1. N318b Winter 2002 Nursing Statistics Specific statistical tests: The T-test for means Lecture 8

2. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 2 Today’s Class  Outline of mid-term exam  Example of basic t-test  Example of paired t-test >  Applying knowledge to assigned reading  Arathuzik (1994) Followed by small groups 12-2 PM Focus on interpreting t-test results

3. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 3 Class Website http://instruct.uwo.ca/nursing/318b Lectures 1-8 are there, 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 Course web page will eventually have other options, including syllabus, etc. E-mail address: mkerr@uwo.ca

4. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 4 “In Group” Session Focuses on 3 assigned readings. Q1&2 both focus on reading and understanding tables of t-test results Key points from the three papers will be covered in the 2 nd part of the lecture Q3 NO ANSWERS NEEDED – A REMINDER !

5. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 5 Mid-term exam outline Focuses on INTERPRETATION not calculation (i.e. calculator not required!). 4 parts (50 marks): Section A: true/false (6 marks) Section B: multiple choice (14 marks) Section C: short answer (15 marks) Section D: article interpretation (15 marks) INCLUDES MATERIAL UP TO END OF TODAY !

6. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 6 Statistical Tests – Review All these tests do basically the same 3 things: 3. “test statistic” follows known distributions such that the probability of its value occurring can be determined (i.e. its “p-value”) 2. Generate a “test statistic” whose value increases as difference between groups increases (i.e. larger values more significant) 1. Compare 2 or more study groups to each other (or one group to a reference group) Example: t-statistic

7. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 7 Statistical Tests – cont’d 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

8. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 8 T-tests How do you known when to use t-tests? 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 (two groups) - two only (typically pre-post samples on one group or two different intervention groups) Referring back to the 3 “basic questions”:

9. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 9 T-tests (cont’d) One of the most common statistical tests ! (Basic) t-test: used when data in two groups come from different samples (i.e. different subjects, mutually exclusive groups) Paired t-test: used when data come from same set of subjects at two different time points (e.g. pre and post intervention) Both compare 2 means, but different formulae

10. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 10 T-test assumptions 1. Only two groups, either independent (i.e. mutually exclusive) or dependent (i.e. paired) 3. Data are (approximately) normally distributed 4. Data in two 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

11. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 11 Why is the t-test a parametric statistical test? T-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 (i.e. a parameter, the mean)

12. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 12 For situations where there are two groups with ordinal data Mann-Whitney test is used, which assigns ranks to ordinal levels and then compares overall (“mean”) ranks between groups Non-Parametric Equivalent for T-tests e.g. Note: also useful if data are non-normal e.g. very heavily skewed health status (excellent  poor)

13. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 13 A new family therapy developed to treat anorexia in teenage girls is tested in 17 girls in a before-after (or pre-post) study Paired T-test example Paired t-test uses differences within subjects H 0 : no weight gain, i.e. mean change=0 H a : girls have different weights before/after Study hypotheses

14. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 14 SubjectBeforeAfterChange 183.895.211.4 283.394.311.0 386.091.55.5 482.591.99.4 586.7100.313.6 679.676.7-2.9 776.976.8-0.1 894.2101.67.4 973.494.921.5 1080.575.2-5.3 1181.677.8-3.8 1282.195.513.4 1377.690.713.1 1483.592.59.0 15 89.993.83.9 16 86.091.75.7 17 87.398.010.7 Mean 83.290.57.3 SD 5.028.487.2 t = ---------  diff -  SD /  n Need to calculate change scores for each girl and then get mean of those and then test if different from zero  diff Sample data NOTE:  = 0, since we are testing null hypothesis

15. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 15 Paired T-test (cont’d) Note that the z-score from Lecture 5 and the paired t-statistic calculated here are very similar, except we did not know the population variance (  ) here as in Lecture 5, so we use SD from sample of differences to determine the standard error of mean Not knowing  is typical for research, as is comparing between samples (groups) so in almost all cases testing means (for two groups) will use t-test, not z-scores (more than 2 groups uses ANOVA)

16. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 16 t-statistic for mean of differences t = --------- 7.3 - 0 = --------- ( 7.2 / 4.1) = 4.2 t = 4.2 for 16 df, p < 0.001 (for paired t-test, df=n-1 as only 1 term “fixed” by using changes) From t-statistic Table in Appendix C Can we conclude …  diff -  SD /  n 1. that girls weighed more after study ? 2. that therapy was effective? YES ! NOT YET !

17. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 17 10 minute break !

18. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 18 What else might have resulted in heavier post-therapy girls? How do we test for effect of therapy then? Girls were now older / taller ? How do we set up study to remove age effect? Use a group of girls similar to therapy group but not getting the intervention A control group (independent) !

19. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 19 T-test for independent samples Can now use 17 girls not getting therapy followed and measured in same way such that: Mean weight difference =  2 = - 0.45 SD 2 = 7.99, S 2 =63.82 (variance) t = ---------  1 -  2 S  1 -  2 For a 2 sample t-test (group 1= therapy): Basically a ratio of difference in means adjusting for the standard error of difference For t-test, df=(n1+ n2) -2 = 17+17-2= 32 [each group has 1 “fixed” term in this test] DATA not shown

20. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 20 T-test (cont’d) Formula is much more complicated than the previous version as trick is determining the standard error component of the equation Family therapy appears to lead to weight gain ! t = ---------------- 7.3 – (- 0.45) 2.6 = 2.98 t = 2.98 for 32 df, p < 0.01 (from Appendix C) S  1 -  2 = (s 2 1 / N 1 ) + (s 2 2 / N 2 ) = 2.6

21. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 21 Part 2: Application to the Assigned Readings

22. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 22 “Interpret t-test results in Table #2 in paper by Turk et. al. and table #4 in Arathuzik Make sure you pick the ones that are t- tests (hint - look at level of measurement- NOIR. What levels are needed for t-test).” Some general points … In both questions 1 & 2 you are asked to write hypotheses that could be tested. Remember, a good hypothesis should address the 4 key points used in class

23. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 23 Summarizing Hypotheses  Null or Research?  Directional or Non-directional?  Causal or Associative?  Simple or Complex? The 4 categories are not mutually exclusive – i.e. hypotheses can be categorized using all 4 levels e.g. Dietary intervention A will induce more weight loss than dietary intervention B in obese children ResearchDirectionalCausalSimple

24. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 24 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

25. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 25 Interpreting Table 4 … Example: ability to decrease pain “A combination of relaxation visualization and coping skills intervention in cancer patients experiencing physical pain can increase patients ability to control pain symptoms compared to either relaxation visualization alone or to a control group.” ResearchDirectionalCausalComplex Write a hypothesis based on Table 4 …

26. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 26 Interpreting Table 4 …cont’d Was the hypothesis supported? Look at elements of the hypothesis … 5. Was it clinically important? 4. Was it in the expected pattern? 3. Was it in the expected direction? 2. Was it statistically significant? 1. Was any effect observed? Some questions to ask yourself …

27. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 27 “Identify the type of t-test and provide rationale for your answer” Interpreting Table 4 …cont’d 2. Who are the subjects in the table? 1. What kind of study design is it? Some questions to ask yourself … Pre-post, observational, survey, etc. Same subjects (e.g. pre/post) or mutually exclusive groups? 3. What mean is being tested? Actual measurement scores or differences?

28. School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 8: page 28 Next Week: Mid-term exam Based on lecture material + workshops 1.True false questions (6) 2.Multiple choice questions (14) 3.Short answer (15) 4.Study interpretations (15)