Correlational Methods and Statistics

Transcription

1 Correlational Methods and Statistics

2 Scatterplots and correlations Relationship between time spent studying and performance on exam

3 Scatterplots Graphical tool for exploring the relationship between 2 quantitative variables

4 Correlations Direction of relationship: Positive: As value of 1 variable increases, so does the other Direct correlation Negative: As value of 1 variable increases, the other decreases Indirect correlation No relationship Magnitude, size or strength of relationship: to 0 to ( correlation coefficient ) 0 = no relationship 1 = perfect predicted relationship

5 What is size of correlation? Time spent studying and exam performance r = +.58 r =

6 Fuel used Types of relationships Linear Amount of change on X, same amount of change on Y Nonlinear Curvilinear Amount of change on X, smaller change on Y (or vice versa) U or V function Multilinear Other Speed(km/h) 150

7 Interpretation of correlations Causality Correlation does not imply causation Directionality Unsure of whether A causes B or reverse Third variable problem Another factor causing relationship Other considerations: Restricted range Heterogeneous subgroups Outliers

8 Lang & Heckhausen (2001) Examine relationship between perceived control over development (PCD) and subjective well-being (SWB) Study 1: 480 adults yrs 4 PCD items 5 strongly agree to 1 strongly disagree: I am able to make my goals come true. My abilities and efforts are significant to my success. 4 Life satisfaction - 5 strongly agree to 1 strongly disagree: I am satisfied with my life these days. As I get older, life is better than I thought it would be. 20 Positive and negative affect 5 very often to 1 not at all: How often they felt each of 10 pos (interested, inspired, excited, attentive) or neg states (nervous, guilty, distressed, irritated) Also examined: SES, negative social support, cognitive functioning, health functioning

9 Lang & Heckhausen (2001)

10 Correlations Examples from Lang & Heckhausen (2001) Direction of relationship: Positive: As value of 1 variable increases, so does the other Direct correlation e.g.: Perceived control over life with life satisfaction (r =.35) Negative: As value of 1 variable increases, the other decreases Indirect correlation e.g.: # negative events in life and perception of control (r = -.13) No relationship e.g.: Life satisfaction and gender (r = -.02)

11 Horne and Ostberg (1976) Scale of morningness Considering only your own feeling best rhythm, at what time would you get up if you were entirely free to plan your day? 5-6:30am; 6:30-7:45am; 7:45-9:45am; 9:45-11am; At what time would you go to bed if you were entirely free to plan? 8-9pm; 9-10:15pm, 10:15-12:30am; 12:30-1:45am; 1:45-3 Assuming normal circumstances, how easy do you find getting up in the morning? Not at all easy; slightly easy; fairly easy; very easy How alert do you feel during the first half-hour after waking? Not at all; slightly alert, fairly alert, very alert If you had to be at peak performance for a test that is going to be mentally exhausting and lasting 2 hours. You are free all day what time do you choose? 8-10am; 11am-1pm; 3-5pm; 7-9pm

12 Correlational studies Why do people act the way they do? Examine patterns and relationships to predict behavior e.g. Guthrie, Ash, & Bendapudi (1995) Examine relationship between college students GPA and tendency of morningness Scale by Smith, Reilly & Midkiff (1989) Score 0 to 55 Evening type: 22 or lower; Intermediate: 23-43; Morning type; 44 or higher Method 454 undergrads; records of gpa and time of day first class scheduled Is the measure of morningness predictive of patterns of sleep, studying and class schedule?

13 Guthrie, Ash, & Bendapudi (1995) What are the conclusions you can make from the results?

14 Letter from your HMO To improve service to our valued customers, we have determined it is beneficial to manage inpatient recovery by accelerating standard patient discharge. Results suggest this will not have any adverse impact on patient care, and may in fact reduce the chance of hospital acquired infection, r(90) = +.55, p <.05. Is it an accurate conclusion?

15 Write-up Pearson correlations were used to examine the relationship between the ages of younger and older participants first memories and their scores on three psychometric measures. Results indicated an inverse relationship between the age of first memories and the scores on the WAIS-R digit span for younger adults, r(46) = -0.31, p <.02, and older adults, r(46) = -0.29, p <.02. This suggests that smarter individuals have earlier first memories!

16 Reporting results What test is used Report variables investigated Sample size Value of statistic Probability level If it is significant or not Example of correlation: The correlation between IQ and SAT scores was found to be statistically significant, r(30) = 0.65, p <.01.