OF YOUR UNDERSTANDING OF CONFIDENCE INTERVALSAlthough the reporting of confidence intervalswhen analyzing data is strongly recommended,their use is only beginning to be seen in many psychologyjournals. Confidence intervals do sharesome of the problems of interpretation frequentlyassociated with tests of statistical significance,specifically, with null hypothesis significancetesting (NHST). Nevertheless, confidence intervalscan and should be incorporated in your dataanalysis. To make sure you use them correctly,we have provided the following test of your understandingof this analysis technique.Assume that an independent groups designwas used to examine the effect on behavior ofan independent variable with three levels (A, B,C). There were 15 participants randomly assignedto each condition, and measures of central tendencyand variability were determined for eachcondition. The investigator also constructed 95%confidence intervals for each of the means. Trueor false? The researcher may reasonably concludeon the basis of this outcome that1 The width of the confidence interval indicates howpre cise is the estimation of the population means.2 If two intervals overlap, we know for sure that thepop ulation means are the same.3 The odds are 95% that the true population meanfalls in each interval.4 If two intervals do not overlap, there is a 95%proba bility that the population means differ.5 If two intervals do not overlap, we have goodevi dence that the population means differ.