Advanced Quantitative Methods William L Holzemer RN Ph

Advanced Quantitative Methods William L. Holzemer, RN, Ph. D. , FAAN Professor, School of Nursing University of California, San Francisco bill. holzemer@nursing. ucsf. edu

Objectives • Develop your definition of nursing science • Use the Outcomes Model to think about your area(s) of interest • Review quantitative methods • Think about how we build knowledge to improve health and nursing practice. 2

Assignments • Ph. D Students -individual assignments • MS Students – group assignment – Mini-literature review • • Outcomes Model Substruction Synthesis Tables Summary 3

Nursing = Nursing Science? Definition of Nursing American Nurses Association: “Nursing is the assessment , diagnoses, and treatment of human responses” 4

Definition of Nursing Japan Nurses Association “Nursing is defined as to assist the individual and the group, sick or well, to maintain, promote and restore health. ” 5

Definition of Nursing International Council of Nurses “Nursing encompasses autonomous and collaborative care of individuals of all ages, families, groups and communities, sick or well and in all settings. Nursing includes the promotion of health, prevention of illness, and the care of ill, disabled and dying people. Advocacy, promotion of a safe environment, research, participation in shaping health policy and in patient and health systems management, and education are also key nursing roles. ” 6

Common Elements: Definitions of Nursing • • Person (individual, family, community) Health (Wellness & Illness) Environment Nursing (care, interventions, treatments) 7

Nursing Science The body of knowledge that supports evidence-based practice 8

Nursing Science Uses Various Research Methodologies Qualitative Understanding Interview/observation Discovering frameworks Textual (words) Theory generating Quality of informant more important than sample size Rigor Subjective Intuitive Embedded knowledge Quantitative Prediction Survey/questionnaires Existing frameworks Numerical Theory testing (RCTs) Sample size core issue in reliability of data Rigor Objective Public 9

Types of Research Methods: (all have rules of evidence!) Qualitative Quantitative Grounded theory Ethnography Critical feminist theory Phenomenology Non-Experimental or Descriptive Experimental or Randomized Controlled Trials Ethnography Content Analysis Models of analysis: fidelity to text or words of interviewees Models of analysis: Parametric vs. nonparametric 10

Outcomes Model for Health Care Research (Holzemer, 1994) Inputs 1970’s Processes Outcomes 1980’s 1990’s Client Provider Setting 11

Outcomes Model • Heuristic • Systems model (inputs are outputs, outputs become inputs) • Relates to Donabedian’s work on quality of care (Structure, Process, and Outcome Standards) 12

Outcomes Model: Nursing Process Inputs Client Provider Processes Outcomes Problem Outcome Intervention Setting 13

Outcomes Model for Health Care Research Inputs (Covariate, confounding variable) Processes Outcomes (Independent Variable) (Outcome Variable) Client Age, gender, SES, Ethnicity Severity of Illness Self-care Adherence Family care Quality of Life Pain control Pt. satisfaction Pt. falls, Provider Age, gender, SES, Education, Experience, Certification Perc. Autonomy Interventions Care Talking, touch, time Vigilance, communication Quality of Work life Turnover Errors Satisfaction Setting Resources Philosophy Staffing levels Actual staffing ratios Mortality Morbidity Cost 14

Outcomes Model: Your assignment (Think about a project or program of research) Inputs z Processes Outcomes x y Client Provider Setting 15

Where Should We Find Evidence. Based Practice Guidelines? • Clinical practice guidelines • Nursing Standards/ Procedural Manuals • Great demand, low level of delivery (Great demand, growing level of delivery) • Knowledge base from research literature 16

Types of Evidence: How do we know what we know? • • • Clinical expertise Intuition Stories Preferences, values, beliefs, & rights Descriptive/quasi-experimental studies Randomized clinical (controlled) trials (RCTs) - the gold standard 17

Summary: Introduction to Research • Think about nursing research – nursing science • Outcomes Model designed to put boundaries around your area of study and expertise (very difficult challenge in nursing!) • Variable identification • Understanding rigor – correct methods for any type of research design • Enhance enjoyment in reading research articles • Understand the challenge of the words so easily used, “evidence-based practice. ” 18

Some Challenges: • Think about developing your definition of nursing science. • Use the Outcomes Model to help you think about your program of research. • Enhance your understanding of rigor in all types of research designs. • Increase your enjoyment of reading research articles. • Understand the complexities of “evidence-based practice. ” 19

