N318b Winter 2002 Nursing Statistics Specific statistical tests: Regression Lecture 11

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 2  Discussion of final exam  Regression >  Applying knowledge to assigned reading  Ferketich & Mercer (1995) Followed by small groups 12-2 PM Focus on interpreting Regression results Today’s Class

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 3 Focuses on Ferketich & Mercer (1995) Q1. Chance to interpret regression findings Q2. Know main advantage of regression Key points about regression relating to group work will be covered in the 2 nd part of lecture “In Group” Session

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 4 Last year’s exam is now on class web page Answers will go up next week ! 3 parts (60 marks): (3 hours) Section A: true/false (8 marks) Section B: multiple choice (22 marks) Section C: short answer (30 marks) on interpreting results of a research study (4 questions – choose 10 marks each) INCLUDES ALL LECTURES (TODAY) ! Outline of Final Exam

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 5 First part focuses on answering select questions from each of the 3 sections Second part focuses on addressing questions directly from students in class Work group will be a chance to review own mid-term results and ask further questions Outline of Review Lecture

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 6 CorrelationRegression Used for?associationprediction Variables?two onlytwo or more Statistics?“r” (+’ve or –’ve)“b” (+’ve or –’ve) and “R 2 ” Tells you?direction & strength direction, strength & magnitude Correlation vs. Regression

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 7 Multiple linear regression – one dependent variable and >1 independent variables Simple linear regression – one dependent variable and one independent variable Multiple logistic regression – one binary (e.g. Y/N) dependent variable and >1 independent variables (especially useful for case-control) Like ANOVA, regression is a family of methods Plus MANY others ! Types of Regression

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 8 Correlation tells you only if there is a relationship between two variables – strength (“r”) and direction (positive or negative) Simple linear regression tells you if there is a relationship between two variables and uses score on one to predict score on the other Multiple linear regression tells you if there is a relationship between two variables and uses score on one to predict score on the other and controls for other factors that might influence (“confound”) the relationship being studied Main Purpose of Regression

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 9 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 Statistical Tests – Review

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 10 How do you known when to use regression? 1.What kind of data are used? 2. What kind of relationship is of interest? 3. How many groups (samples) involved? - most often numeric/continuous (ratio/interval) - can also be binary (logistic regression) - prediction (and/or association) - often just one sample involved (in some ways regression tries to “find” groups ) Referring back to the 3 “basic questions”: Regression – when to use it?

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page The relationship under study is linear – important non-linear relationships can be overlooked with simple regression analysis 2. Data are (approximately) normally distributed 3. Data in the (two) variables have roughly equal range of variability (i.e. homoscedasticity) BASICALLY SAME AS FOR CORRELATION Regression (linear) assumptions

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 12 Although useful for understanding concepts behind regression it is not used very often in research articles (as main analytic tool) – why? Example – can use simple linear regression to determine if there is a relationship between mother’s age and baby’s birth weight Analysis shows a significant relationship between age and birth weight (for each 1 yr of age there was a 12.3 g increase in birth weight) Any doubts about this result? Simple Linear Regression

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 13 What other things might be related to child’s birth weight other than just mother’s age? Mother’s weight? Smoking? Gestational age? Diabetes? Income? Simple linear regression can be used to separately examine relationship between birth weight and each of these but not the combined effects of any of them together Need multiple regression to do this ! Simple Linear Regression – cont’d

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 14 Regression quantifies a (linear) relationship that minimizes variation in predicted versus observed values around the regression line Y' = a + bX + e Y' = predicted value (of dependent variable) a = intercept (value of Y' when X = 0) b = slope of regression line (“beta” coefficient) X = value of independent variable (“predictor”) e = error (how much Y' differs from observed) The Simple Regression Model

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 15 Very similar to ANOVA – how was that done? F = Between-group variability Within-group variability Variance attributed to model term(s) Variance from random error For regression, we also use variance from two sources: model (variables) and error (chance) F = larger F-statistic = smaller p-value Testing Fit of Regression Model

