N318b Winter 2002 Nursing Statistics

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

2. Today’s Class • Brief discussion about issues related to term paper and research paper • Correlation lecture << 10 min break >> • Applying knowledge to assigned reading • Turk et al. (1995) Followed by small groups 12-2 PM Focus on interpreting correlation results

3. Class Website http://instruct.uwo.ca/nursing/318b E-mail address: mkerr@uwo.ca 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. Exam questions and answers to be put online

4. “In Group” Session Focuses on 1 assigned reading. Q1. Chance to interpret correlation results Q2. Know difference between “R2” and “r” Key points about correlation workshop will be covered in the 2nd part of the lecture

5. Term papers Both are due by April 11th (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. 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? - ratio/interval or categorical (ordinal/nominal) - dependent (e.g. follow-up) or independent - prediction, association or difference? - one, two, or more than two

7. Correlation (Pearson product) How do you known when to use correlation? Referring back to the 3 “basic questions”: 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

8. Correlation - assumptions 1. The relationship under study is linear – important non-linear relationships can be overlooked with simple correlation analysis e.g. see Figure 10-1 in textbook 2. Data are (approximately) normally distributed 3. Data in the two variables have roughly equal range of variability (i.e. homoscedasticity)

9. Correlation Why is correlation a parametric statistical test? 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. Non-Parametric Equivalent for correlation For situations where there are non-normal data or with ordinal data e.g. Pain score (extreme  no pain) with breast CA tumour grade (I-IV) 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

11. Correlation does not equal causation ! Correlation – cont’d 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

12. As “r”  0, strength of relationship  0 Correlation – direction Can be either positive or negative, as coefficient “r” ranges from –1.0 to +1.0 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. Correlation – strength

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

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) 1. Hours worked AND 2. burnout Would you expect +’ve or –’ve correlation here? How strong do you think it should be?

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

17. 10 minute break !

18. Part 2: Application to the Assigned Readings

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. 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? Which came first (“chicken-and-egg”)? Can a correlation analysis address this problem adequately? NO ! It looks only at relationship between two variables (typically at one point in time)

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) See Figure 2 page 98 of Turk et al. paper What do these two diagrams illustrate? Why did they split the old and “young” groups? This was part of their main hypothesis !

22. Interpreting Correlations - cont’d When interpreting results of Turk et al. paper for workshop … General questions to ask about correlations … 1. Any statistically significant correlations? 2. Were they in the expected direction? 3. How strong were the correlations? 4. How do the correlation results relate back to the study hypothesis?

23. Next Week: Regression • For next week’s class please review: • Page 18 (top) in syllabus • Textbook Chapter 11 (see syllabus) • Syllabus paper: Ferketich & Mercer (1995)