1 advanced quantitative methods william l. holzemer, rn, ph.d., faan professor, school of nursing...
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Advanced Quantitative Methods
William L. Holzemer, RN, Ph.D., FAANProfessor, School of NursingUniversity of California, San [email protected]
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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.
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Assignments
• PhD Students -individual assignments
• MS Students – group assignment– Mini-literature review
• Outcomes Model• Substruction• Synthesis Tables• Summary
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Nursing = Nursing Science?
Definition of Nursing
American Nurses Association:
“Nursing is the assessment , diagnoses, and treatment of human responses”
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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.”
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Definition of NursingInternational 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.”
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Common Elements:Definitions of Nursing
• Person (individual, family, community)
• Health (Wellness & Illness)
• Environment
• Nursing (care, interventions, treatments)
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Nursing Science
The body of knowledge that supports
evidence-based practice
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Nursing Science Uses Various Research Methodologies
QualitativeUnderstandingInterview/observationDiscovering frameworksTextual (words)Theory generatingQuality of informant more
important than sample sizeRigorSubjectiveIntuitiveEmbedded knowledge
QuantitativePredictionSurvey/questionnairesExisting frameworksNumericalTheory testing (RCTs)Sample size core issue in
reliability of data RigorObjectivePublic
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Types of Research Methods: (all have rules of evidence!)
QuantitativeNon-Experimental or
Descriptive Experimental or Randomized
Controlled TrialsEthnographyContent Analysis
Models of analysis: Parametric vs. non-parametric
QualitativeGrounded theoryEthnographyCritical feminist theoryPhenomenology
Models of analysis: fidelity to text or words of interviewees
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Outcomes Model for Health Care Research(Holzemer, 1994)
Inputs1970’s
Processes 1980’s
Outcomes
1990’s
Client
Provider
Setting
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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)
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Outcomes Model: Nursing Process
Inputs Processes Outcomes
Client Problem Outcome
Provider Intervention
Setting
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Outcomes Model for Health Care Research
Inputs(Covariate,
confounding variable)
Processes (Independent
Variable)
Outcomes(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
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Outcomes Model: Your assignment(Think about a project or program of research)
Inputsz
Processes x
Outcomes
y
Client
Provider
Setting
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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
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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
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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.”
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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.”
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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?
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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.
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Uses of Substruction
• Critique a published study
• Plan a new study
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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
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Substruction
Theory
(Theoretical system)
Construct
Concept
Deductive
(qualitative)
Methods
(Operational System)
Measures
Scaling/Data
analysis
(quantitative)
Inductive
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Substruction: Building Blocks or Statements of Relationships
Construct
Pain
axiom Construct
quality of life
Concept
Intensity
proposition Concept
functional status
Measure
10 cm scale
hypothesis Measure
mobility scale
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Statements of Relationships
Construct:
Postulate:Statement of relationship between a construct and concepts
Pain consists of three concepts
Concepts:
Intensity
Location
Duration
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Substruction: Research Design Perspective
Focus of Study (RCT?)
Co-variates ZSeverity of illness for risk adjustment
(analysis of covariance)
Independent Variable Xtreatment
how measured?Dependent Variable Y
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Substruction: Theoretical System, an example
Pain Intervention Study
Post Surgical Patient Severity of
illness age
gender
Pain Management Intervention
Patient communicationStanding PRN orders
Non pharmacological tx
Pain Control
Length of stay
Patient Satisfaction
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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?
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Scaling
Discrete: non-parametric (Chi square)• Nominal gender• Ordinal low, medium, high incomeContinuous: parametric (t or F tests)• Interval Likert scale, 1-5
functionality• Ratio money, age, blood
pressure
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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?
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Is there a relationship between touch and pain control, accounting for initial amount
of post-operative pain? rx,y.z
InputsZ
Processes X
Outcomes
Y
Client Post operative pain
Pain Control
Provider Therapeutic Touch vs NL care
Setting
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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?
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Literature Review
• What is known?
• What is not known?
• Resources– The Cochran Library – Library Data Bases
• PubMed• CINYL
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Literature Review:How to combine, synthesis, and demonstrate direction?