When thinking about your research problem: • • Is it significant? Are you really interested in it? Is it novel? Is it an important area? – High cost, high risk? • Can it be studied? • Is it relevant to clinical practice? 20

Where do ideas come from? • • Literature reviews Newspaper stories Being a research assistant Mentors/teachers Fellow students Patients Clinical experience Experts in the field Build your area of expertise from multiple sources. 21

Uses of Substruction • Critique a published study • Plan a new study 22

Substruction • A strategy to help you understand theory and methods (operational system) in a research study • Applies to empirical, quantitative research studies • There is no word, Substruction, in the dictionary. It has an inductive meaning, constructing and a deductive meaning, deconstructing • Hueristic 23

Substruction Theory (Theoretical system) Construct Deductive (qualitative) Methods (Operational System) Measures (quantitative) Inductive Concept Scaling/Data analysis 24

Substruction: Building Blocks or Statements of Relationships Construct Pain Concept Intensity Measure 10 cm scale axiom proposition hypothesis Construct quality of life Concept functional status Measure mobility scale 25

Statements of Relationships Construct: Postulate: Statement of relationship between a construct and concepts Pain consists of three concepts Concepts: Intensity Location Duration 26

Substruction: Research Design Perspective Focus of Study (RCT? ) Co-variates Z Severity of illness for risk adjustment (analysis of covariance) Independent Variable X treatment how measured? Dependent Variable Y 27

Substruction: Theoretical System, an example Pain Intervention Study Post Surgical Patient Severity of illness age gender Pain Management Intervention Patient communication Standing PRN orders Non pharmacological tx Pain Control Length of stay Patient Satisfaction 28

Substruction: Operational System Pain Intensity Instrument: VAS 10 cm scale (low to high pain) Functional Status Instrument: 1 -5 Likert scale, 1=low & 5=high function Scale: continuous or discrete? 29

Scaling Discrete: non-parametric (Chi square) • Nominal gender • Ordinal low, medium, high income Continuous: parametric (t or F tests) • Interval Likert scale, 1 -5 functionality • Ratio money, age, blood pressure 30

Issues • • • What is the conceptual basis of the study? What are the major concepts and their relationships? Are the proposed relationships among the constructs and concepts logical and defensible? How are the concepts measured? valid? reliable? What is the level of scaling and does it relate to the appropriate statistical or data analytical plan? Is there logical consistency between theoretical system and the operational system? 31

Is there a relationship between touch and pain control, accounting for initial amount of post-operative pain? rx, y. z Inputs Processes Outcomes Z X Y Client Post Pain operative Control pain Provider Therapeutic Touch vs NL care Setting 32

Literature Review • We review the literature in order to understand theoretical and operational systems relevant to our area of interest. • What is known about the constructs and concepts in our area of interest? • What theories are proposed that link our variables of interest? 33

Literature Review • What is known? • What is not known? • Resources – The Cochran Library – Library Data Bases • Pub. Med • CINYL 34

Literature Review: How to combine, synthesis, and demonstrate direction? 35

Literature Review 36

Table 1. Outline of study variables related to your topic Covariates Interventions Studies Z Outcomes Independent Dependent variable Variable X Y Smith (1999) Jones (2003) Etc. 37

Table 2. Threats to validity of research studies related to topic Author (year) Type of Design Diagram Smith (1999) RCT O X 1 O O X 2 O O O Statistical Conclusion Validity Construct Validity of Cause & Effect Internal Validity External Validity n/a Jones (2003) 38

Table 3. Instruments Instrument Studies Smith (1999) # items Validity Reliability Utility Mc. Gill Pain Questionnaire Jones (2003) 39

Table 4. Power analysis for literature review on topic. Studies Smith (1999) Sample Size Alpha Power Effect Size 32 –exp 40 – cont 0. 05 0. 60 Est. at medium Jones (2003) 40

Literature Synthesis • Synthesis - what we know and do not know • Strengths – rigor, types of design, instruments? • Weaknesses –lack of rigor, no RCTs, poorly developed instruments • Future needs – what is the next step? 41

Research Designs 42

Research Design: Qualitative • • Ethnography Phenomenology Hermeneutics Grounded Theory Historical Case Study Narrative 43

