Advanced Quantitative Methods William L. Holzemer, RN, Ph.D., FAAN Professor, School of Nursing University of California, San Francisco [email protected] 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 • PhD 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 1980’s Outcomes 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 Problem Outcomes 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 x Outcomes y Client Provider Setting 15 Where Should We Find EvidenceBased 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 the 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 Methods (Operational System) Measures Concept Deductive (qualitative) Scaling/Data analysis (quantitative) Inductive 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? 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 the 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 the 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 • PubMed • CINYL 34 Literature Review: How to combine, synthesis, and demonstrate direction? Topic Study 1 Study 2 Study 3 35 Literature Review Topic Study 1 Study 2 Study 3 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 X1 O O X2 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 McGill 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 Aims Study Question 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: H0: 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 O1exp X O2exp O1con O2con 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 O1exp X O2exp O1con O2con 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 O1exp X O2exp Groups (n=2 experimental & control) O1con O2con ----------------------------------------------- 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 • O1 O2 O3 - descriptive, cohort, repeated measures) • O1 X O2 (not an experimental design!) - prepost-test 61 Types of Designs • O1 O1 X O2 O2 RCT randomized controlled trial 62 Types of Designs • O 1 O 2 O 3 X O4 O 5 O 6 O 1 O2 O3 O4 O5 O6 • O1 X O2 Xno O3 X O4 Xno O5 (repeated measures vs. time series designs) 63 Types of Design R O1 O1 O1 X1 X2 O2 O2 O2 # of groups? ___ # points in time? ___ 64 Types of Designs Post-test only design: X O2 O2 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 10th 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 Population (n=1000) Mean Age: 36.5 years Samples (n=50) Mean Age: 34.6 yrs 37.1 yrs 36.4 yrs. 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 small Sampling Error large small large Sample Size 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 • nQuery 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 R2 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: H0 – Mean (experimental) = Mean (control) • Alternative hypothesis: H1 – Mean (experimental) =/= Mean (control) 93 Hypothesis Testing and Power Goal: Reject H0 REALITY REALITY Null H0 True H0:Mc=Me Null H0 False H0:Mc=/=Me DECISION Reject H0 Type I Error Power (1-Beta) DECISION Accept H0 Correct Decision Type II Error (Beta) 94 Quiz: • If sample size goes up, what happens to power? • If alpha goes from .05 to .l01, 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: Measurement: Reliability Observation = Truth (fact) +/- Error Validity 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 n 2 1 SD items n 1 alpha = 2 n 1 SD n SD = 2 m X n 1 n 1 108 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 n X n 1 Mean = N n 2 m X n SD = 1 n 1 129 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! 34% 34% 2.5% 2.5% -2 -1 M +1 +2 131 Normal Curves 132 Normal Curve (Mean=Median=Mode) Frequency 50% 50% Mean Median Mode 133 Y-Axis Non-Normal Curves Y-Axis X-Axis X-Axis 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 X-Axis Y-Axis r=? X-Axis Y-Axis r=? Y-Axis Estimate the value of the correlation r=? X-Axis 145 Variance Area under the curve = SD2 Variance 146 Shared variance r2 If r = 0.80, r2 = 0.64 64% 147 Shared variance r2 If r = 1, If r = 0, 100% 0% 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 O1exp X O2exp O1con O2con R (pretest) (posttest) Group: Between Factor Time: Within Factor 153 Tests of Significance 3 4 1 O1 X O2 2 O1 O2 154 Testing Group Differences Between Variance F (or t) = Within Variance 155 Examining Variance Between Variance Within Variance Mc Me 156 Examining Variance: No difference between the means Mc Me 157 Examining Variance: Big difference between means Mc Me 158 Examining Variance: Three groups Mc Me2 Me1 159 Types of Designs O 1 O2 O3 change within group over time, repeated measures design 160 Types of Designs O1e O1c X O2e O2c change within group from O1e to O2e change between groups O2e and O2c 161 How to analyze this design? • O1e O2e O3e X O4e O5e O6e O1c O2c O3c O4c O5c O6c • 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 O2e O2c Unpaired t test Null hypothesis: H0: O2e = O2c Alternative directional hypothesis: H1: O2e > O2c 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 Population (n=1000) Mean Age: 36.5 years Samples (n=50) Mean Age: SD 34.6 yrs 3.4 37.1 yrs 3.8 36.4 yrs. 4.1 165 Conceptual: MeanE – MeanC 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 O1exp X1 O2exp O1exp X2 O2exp O1con O2con One between factor: group (3 levels) One within factor: time (2 levels) 168 Omnibus F Test R O1exp X1 O2exp O1exp X2 O2exp O1con O2con 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 O1exp1 X1 O2exp1 O1exp2 X2 O2exp2 O1con O2con R Types: Scheffé, Tukey – control for degrees of freedom in different ways; compares all possible two way comparisons H0: O2exp1 = O2exp2 = O2con If you reject Null, or F test is significant, then you can look for two-way differences. (O2exp1= O2exp2?) or (O2exp2= O2con?) or (O2exp1 = O2con?) 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 = X1+X2+X3 Y = dependent variable (health status) X1-3 = 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 X1 Gender X2 Smoking X3 Health Status Y Age X1 r2 Gender X2 r2 Smoking X3 r2 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 r2 • 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 – (CD4 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: Y1+Y2+Y3=X1+X2+X3 -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 Relationships are based upon the literature review and then potentially explored, discovered, tested, or validated in a study Age Severity of illness Adherence to diet Gender Diabetic Control Cognitive Ability Social Support 185 Structural Equation Modeling Muscle ache Month 0 Fatigue Month 0 Intercep t Intercept Muscle ache Month 1 Fatigue Month 1 Muscle ache Month 3 Fatigue Month 3 Muscle ache Month 6 Slope 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 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 I Factor II 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% 10% 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 Best Wishes

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