1. N318b Winter 2002 Nursing Statistics Specific statistical tests: Correlation Lecture 10

2. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 2 Today’s Class  Brief discussion about issues related to term paper and research paper  Correlation lecture >  Applying knowledge to assigned reading  Turk et al. (1995) Followed by small groups 12-2 PM Focus on interpreting correlation results

3. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 3 Class Website http://instruct.uwo.ca/nursing/318b Lectures now online and can be printed using web browser (e.g. MS Explorer) Use the “Handout” and “pure black and white” options for printing, at 3 per page as this will allow you to put notes on them. E-mail address: mkerr@uwo.ca Exam questions and answers to be put online

4. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 4 “In Group” Session Focuses on 1 assigned reading. Q1. Chance to interpret correlation results Q2. Know difference between “R 2 ” and “r” Key points about correlation workshop will be covered in the 2 nd part of the lecture

5. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 5 Term papers Both are due by April 11 th (not April 4) If there are questions about how to approach either type of paper don’t wait until last minute – get it sorted out ASAP Research experience – emphasis is on describing experience and what YOU learned Research Critique – emphasis is on showing that YOU understand what has happened in the paper, especially the results section

6. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 6 Statistical Tests – Review How do you known when to use which test? Helps to ask some basic questions: 1. What kind of data are used? 2. What kind of relationship is of interest? 3. How many groups (samples) involved? - one, two, or more than two - prediction, association or difference? - ratio/interval or categorical (ordinal/nominal) - dependent (e.g. follow-up) or independent

7. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 7 Correlation (Pearson product) How do you known when to use correlation? 1.What kind of data are used? 2. What kind of relationship is of interest? 3. How many groups (samples) involved? - usually numeric/continuous (ratio/interval) - two different variables from SAME subjects - direction and strength - (usually) one sample, with  2 variables Referring back to the 3 “basic questions”:

8. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 8 Correlation - assumptions 1. The relationship under study is linear – important non-linear relationships can be overlooked with simple correlation analysis 2. Data are (approximately) normally distributed 3. Data in the two variables have roughly equal range of variability (i.e. homoscedasticity) e.g. see Figure 10-1 in textbook

9. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 9 Why is correlation a parametric statistical test? Correlation 1) assumes data are normally distributed (this should be checked before using it) 2) continuous (ratio/interval) data are used 3) involves a population characteristic

10. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 10 For situations where there are non-normal data or with ordinal data Kendall’s Tau or Spearman’s Rho – like tests with ANOVA and t-test, assigns ranks to ordinal levels and then compares relationship between variables Non-Parametric Equivalent for correlation e.g. Pain score (extreme  no pain) with breast CA tumour grade (I-IV)

11. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 11 Why not just use a scatter plot (e.g. Fig. 10-1)? Plot is an important first step but correlation takes next step and statistically quantifies strength of relationship between variables Test statistic is “r”, the correlation coefficient, that ranges from –1.0 to +1.0, with larger values indicating stronger relationship Correlation – cont’d Correlation does not equal causation !

12. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 12 Correlation – direction Can be either positive or negative, as coefficient “r” ranges from –1.0 to +1.0 As “r”  0, strength of relationship  0 What does a negative value of “r” mean? As one variable increases the other decreases What does a positive value of “r” mean? As one variable increases the other increases

13. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 13 Correlation – strength Value of “r” (either +’ve or –’ve) Strength of relationship 0 – 0.25none 0.26 – 0.49weak 0.50 – 0.69moderate 0.70 – 0.89strong 0.90 – 1.0very strong

14. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 14 “r” has a known distribution and thus probability of a given “r” value arising by chance alone can be determined (when assumptions are valid) BUT, statistical significance not as imprtant here since large samples can generate small p-values even for very weak correlations In general, larger “r” values have smaller p-values Correlation – p-values e.g. see Tables 10-1 and 10-2 in textbook

15. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 15 Correlation – Sample scenario 1 We want to know if there is a relationship between hours worked per week and stress levels in nurses (i.e. burnout) How strong do you think it should be? 1. Hours worked Would you expect +’ve or –’ve correlation here? AND2. burnout

16. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 16 Correlations provide useful background information but no causal evidence if stress levels did NOT correlate positively (as expected) with hours worked we might be worried about data errors or selection bias Correlation – Sample scenario 1 Especially useful for interpreting results of more powerful analyses such as regression that can be influenced by high correlations

17. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 17 10 minute break !

18. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 18 Part 2: Application to the Assigned Readings

19. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 19 Turk et al. (1995) Quick summary of the paper: – a cross-sectional study examining the cognitive-behavioral mediation model of depression in chronic pain patients – 100 chronic pain subjects divided into two groups: 73 randomly chosen younger (<70); and 27 older (  70 yrs) patients – found a strong link between pain and depression for older subjects but not for younger ones (i.e. an age effect)

20. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 20 Some design issues? Do you have any concerns with design of the study – e.g. using a cross-sectional design to examine chronic pain and depression? Can a correlation analysis address this problem adequately? Which came first (“chicken-and-egg”)? NO ! It looks only at relationship between two variables (typically at one point in time)

21. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 21 Interpreting Correlations … Correlation is rarely the main analytic tool for a research paper, thus correlation results are typically used to provide context or “help” with interpreting other results (especially regression) Why did they split the old and “young” groups? See Figure 2 page 98 of Turk et al. paper What do these two diagrams illustrate? This was part of their main hypothesis !

22. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 22 When interpreting results of Turk et al. paper for workshop … 3. How strong were the correlations? 2. Were they in the expected direction? 1. Any statistically significant correlations? General questions to ask about correlations … Interpreting Correlations - cont’d 4. How do the correlation results relate back to the study hypothesis?

23. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 10: page 23 Next Week: Regression For next week’s class please review: 1.Page 18 (top) in syllabus 2.Textbook Chapter 11 (see syllabus) 3.Syllabus paper: Ferketich & Mercer (1995)