Rigor in Qualitative Research • • Dependability Credibility Transferability Confirmability 44

Types of Quantitative Research Designs • We will focus on RIGOR: – Experimental – Non-experimental 45

X, Y, Z notation • Z = covariate • Severity of illness • X = independent variable (interventions) • Self-care symptom management • Y = dependent variable (outcome) • Quality of life 46

Types of Quantitative Research Designs – Descriptive X? Y? Z? • What is X, Y, and Z? – Correlational rxy. z • Is there a relationship between X and Y? – Causal ΔX ΔY? • Does a change in X cause a change in Y? 47

Rigor in Quantitative Research • Theoretical Grounding: Axioms & postulates – substruction-validity of hypothesized relationships • Design validity (internal & external) of research design; Instrument validity and reliability • Statistical assumptions met (scaling, normal curve, linear relationship, etc. ) (Note: Polit & Beck: reliability, validity, generalizability, objectivity) 48

Literature Review Study Aims Study Question Study Hypothesis 49

Aim, Question, and Hypothesis • Study Aim: To explore if it is possible to reduce patient falls for elderly in nursing homes. • Study Question: Does putting a “sitter” in a patient room reduce the incidence of falls? • Study Hypothesis: Null: H 0: There is no difference between patients who have a “sitter” and those who do not in the incidence of falls. 50

Experimental Designs 51

Definition: Experimental Design 1. There is an intervention that is controlled or delivered 2. There is an experimental and control group 3. There is random assignment to groups 52

Classic Experimental Design O 1 exp X O 2 exp O 1 con O 2 con R (pretest) (posttest) O=observation 1 = pretest or time one; 2 = posttest or time two X = intervention R = random assignment to groups 53

Classic Experimental Design O 1 exp X O 2 exp O 1 con O 2 con R (pretest) (posttest) The RCT is the Gold Standard for Evidence-Based Practice 54

Randomization 1. Random assignment to groups (internal validity issue) – equals Z variables in both groups 2. Random selection from population to sample (external validity issue) – equals Z variables in the sample that are true for the population 55

Goal: Statement of Causal Relationship 56

Conditions Required to Make a Causal Statement: X causes Y 1. X precedes Y 2. X and Y are correlated 3. Everything else controlled or eliminated. No Z variables impacting outcome. 4. We never prove something, we gather evidence that supports our claim. 57

Controlling Z variables: 1. Minimize threats to internal validity 2. Limit sample (e. g. under 35 years only) to control variation 3. Statistical manipulation (ANCOVA) 4. Random assignment to groups 58

Dimensions of Research Designs: Groups & Time O 1 exp X O 2 exp Groups (n=2 experimental & control) O 1 con O 2 con ------------------------ Time (n=2) (repeated measures) 59

Dimensions of Research Designs: Groups & Time Groups = between factors Time = within factors 60

Types of Designs • O - descriptive, one time • O 1 O 2 O 3 - descriptive, cohort, repeated measures) • O 1 X O 2 (not an experimental design!) - prepost-test 61

Types of Designs • O 1 X O 2 RCT randomized controlled trial 62

Types of Designs • O 1 O 2 O 3 X O 4 O 5 O 6 O 1 O 2 O 3 O 4 O 5 O 6 • O 1 X O 2 Xno O 3 X O 4 Xno O 5 (repeated measures vs. time series designs) 63

Types of Design R O 1 O 1 X 2 O 2 O 2 # of groups? ___ # points in time? ___ 64

Types of Designs Post-test only design: X O 2 What is the biggest threat to this post -test only design? 65

Types of Research Design • Experimental (true) • Quasi-Experimental (quasi) – No random assignment to groups 66

Design Validity – Statistical conclusion validity – Construct validity of Cause & Effect (X & Y) – Internal validity – External 67

Design Validity • Statistical Conclusion Validity rxy? – Type I error (alpha 0. 05) – Type II error (Beta) Power = 1 -Beta, inadequate power, i. e. low sample size – Reliability of measures Can you trust the statistical findings? 68

Design Validity • Construct Validity of Putative Cause & Effect ( X Y? ) – Theoretical basis linking constructs and concepts (substruction) – Outcomes sensitive to nursing care – Link intervention with outcome theoretically Is there any theoretical rationale for why X and Y should be related? 69