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 16 What does a significant F-statistic tell you? independent variable(s), X significantly predicts value of dependent variable, Y' (i.e. a “good” fit) What if F is non-significant? X not associated with Y' or there is a non-linear relationship (i.e. model not a “good” fit for data) What does a significant beta coefficient tell you? amount Y' increases for each unit change in X What does a significant “R 2 ” tell you? total variation in Y' attributable to model terms Interpreting Regression Output

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 17 Regression Output – Example Systolic BPAge Is there a relationship between systolic BP and age? Sample of ten subjects

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 18 Regression Table Same as correlation coefficient seen before ! (true only for simple reg.)

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 19 Plot of BP and Age Is age is a good predictor of systolic BP?

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page minute break !

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 21 What about other factors – e.g. weight? Systolic BPAgeWeight Does weight affect the relationship between systolic BP and age? Same ten subjects Multiple Linear Regression

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 22 Multiple Regression Table Note R 2 increases since more terms are in this model (thus less “unexplained” variance)

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 23 Multiple Regression Summary What does a significant F-statistic tell you? together age and weight are strong predictors of systolic BP (i.e. model is a “good” fit of data) Why did effects of age change so much? age and weight are strongly correlated with each other (note “r” = 0.93 !) What do non-significant beta coefficients tell you? each has non-significant (independent) effect

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 24 Model Building in Regression How does this happen? Statistical models are developed that (should) fit the theoretical model proposed by researchers The main advantage of regression is that is allows you to “control” for multiple factors Different procedures available but all essentially try to “weed out” non-significant factors to explain the most variation with least number of variables As terms are added (or deleted) in model process, you look for significant changes in R 2 – if not, then variable has no significant (independent) effect

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 25 Part 2: Application to the Assigned Readings

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 26 Quick summary of the paper: – a follow-up study examining the effects of previous fatherhood experience on paternal competence – also looked at “predictors” of competence – 172 subjects (79 exp., 93 inexp.) were recruited during partner’s pregnancy – analysis included t-tests, ANOVA and multiple regression Ferketich & Mercer (1995)

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 27 “Are there any differences in paternal competence between first-time (inexp) and experienced (exp) fathers in the transition to the father role?.” Is this question related to regression results? Not directly – more specific if rephrased as: “Are there any differences in “predictors” of paternal competence between … e.g. last sentence of 1 st paragraph under “Method” see first sentence of article – page 53 of syllabus Main study research question

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 28 How did the researchers “structure” analysis? 1. Comparison of the two main groups on several demographic characteristics Started with ….. 2. Comparison of the two main groups on key independent variables  How Then ….. (t-tests, RANOVA) 3. Identification of predictors of competence for the two main groups  How Then ….. (multiple regression) Overview of analysis

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 29 See Table 1 page 92 of paper Look at structure of the table … 4. Was it statistically significant – e.g. p< 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 ? - only the experienced fathers - predictors of competence (many factors) - multiple regression (at 4 time points) - everything ?! (What happened to rest?) Interpreting Table 1 …

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 30 What do all the columns mean (at each time)? Unique R 2 = variance for that term only Why does Table 1 seem to have different variables being tested at each time point? Only those that were significant shown ! Cumulative R 2 = variance for all model terms Beta = change in Y per unit of X F = test statistic from regression output (model) p = significance of test statistic, F (model) Interpreting Table 1 - cont’d

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 31 Questions for interpreting results in workshop … 4. What seems to be related? 3. Was it in the expected direction? 2. How was model developed? 1. What is the relative contribution of the terms in each model? - i.e. what is its change in R 2 ? - i.e. where are the other terms? - i.e. is there a +’ve or –’ve relationship? - i.e. how can a term be significant in one model but not in another? For Table 1 (cont’d)

School of Nursing Institute for Work & Health Nur 318b 2002 Lecture 11: page 32 For next week’s class please review: 1.Last year’s final exam (web page) Next Week: Review