1. N318b Winter 2002 Nursing Statistics Specific statistical tests: Tests for means when there are more than 2 groups ANOVA Lecture 9

2. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 2 Today’s Class  Discussion of mid-term exam  Review of how to read a journal article  Example of basic ANOVA >  Applying knowledge to assigned reading  Arathuzik (1994) Followed by small groups 12-2 PM Focus on interpreting ANOVA results

3. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: 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 9: page 4 “In Group” Session Focuses on 1 assigned reading. Q1. Chance to interpret ANOVA findings Q2. Know when to use t-test or ANOVA Key points about ANOVA relating to workshop will be covered in the 2 nd part of the lecture

5. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 5 Mid-term exam results To be completed as time permits 4 parts (50 marks): Section A: mean = ?/6 Section B: mean = ?/14 Section C: mean = ?/15 Section D: mean = ?/15 Class average = ?/50 = ??%

6. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: 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 9: page 7 Analysis of Variance - ANOVA How do you known when to use ANOVA? 1.What kind of data are used? 2. What kind of relationship is of interest? 3. How many groups (samples) involved? - numeric/continuous (ratio/interval) - independent OR dependent samples - differences between means (>2 means) - more than two groups (although can be two pre-post samples from multiple time points) Referring back to the 3 “basic questions”:

8. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 8 ANOVA assumptions 1. Three or more “groups”, independent (i.e. mutually exclusive) or dependent (i.e. follow-up) 3. Data are (approximately) normally distributed 4. Data in the groups come from same underlying population (i.e. equal variances) Some flexibility on points #3 & #4 but not #1 & #2 2. Used only for comparing means

9. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 9 Why is the ANOVA a parametric statistical test? ANOVA 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 (i.e. a parameter, the mean)

10. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 10 For situations where there are more than two independent groups with ordinal data Kruskal-Wallis test is used, which assigns ranks to ordinal levels and then compares overall rank scores between the groups Non-Parametric Equivalent for ANOVA e.g. Note: also tests for dependent data sets e.g. Friedman test Pain score (extreme  no pain)

11. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 11 Why not just use multiple t-tests? ANOVA allows you to compare overall differences between all groups involved in study, not just one pair at a time Individual t-tests can be time consuming and if there are several groups then the number of tests and calculations becomes unwieldy ANOVA – cont’d ANOVA tells you only if a difference exists between means, not which means are different

12. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 12 T-test versus ANOVA Very similar to one another with respect to underlying assumptions and mathematical basis for calculating relevant test-statistic Remember: “T” for “two” ! Paired t-test ~ Repeated measures ANOVA Independent t-test ~ One-way ANOVA e.g. 3 distinct groups, one variable examined e.g. 3 related groups, one variable examined

13. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 13 Multifactor ANOVA (MANOVA) – e.g. two- way ANOVA uses two independent variables, such as gender by drug groups 3 Types of ANOVA One-way ANOVA - used when data come from distinct samples (i.e. unrelated subjects) and only one independent variable is used Repeated measures ANOVA (RANOVA) - e.g. two groups of subjects (experimental and control groups) compared at two different time points (such as pre-post)

14. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 14 ANOVA – Sample scenario 1 Want to compare somatic health complaints (using scores on the Physical Symptom Survey) between 3 groups of unrelated subjects: One-way ANOVA: data come from independent samples (i.e. unrelated subjects) and only one outcome and exposure variable used 3. non-smokers 2. recent ex-smokers 1. smokers What do we do here?

15. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 15 ANOVA – Sample scenario 2 Want to examine the effect of gender and education level on sexual knowledge with respect to HIV transmission Two-way ANOVA: data come from independent samples (i.e. unrelated subjects) but now have one outcome and TWO exposure variables 3. Post-secondary 2. High school 1. No high school What do we do here? AND 2. Female 1. Male

16. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 16 ANOVA – Sample scenario 3 Want to examine the effect of 3 forms of psychiatric therapy over 1 year, using endpoints of 1 wk, 1-, 3- 6- and 12-months Repeated measures ANOVA: data come from 3 independent samples but also have repeat data collections within the groups of same subjects 1. Therapy 1 What do we do here? AT1 wk, 1-, 3- 6- and 12-months 2. Therapy 2 3. Therapy 3

17. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 17 ANOVA – what is it? What does “variance” mean again? When you take a mean, you want some idea of how much the individual subjects vary from each other “on average” (i.e. the SD) while the total amount of this variation is the “variance” So what does ANOVA do? ANOVA takes advantage of this notion of total variation, comparing variation both within the group samples AND between the group means

18. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 18 ANOVA – splitting the variance Steps in calculating ANOVA: 1. Separate calculations are done to find: i) the variation between the groups ii) the variation within each group 2. Then the ratio of “between to within” variation is calculated (the “F” test statistic) F = Between-group variability Within-group variability

19. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 19 Where does variance come from? 1. variation between the groups 2. variation within each group (“subject-to-subject”) ii) effect of independent variable (e.g. drug) i) random sampling “error” F = effect of independent variable + sampling “error” sampling “error” Thus can now interpret F-statistic as:

20. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 20 Interpreting the F-statistic - like other test statistics (eg. Z, t ) the bigger the value of F (for a given set of df), the larger the difference between the groups examined - distributions for F-statistics known thus tables used (again with df) to translate “F” into a p-value for observing study means larger F-statistic = smaller p-value - now have two types of df though since we have variation from subjects AND groups

21. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 21 Interpreting the F-statistic – cont’d F-statistic typically written specifying group and subject degrees of freedom, as these are needed to obtain table values: F (group df, subject df) = ratio (p-value) F (2, 60) = 2.86 p > 0.05 (Where group df = k-1 and subject df = n-k) k = number of groups; n = number of subjects Example:

22. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 22 Interpreting the F-statistic – cont’d What does P-value from F-statistic tell you? Only that the group means are NOT the same What do you do next if F is significant? Need to do post-hoc analysis of means to see where differences are greatest or actually significantly different from one another Example – Duncan’s test for pairwise comparisons

23. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 23 10 minute break !

24. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 24 Reading research – First steps 4. Were the methods appropriate? 5. What were the conclusions? 2. What was the hypothesis/research question? 3. Scan tables – what do they show? 1. Read abstract – is study relevant to me? Start with the overall structure and work in …

25. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 25 Tips on reading research results Before you can interpret the results … 5. Was it clinically important? 4. Was it statistically significant – e.g. p<0.05 3. How is it being tested – e.g. test used? 2. What is being tested – e.g. dep/indep? 1. Who is in the table – e.g. groups explicit? Some questions to ask yourself …

26. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 26 Reading research – cont’d Some general points on research results … 4. Not all results in tables are significant ! 3. “Discussion Section” interprets findings 2. Need to read text to be sure of results 1. Not all key results are in tables/graphs Check footnotes for significance symbols !

27. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 27 Part 2: Application to the Assigned Readings

28. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 28 Arathuzik (1994) Quick summary of the paper: – a pilot study examining the effects of a combination of interventions on pain perception, pain control and mood in metastatic breast cancer patients – pre-test / post-test experimental design – 3 groups enrolled with 24 (convenience sample) subjects randomly allocated to the three (intervention) groups, only 8 per group

29. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 29 Main study hypothesis “Breast cancer patients who received relaxation, visualization, and cognitive coping skills training would would perceive less pain intensity [and distress] than breast cancer patients who received relaxation and visualization training and than a control group.” Was this hypothesis [for intensity] supported? - look for table that compares means (i.e. an ANOVA is a good way to answer this)

30. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 30 Interpreting Table 3 … See Table 3 page 26 of Arathuzik paper Look at structure of the table … 4. Was it statistically significant – e.g. p<0.05 3. How is it being tested – e.g. test used? 2. What is being tested – e.g. dep/indep? 1. Who is in the table – e.g. groups ? - all 3 study groups (separately by pre/post) - mean scores (separately by pre/post) - ANOVA (one-way, separately by pre/post) - only fatigue in pre-, and ability to decrease pain in post-period

31. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 31 Interpreting Table 3 - cont’d Does Table 3 make sense on its own? - Table 2 shows you group means by key variables by pre/post status, then Table 3 tests if any of these means are different What else must go together with Table 3? NO ! - Table 4 then tests where change occurred Why does Table 3 test “pre” scores? A check on whether groups are comparable

32. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 32 For Table 1 in Good (1995) When interpreting results for workshop 5. Was it clinically important? 4. Was it in the expected pattern? 3. Was it in the expected direction? 1. Any statistically significant differences? Some questions to ask yourself …

33. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 9: page 33 Next Week: Correlation For next week’s class please review: 1.Page 17 (bottom) in syllabus 2.Textbook Chapter 10 3.Syllabus papers: Birenbaum et al. (1996); Turk et al. (1995)