Design Validity Internal Validity – – – Threat of history (intervening event) Threat of maturation (developmental change) Threat of testing (instrument causes an effect) Threat of instrumentation (reliability of measure) Threat of mortality (subject drop out) Threat of selection bias (poor selection of subjects) Are any Z variables causing the observed changes in Y? 70

Design Validity External Validity – Threat of low generalizability to people, places, & time – Can we generalize to others? 71

Building Knowledge • Goal is to have confidence in our descriptive, correlational, and causal data. • Rigor means to follow the required techniques and strategies for increasing our trust and confidence in the research findings. 72

Sampling [Sample selection, not assignment] 73

Terms • Population - All possible subjects • Sample -A subset of subjects • Element - One subject 74

What do we sample? • People (e. g. subjects) • Places (e. g. hospitals, units, cities) • Time (e. g. season, am vs. pm shift ) 75

Sampling: What do we do? • Random Assignment • Random Selection -is designed to equalize the “Z” variables in the experimental and control groups -is designed to equalize the “z” variables that exist in the population to be equally distributed in a sample 76

Types of Probability Sampling Probability Simple random sampling –using a random table of numbers Stratified random sampling –divide or stratify by gender and sample within group Systematic random sampling –take every 10 th name Cluster sampling – select units (clusters) in order to access patients or nurses 77

Types of Non-probability sampling • Convenience – first patients to walk in the door • Purposive –patients living with an illness • Quota – equal numbers of men & women • (volunteers) • (convenience) 78

Types of Samples Homogeneous: subjects are similar, all females, all between the ages of 21 -35 Heterogeneous: subjects are diverse, wide age range, all types of cancer patients 79

Sampling Error 80

How to control sampling error? • Use random selection of subjects • Use random assignment of subjects to groups • Estimate required sample size using power analysis to ensure adequate power • Overestimate required sample size to account for sample mortality (drop out) 81

Sample Size and Sampling Error 82

Sample Size Calculations • • • Type of design Accessibility of participants Statistical tests planned Review of the literature Cost (time and money) 83

Strategies for Estimating Sample Size • Ratio of subjects to variables in correlational analysis. 3: 1 up to 30: 1 subjects to variables. 30 item questionnaire requires 90 to 900 subjects. • Chi square – can’t work if less than 5 subjects per cell 84

Power Analysis Power - commonly set at 0. 80 Alpha - commonly set at 0. 05 or 0. 01 Effect Size - based upon pilot studies or literature review; small, medium, large Sample Size - # subjects required to ensure adequate power Power is a function of alpha, effect size, and sample size. 85

Power Analysis Programs • SPSS Pakcage • n. Query Adviser Release 4. 0 (most recent? ) http: //www. statsolusa. com 86

Power • Power is the ability to detect a difference between mean scores, or the magnitude of a correlation. • If you do not have enough power in a study, it does not matter how big the effect size, i. e. how successful your intervention, you can not statistically detect the effect. • Many studies are under powered. 87

Effect Size • Effect size can be thought of as how big a difference the intervention made. • Statistical significance and clinical significance are often not the same thing 88

Effect Size • Small (correlations around 0. 20) – Requires larger sample size • Medium (correlations around 0. 40) – Requires medium sample size • Large (correlations around 0. 60) – Requires smaller sample size 89

Effect Size Meanexp – Meancon Effect Size = SD e&c 90

Eta Squared (ŋ2) • In ANOVA, it is the proportion of dependent variable (Y) explained. • Estimate of Effect Size • Similar to R 2 in multiple regression analysis. 91

alpha • alpha relates to hypothesis testing and how often you are willing to make a mistake in drawing a conclusion • alpha is equivalent to Type 1 error – or saying that the intervention worked, when in fact the effect size observed, is just due to chance • alpha of 0. 01 is more conservative than 0. 05 and therefore, harder to detect differences 92

Hypothesis Testing: Is it true or false? • Null hypothesis: H 0 – Mean (experimental) = Mean (control) • Alternative hypothesis: H 1 – Mean (experimental) =/= Mean (control) 93

Hypothesis Testing and Power Goal: Reject H 0 REALITY Null H 0 True Null H 0 False H 0: Mc=Me H 0: Mc=/=Me DECISION Reject H 0 Type I Error Power (1 -Beta) DECISION Accept H 0 Correct Decision Type II Error (Beta) 94