S tud y 1 S tud y 2 S tud y 3
T o p ic
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Literature Review
S tud y 1 S tud y 2 S tud y 3
T o p ic
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Table 1. Outline of study variables related to your topic
Studies
Covariates
Z
Interventions
Independent variable
X
Outcomes
Dependent Variable
Y
Smith (1999)
Jones (2003)
Etc.
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Table 2. Threats to validity of research studies related to topic
Author (year)
Type of Design
Diagram Statistical Conclusion Validity
Construct Validity of Cause & Effect
Internal Validity
External Validity
Smith (1999)
RCT O X1 O
O X2 O
O O
n/a
Jones (2003)
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Table 3. Instruments
Studies
Instrument # items
Validity Reliability Utility
Smith (1999) McGill Pain Questionnaire
Jones (2003)
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Table 4. Power analysis for literature review on topic.
Studies
Sample
Size
Alpha Power Effect Size
Smith (1999) 32 –exp
40 – cont
0.05 0.60 Est. at medium
Jones (2003)
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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?
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Research Designs
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Research Design: Qualitative
• Ethnography
• Phenomenology
• Hermeneutics
• Grounded Theory
• Historical
• Case Study
• Narrative
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Rigor in Qualitative Research
• Dependability
• Credibility
• Transferability
• Confirmability
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Types of Quantitative Research Designs
• We will focus on RIGOR:
– Experimental
– Non-experimental
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X,Y, Z notation
• Z = covariate • Severity of illness
• X = independent variable (interventions)• Self-care symptom management
• Y = dependent variable (outcome)• Quality of life
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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?
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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)
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Literature Review Study Aims
Study Aims Study Question
Study Question Study Hypothesis
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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.
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Experimental Designs
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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
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Classic Experimental Design
O1exp X O2exp
R
O1con O2con
(pretest) (posttest)
O=observation1 = pretest or time one; 2 = posttest or time twoX = intervention
R = random assignment to groups
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Classic Experimental Design
O1exp X O2exp
R
O1con O2con
(pretest) (posttest)
The RCT is the Gold Standard for Evidence-Based Practice
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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
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Goal:
Statement of Causal Relationship
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Conditions Required to Make a Causal Statement: X causes Y
1. X precedes Y2. X and Y are correlated3. Everything else controlled or
eliminated. No Z variables impacting outcome.
4. We never prove something, we gather evidence that supports our claim.
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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
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Dimensions of Research Designs: Groups & Time
O1exp X O2exp
Groups (n=2 experimental & control)O1con O2con
-----------------------------------------------
Time (n=2) (repeated measures)
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Dimensions of Research Designs: Groups & Time
Groups = between factors
Time = within factors
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Types of Designs
• O - descriptive, one time
• O1 O2 O3 - descriptive, cohort, repeated measures)
• O1 X O2 (not an experimental design!) - pre-post-test
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Types of Designs
• O1 X O2
O1 O2
RCT randomized controlled trial
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Types of Designs
• O1 O2 O3 X O4 O5 O6
O1 O2 O3 O4 O5 O6
• O1 X O2 Xno O3 X O4 Xno O5
(repeated measures vs. time series designs)
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Types of Design
O1 X1 O2
R O1 X2 O2
O1 O2
# of groups? ___
# points in time? ___
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Types of Designs
Post-test only design:
X O2
O2
What is the biggest threat to this post-test only design?
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Types of Research Design
• Experimental (true)
• Quasi-Experimental (quasi)– No random assignment to groups
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Design Validity
– Statistical conclusion validity
– Construct validity of Cause & Effect (X & Y)
– Internal validity
– External
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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?
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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?
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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?
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Design Validity
External Validity– Threat of low generalizability to people,
places, & time
– Can we generalize to others?
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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.
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Sampling[Sample selection, not assignment]
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Terms
• Population
• Sample
• Element
- All possible subjects
-A subset of subjects
- One subject
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What do we sample?
• People (e.g. subjects)
• Places (e.g. hospitals, units, cities)
• Time (e.g. season, am vs. pm shift )
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Sampling: What do we do?
• Random Assignment
-is designed to equalize the “Z” variables in the experimental and control groups
• Random Selection
-is designed to equalize the “z” variables that exist in the population to be equally distributed in a sample
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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
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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)
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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
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Sampling Error
Population (n=1000) Mean Age: 36.5 years Samples (n=50) Mean Age: 34.6 yrs 37.1 yrs 36.4 yrs.