Quiz: • If sample size goes up, what happens to power? • If alpha goes from. 05 to. l 01, what happens to required sample size? • If power falls from. 80 to. 60, what type of error is most likely to occur? • If effect size is estimated based upon the literature as large, what effect does this have on the required sample size? 95

Sample Loss in RCT N=243 Randomization N=118 N=122 1 month N=105 N=110 6 months N=91 N=89 96

Measurement “If it exists, it can be measured” R. Cronbach 97

What we measure: • Knowledge, Attitudes, Behaviors (KAB) • Physiological variables • Symptoms • Skills • Costs 98

Classical Measurement Theory: 99

Type of Measures • Standardized – evidence as follows: 1. 2. 3. 4. • Systematically developed Evidence for instrument validity Evidence for instrument reliability Evidence for instrument utility – time, scoring, costs, sensitive to change over time Non-standardized 100

Types of Measurement Error • Systematic - can work to minimize systematic error due to poor instructions, poor reliability of measures, etc. • Random - can do nothing about this, always present, we never measure anything perfectly, there is always some error. 101

Validity Question: Does the instrument measure what it is supposed to measure? • Theory-related validity – Face validity – Content validity – Construct validity • Criterion-related validity – Concurrent validity – Predictive validity 102

Theory-related Validity • Face validity – participant believability • Content validity (observable) – Blue print – Skills list • Construct validity (unobservable) – Group differences – Changes of times – Correlations/factor analysis 103

Criterion-related Validity • Concurrent – Measure two variables and correlate them to demonstrate that measure 1 is measuring the same thing as measure 2 –same point in time. • Predictive – Measure two variables, one now and one in the future, correlate them to demonstrate that measure 1 is predictive of measure 2, something in the future. 104

Reminder: • Design Validity Does the research design allow the investigator to answer their hypothesis? (Threats of internal and external validity) • Instrument Validity Does the instrument measure what it is supposed to measure? 105

Instrument Reliability Question: can you trust the data? • Stability – change over time • Consistency – within item agreement • Rater reliability – rater agreement 106

Instrument Reliability • Test-retest reliability (stability) – Pearson product moment correlations • Cronbach’s alpha (consistency) – one point in time, measures inter-item correlations, or agreements. • Rater reliability (correct for change agreement) – Inter-rater reliability Cohen’s kappa – Intra-rater reliability Scott’s pi 107

Cronbach’s alpha = SD = 108

Cronbach alpha Reliability Estimates: • > 0. 90 – Excellent reliability, required for decisionmaking at the individual level. • 0. 80 – Good reliability, required for decision-making at the group level. • 0. 70 – Adequate reliability, close to unacceptable as too much error in the data. Why? 109

Internal Consistency: Cronbach’s alpha Person A: Internally consistent Person B: Internally inconsistent All the time Much of the time A little of the time Rarely 1 4 A 3 2 1 B 2 4 B 3 A 2 1 3 4 3 A 2 B 1 4 4 A 3 B 2 1 Item 110

Error in Reliability Estimates “Error = 1 – (Reliability Estimate)2” If alpha = 0. 90, 1 -(0. 90)2 1 -0. 89 =. 11 error If alpha = 0. 70, 1 – (0. 70)2 1 -. 49 =. 51 error If alpha = 0. 70, it is the 50: 50 point of error vs. true value 111

Reliability Values • Range: 0 to 1 • No negative signs like correlations • Cohen’s kappa and Scott’s pi are always lower, i. e. 0. 50, 0. 60 112

Utility Things you would like to know about an instrument. • • Time to complete (subject fatigue)? Is it obtrusive to participants? Number of items (power analysis)? Cultural, gender, ethnic appropriateness? • Instructions for scoring? • Normative data available? 113

Reporting on Instruments • Concept(s) being measured • Length of instrument or number of items • Response format (Likert scale, etc. ) • Evidence of validity • Evidence of reliability • Evidence of utility 114

Quiz: • Can a scale be valid and not reliable? • Can a scale be reliable and not valid? 115

Scale Development • Generation items from focus groups/interviews • Scaling decisions capture variation • Face validity - check with experts and participants • Standardize scale (evidence for validity, reliability, & utility) • Estimate correlates of concept • Explore sensitivity to change over time 116

Translation • Forward translation (A to B) • Backward translation (B to A) • Conceptual equivalency across cultures • Using of slang, idioms, etc. 117

Data Analysis 118

Data Analysis: Why? • Capture variability (variance) – how the scores vary across persons • Parsimony – data reduction technique, how to describe many data points in simple numbers • Discover meaning and relationships • Explore potential biases in data (sampling) • Test hypotheses 119

Where to begin: • After data is collected, we begin a long process of data entry & cleaning • Data entry requires a code book be developed for the statistical program you plan to use, such as SPSS. • Data codebooks allow you to give your variables names, values, and labels. 120

Data Entry & Cleaning • Data entry is a BIG source of error in data • Double data entry is one strategy • Cleaning data looking for values outside the ranges, e. g. age of 154 is probably a typo. • We examine frequencies, high score, low scores, outliers, etc. 121

Coding Variables Capture data in its most continuous form possible. Age: 35 years - get the actual value vs. Check one: _<25 _ 25 -35 _ 36 -45 _ >45 122

Dichotomous Variables Do not do this: 1 = Male 2= Female Do this! 1 = male 0 = female Why? Add function 123

Dummy Coding Ethnicity 1 = Black; 2 = White; 3 = Hispanic N-1 or 3 -1 = 2 variables Black: 1 = Black; 0 = White and Hispanic White: 1 = White; 0 = Black and Hispanic 124

Missing Data • SPSS assigns a dot “. ” to missing data • SPSS often gives you a choice of pairwise or listwise deletion for missing values. Mean Substitution: give the variable the average score for the group, e. g. age, adds no variation to the data set. 125

Missing Data Pairwise: just a particular correlation is removed, best choice to conserve power Listwise: removes variables, required in repeated measures designs. 126

Measures: • Central Tendency • Relationships • Effects 127

Measures of Central Tendency • Mean – arithmetic average score • Standard deviation (SD) – how the scores cluster around the mean • Range – high and low score. (Example: M = 36. 4 years SD= 4. 2 Range: 22 -45) 128

Formulas Mean = SD = 129

Measures of Central Tendency • Mean – arithmetic average • Median – score which divides the distribution in half (50% above and 50% below) • Mode – the most frequently occurring value When does the mean=median=mode? 130

Normal Curve: very robust! 131

Normal Curves 132

Normal Curve (Mean=Median=Mode) 133

Non-Normal Curves 134

Scaling • Discrete (qualitative) – Nominal – Ordinal • Continuous (quantitative) – Interval – ratio • Non-parametric (no assumptions required; Chi square) • Parametric (assumes the normal curve, e. g. t and F tests) 135

Degrees of Freedom • Statistical correction so one does not over estimate 136

Degrees of Freedom for ball 1? 137

Degrees of Freedom for ball 2? 138

Degrees of Freedom for ball 3? 139

Degrees of Freedom • Sample size (n-1) • Number of groups (k-1) • Number of points in time (l-1) 140

Relationships or Associations 141

Measures of Association: Correlations • Range: -1 to 1 • Dimensions: – Strength (0 -1) – Direction (+ or -) • Definition: a change in X results in a predictable change in Y; shared variation or variance. 142

Correlations • Sample specific (each sample is a subset of the population) • Unstable • Dependent upon sample size • Everything is statistically significant with a very large sample size; may not be clinically significant. • Expresses relation not a causal statement 143

Types of Correlations • Pearson product moment r – continuous by continuous variable • Phi correlation – discrete by discrete variable (Chi square) • Rho rank order correlation – discrete ranks by ranks • Point-biserial – discrete by continuous variable • Eta Squared 144

Estimate the value of the correlation 145

Variance 146

Shared variance r 2 147

Shared variance r 2 148

Types of Data Analyses Descriptive X? Y? Z? Measures of central tendency Correlational rx, y? Is there a relationship between X and Y? Measures of relationships (correlations) Causal ΔX ΔY? • Does a change in X cause a change in Y? Testing group differences (t or F tests) 149

Testing Effects of Interventions 150

Testing Group Differences • t tests • F tests (Analysis of Variance or ANOVA) (t tests are F tests with two groups) 151

Types of tests of group differences • Between groups – (unpaired) • Within groups – (paired or repeated measures; if two groups it is also test-retest) – requires identified subjects 152

Classic Experimental Design O 1 exp X O 2 exp O 1 con O 2 con R (pretest) (posttest) Group: Between Factor Time: Within Factor 153