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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)
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Sample Size and Sampling Error
small Sampling Error large
small large Sample Size
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Sample Size Calculations
• Type of design
• Accessibility of participants
• Statistical tests planned
• Review of the literature
• Cost (time and money)
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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
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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.
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Power Analysis Programs
• SPSS Pakcage
• nQuery Adviser Release 4.0 (most recent?)http://www.statsolusa.com
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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.
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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
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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
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Effect Size
Meanexp – Meancon
Effect Size = SD e & c
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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.
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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
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Hypothesis Testing: Is it true or false?
• Null hypothesis: H0
– Mean (experimental) = Mean (control)
• Alternative hypothesis: H1
– Mean (experimental) =/= Mean (control)
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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)
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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?
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Sample Loss in RCT
N=243
N=91
N=105
N=118
N=89
N=110
N=122
6 months
1 month
Randomization
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Measurement “If it exists, it can be measured”
R. Cronbach
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What we measure:
• Knowledge, Attitudes, Behaviors (KAB)
• Physiological variables
• Symptoms
• Skills
• Costs
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Classical Measurement Theory:
Measurement: Reliability Observation = Truth (fact) +/- Error Validity
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Type of Measures
• Standardized – evidence as follows:1. Systematically developed
2. Evidence for instrument validity
3. Evidence for instrument reliability
4. Evidence for instrument utility – time, scoring, costs, sensitive to change over time
• Non-standardized
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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.
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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
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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
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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.
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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?
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Instrument Reliability
Question: can you trust the data?
• Stability – change over time
• Consistency – within item agreement
• Rater reliability – rater agreement
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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
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Cronbach’s alpha
11
2
n
Xmn
nSD =
2
1
21
1 SD
itemsSD
n
n
n
alpha =
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Cronbach alpha Reliability Estimates:
• > 0.90– Excellent reliability, required for decision-
making 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?
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Internal Consistency: Cronbach’s alphaPerson A: Internally consistent
Person B: Internally inconsistent
Item
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
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Error in Reliability Estimates
“Error = 1 – (Reliability Estimate)2”If alpha = 0.90, 1-(0.90)2
1-0.89 = .11 errorIf alpha = 0.70, 1 – (0.70)2
1-.49 = .51 errorIf alpha = 0.70, it is the 50:50 point
of error vs. true value
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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
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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?
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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
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Quiz:
• Can a scale be valid and not reliable?
• Can a scale be reliable and not valid?
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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
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Translation• Forward translation (A to B)
• Backward translation (B to A)
• Conceptual equivalency across cultures
• Using of slang, idioms, etc.
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Data Analysis
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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
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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.
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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.
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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
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Dichotomous Variables
Do not do this:1 = Male2= Female Do this!1 = male0 = female
Why? Add function
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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
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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.
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Missing Data
Pairwise: just a particular correlation is removed, best choice to conserve power
Listwise: removes variables, required in repeated measures designs.
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Measures:
• Central Tendency
• Relationships
• Effects
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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 yearsSD= 4.2Range: 22-45)
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Formulas
N
Xn
n1
Mean =
SD =
11
2
n
Xmn
n
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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?
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Normal Curve: very robust!
M +1 +2-1-2
34% 34%
2.5% 2.5%
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Normal Curves
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Normal Curve(Mean=Median=Mode)
50% 50%
MeanMedianMode
Frequency
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Non-Normal Curves
Y-A
xis
X-AxisY
-Axi
s
X-Axis
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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)
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Degrees of Freedom
• Statistical correction so one does not over estimate
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Degrees of Freedom for ball 1?
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Degrees of Freedom for ball 2?
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Degrees of Freedom for ball 3?
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Degrees of Freedom
• Sample size (n-1)
• Number of groups (k-1)
• Number of points in time (l-1)
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Relationships or Associations
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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.
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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
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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
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Estimate the value of the correlation
Y-A
xis
X-AxisY
-Ax
is
X-AxisY
-Ax
is
X-Axis
r = ?r = ?
r = ?