Tests of Significance 3 4 1 O 1 X O 2 2 O 1 O 2 154

Testing Group Differences Between Variance F (or t) = Within Variance 155

Examining Variance 156

Examining Variance: No difference between the means 157

Examining Variance: Big difference between means 158

Examining Variance: Three groups 159

Types of Designs O 1 O 2 O 3 change within group over time, repeated measures design 160

Types of Designs O 1 e O 1 c X O 2 e O 2 c change within group from O 1 e to O 2 e change between groups O 2 e and O 2 c 161

How to analyze this design? • O 1 e O 2 e O 3 e X O 4 e O 5 e O 6 e O 1 c O 2 c O 3 c O 4 c O 5 c O 6 c • Two group repeated measures analysis of variance. • One between factor (group) and one within factor (time) with six levels. 162

Post-test only design • X O 2 e O 2 c Unpaired t test Null hypothesis: H 0: O 2 e = O 2 c Alternative directional hypothesis: H 1: O 2 e > O 2 c 163

• Standard Deviation – how scores vary around a mean • Standard Error of the Mean – how mean scores vary around a population mean 164

Standard Error of the Mean: Average of sample SDs 165

Conceptual: Mean. E – Mean. C t= standard error of the mean 166

Assumptions of ANOVA • • Normal distribution Independence of measures Continuous scaling Linear relationship between variables 167

3 X 2 ANOVA R O 2 exp O 1 exp X 2 O 2 exp O 1 con O 1 exp X 1 O 2 con One between factor: group (3 levels) One within factor: time (2 levels) 168

Omnibus F Test R O 2 exp O 1 exp X 2 O 2 exp O 1 con O 1 exp X 1 O 2 con F test group: Is there a difference among the three groups? F test time: Is there a difference between time 1 and 2? If yes to either question, where is the difference? Interaction: Group by Time 169

Post-hoc comparisons O 1 exp 1 X 1 O 2 exp 1 O 1 exp 2 X 2 O 2 exp 2 O 1 con O 2 con R Types: Scheffé, Tukey – control for degrees of freedom in different ways; compares all possible two way comparisons H 0: O 2 exp 1 = O 2 exp 2 = O 2 con If you reject Null, or F test is significant, then you can look for two-way differences. (O 2 exp 1= O 2 exp 2? ) or (O 2 exp 2= O 2 con? ) or (O 2 exp 1 = O 2 con? ) 170

Tests of Significance Non-parametric Parametric Two-groups Paired Wilcoxin Rank Unpaired Mann-Whitney U Paired t test Unpaired t test More than two-groups Repeated measures Friedman test Independent groups Kruskal -Wallis ANOVA Repeated measures ANOVA 171

Galloping alpha • Danger in conducting multiple t tests or doing itemlevel analysis on surveys • alpha = probability of rejecting the Null hypothesis • alpha 0. 05 divided by number of tests, distributes alpha over tests • If conducting 10 t tests, alpha at 0. 005 per test (0. 05/10=0. 005) 172

ANOVA • ANOVA – analysis of variance • ANCOVA – analysis of co-variance, includes Z variable(s) • MANOVA – multivariate analysis of variance (more than one dependent variable) • MANCOVA – multivariate analysis of co-variance, includes Z variable(s). 173

Multiple Regression Analysis Correlational technique – Unstable values – Sample specific – Reliability of measures very important – Requires large sample size – Easy to get significance with large sample size 174

Multiple Regression Analysis Attempts to make causal statements of relationship Y = X 1+X 2+X 3 Y = dependent variable (health status) X 1 -3 = predictors or independent variables Health Status = Age + Gender + Smoking 175

Multiple Regression Questions: • What is the contribution of age, gender, and smoking to health status? • How much of the variation in health status is accounted for by variation in age, gender, and smoking? 176

Multiple Regression Analysis • Creates a correlation matrix. • Selects the most highly correlated independent variable with the dependent variable first. • Extract the variance in Y accounted for by that X variable. • Repeats the process (iterative) until no more of the variance in Y is statistically explained by the addition of another X variable. 177

Health Status = Age + Gender + Smoking Health Status Y Age X 1 Gender X 2 Smoking X 3 Age X 1 r 2 Gender X 2 r 2 Smoking X 3 r 2 1 0. 25 6% 0. 04 0% 0. 40 16% 1 0. 11 1% . 05 0% 1 . 20 4% 1 178