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Variance
Area under the curve = SD2
Variance
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Shared variance r2
If r = 0.80, r2 = 0.64
64%
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Shared variance r2
If r = 1, 100%
If r = 0, 0%
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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)
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Testing Effects of Interventions
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Testing Group Differences
• t tests
• F tests (Analysis of Variance or ANOVA)
(t tests are F tests with two groups)
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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
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Classic Experimental Design
O1exp X O2exp
R
O1con O2con
(pretest) (posttest)
Group: Between FactorTime: Within Factor
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Tests of Significance
3 4
1 O1 X O2
2 O1 O2
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Testing Group Differences
Between Variance
F (or t) =
Within Variance
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Examining Variance
Mc Me
BetweenVariance
WithinVariance
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Examining Variance: No difference between the means
McMe
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Examining Variance: Big difference between means
Mc Me
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Examining Variance: Three groups
Mc Me2 Me1
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Types of Designs
O1 O2 O3
change within group over time, repeated measures design
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Types of Designs
O1e X O2e
O1c O2c
change within group from O1e to O2e
change between groups O2e and O2c
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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.
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Post-test only design
• X O2e
O2c
Unpaired t test
Null hypothesis:
H0: O2e = O2c
Alternative directional hypothesis:
H1: O2e > O2c
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• Standard Deviation– how scores vary around a mean
• Standard Error of the Mean– how mean scores vary around a population
mean
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Standard Error of the Mean: Average of sample SDs
Population (n=1000) Mean Age: 36.5 years Samples (n=50) Mean Age: 34.6 yrs 37.1 yrs 36.4 yrs. SD 3.4 3.8 4.1
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Conceptual:
MeanE – MeanC
t =
standard error of the mean
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Assumptions of ANOVA
• Normal distribution
• Independence of measures
• Continuous scaling
• Linear relationship between variables
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3 X 2 ANOVA
O1exp X1 O2exp
R O1exp X2 O2exp
O1con O2con
One between factor: group (3 levels)One within factor: time (2 levels)
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Omnibus F Test
O1exp X1 O2exp
R 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
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Post-hoc comparisons
O1exp1 X1 O2exp1
R O1exp2 X2 O2exp2
O1con O2con
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?)
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Tests of Significance
Non-parametric Parametric
Two-groups
Paired
Unpaired
Wilcoxin Rank
Mann-Whitney U
Paired t test
Unpaired t test
More than two-groups
Repeated measures
Independent groups
Friedman test
Kruskal -Wallis
ANOVA
Repeated measures ANOVA
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Galloping alpha
• Danger in conducting multiple t tests or doing item-level 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)
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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).
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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
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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
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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?
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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.
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Health Status = Age + Gender + Smoking
Health Status
Y
Age
X1
r2
Gender
X2
r2
Smoking
X3
r2
Health Status
Y
1 0.25
6%
0.04
0%
0.40
16%
Age
X1
1 0.11
1%
.05
0%
Gender
X2
1 .20
4%
Smoking
X3
1
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Multiple Regression: Shared Variance
Health Status
Smoking
Gender
Age
Gender 4%
Smoking 40%
Age 25%
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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.
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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
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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
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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.
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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.
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Multiple Dependent & Independent Path Analysis Modeling
Age
Gender
Social Support
Severity of illness
Cognitive Ability
Adherence to diet
Diabetic Control
Relationships are based upon the literature review and then potentially explored, discovered, tested, or validated in a study
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Structural Equation Modeling
Intercept
Slope
Muscle ache Month 0
Muscle acheMonth 1
Muscle ache Month 3
Muscle ache Month 6
Intercept
Slope
Fatigue Month 0
Fatigue Month 1
Fatigue Month 3
Fatigue Month 6
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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
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Conceptual Types of Factor Analysis
• Exploratory – see what is in the data set
• Confirmatory – see if you can replicate the reported structure.
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Factor Analysis
• Principal Components –
(principal factor
or
principal axes)
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Correlation Matrix of Scale Items: Which items are related?
Item 1 Item 2 Item 3 Item 4
Item 1 1 0.80 0.30 0.25
Item 2 1 0.40 0.25
Item 3 1 0.70
Item 4 1
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Factor Analysis:
An iterative process
Factor extraction
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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%
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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.
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Factor RotationFactors are mathematically rotated dependingupon 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)
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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
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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.
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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
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Ethical Principles that Guide Research
Confidential– names kept guarded
vs.
Anonymous– no identifiers
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Best Wishes