Multiple Regression: Shared Variance Smoking 40% Health Status Age 25% Gender 4% Age Smoking Gender 179

Multiple Regression • Correlation results in a r • Multiple regressions results in an r 2 • R squared is the total amount of the variance in Y that is explained by the predictors, removing the overlap among the predictors. 180

Multiple Regression Types • Step-wise = based upon highest correlation, that variable is entered first (computer makes the decision), theory building • Hierarchical = choose the order of entry, forced entry, theory testing 181

Multiple Regression • Allows one to cluster variables into Blocks. • Block 1: Demographic variables – (age, gender, SES) • Block 2: Psychological Well-Being – (depression, social support) • Block 3: Severity of Illness – (CD 4 count, AIDS dx, viral load, OIs) • Block 4: Treatment or control – 1= treatment and 0 = control 182

Regression Analysis • Multiple regression: one Y, multiple Xs. • Logistic regression: Y is dichotomous, popular in epidemiology, Y=disease or no disease; odds - risk ratio (not explained variance) • Canonical variate analysis: multiple Y and multiple X variables: Y 1+Y 2+Y 3=X 1+X 2+X 3 -linking physiological variables with psychosocial variables. 183

Multivariate Regression Models: • Path Analysis and now Structural Equation Modeling • Software program: AMOS • Measurement model is combined with predictive model • Keep in the picture the multicolinearity of variables (they are correlated!) • Allows for moderating variables (direct and indirect effects. 184

Multiple Dependent & Independent Path Analysis Modeling 185

Structural Equation Modeling Muscle ache Month 0 Fatigue Month 0 Intercept Muscle ache Month 1 Fatigue Month 1 Muscle ache Month 3 Fatigue Month 3 Muscle ache Month 6 Slope Fatigue Month 6 186

Factor Analysis • Exploration of instrument construct validity • Correlational technique • Requires only one administration of an instrument • Data reduction technique • A statistical procedure that requires artistic skills 187

Conceptual Types of Factor Analysis • Exploratory – see what is in the data set • Confirmatory – see if you can replicate the reported structure. 188

Factor Analysis • Principal Components – (principal factor or principal axes) 189

Correlation Matrix of Scale Items: Which items are related? Item 1 Item 2 Item 3 Item 4 1 0. 80 0. 30 0. 25 1 0. 40 0. 25 1 0. 70 1 190

Factor Analysis: An iterative process Factor extraction 191

Factor Analysis Factor III Communality Item 1 0. 80 0. 20 -0. 30 0. 77 Item 2 0. 75 0. 30 0. 01 0. 65 Item 3 0. 30 0. 80 0. 05 0. 63 Item 4 0. 25 0. 75 0. 20 0. 67 Eigenvalue 2. 10 2. 05 0. 56 % var 34% 30% 192

Definitions: • Communality: Square item loadings on each factor and sum over each ITEM • Eigenvalue: Square items loading down for each factor and sum over each FACTOR • Labeling Factors: figments of the authors imagination. Items 1 & 2 = Factor I; Items 3 & 4 = Factor II. 193

Factor Rotation Factors are mathematically rotated depending upon the perspective of the author. • Orthogonal – right angels, low inter-factor correlations, creates more independence of factors, good for multiple regression analysis, may not reflect well the actual data. (varimax) • Oblique – different types, let’s factors correlate with each other to the degree they actually do correlate, some like this and believe it better reflects that actual data, harder to use in multiple regression because of the multicolinearity. (oblimax) 194

Summary: Data Analysis • • • Measures of Central Tendency Measures of Relationships Testing Group Differences Correlational Multiple regression as a predictive (causal) technique. • Factor analysis as a scale development, construct validity technique 195

Ethical Guidelines for Nursing Research Vulnerability – a power relationship between health care provider and patient, family, or client. Vulnerable participants in research require more protection from harm. 196

Ethical Principles that Guide Research • • • Beneficence – doing good Non-malfeasances – doing no harm Fidelity – creating trust Justice – being fair Veracity – telling the truth Confidentiality – protecting or safeguarding participants identifying information 197

Ethical Principles that Guide Research Confidential – names kept guarded vs. Anonymous – no identifiers 198

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