Advanced Quantitative Methods

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Advanced Quantitative Methods

• William L. Holzemer, RN, Ph.D., FAAN
• Professor, School of Nursing
• University of California, San Francisco
• bill.holzemer_at_nursing.ucsf.edu

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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 ElementsDefinitions 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

• 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

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Types of Research Methods (all have rules of
evidence!)

• Quantitative
• Non-Experimental or Descriptive
• Experimental or Randomized Controlled Trials
• Ethnography
• Content Analysis
• Models of analysis Parametric vs.
  non-parametric

• Qualitative
• Grounded theory
• Ethnography
• Critical feminist theory
• Phenomenology

Models of analysis fidelity to text or words of
interviewees
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Outcomes Model for Health Care Research(Holzemer,
1994)
Inputs? 1970s Processes ? 1980s Outcomes 1990s
Client
Provider
Setting
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Outcomes Model

• Heuristic
• Systems model (inputs are outputs, outputs become
  inputs)
• Relates to Donabedians 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)
Inputs? z 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?)
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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
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Substruction Operational System

• Pain Intensity
• Instrument
• VAS 10 cm scale
• (low to high pain)

• Functional Status
• Instrument1-5 Likert scale, 1low 5high
  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 income
• Continuous 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
Inputs? Z 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 ReviewHow to combine, synthesis, and
demonstrate direction?
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Literature Review
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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 ?X ? ?Y?
• 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)
• Oobservation
• 1 pretest or time one 2 posttest or time
  two
• X 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 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.

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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 (n2 experimental control)
• ?
• O1con O2con
• --------------------------
  ---------------------
• ? Time (n2) ?
• (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
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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
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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. 31 up to 301 subjects to variables.
  30 item questionnaire requires 90 to 900
  subjects.
• Chi square cant 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 (?2)

• 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 H0McMe Null H0 False H0Mc/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
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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
100
Type of Measures

• Standardized evidence as follows
• Systematically developed
• Evidence for instrument validity
• Evidence for instrument reliability
• 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
• Cronbachs alpha (consistency) one point in
  time, measures inter-item correlations, or
  agreements.
• Rater reliability (correct for change agreement)
• Inter-rater reliability Cohens kappa
• Intra-rater reliability Scotts pi

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Cronbachs alpha
alpha
SD
109
Cronbach alpha Reliability Estimates

• gt 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?

110
Internal Consistency Cronbachs alphaPerson A
Internally consistentPerson 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 error
• If alpha 0.70, 1 (0.70)2
• 1-.49 .51 error
• If alpha 0.70, it is the 5050 point
• of error vs. true value

112
Reliability Values

• Range 0 to 1
• No negative signs like correlations
• Cohens kappa and Scotts pi are always lower,
  i.e. 0.50, 0.60

113
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?

116
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.

118
Data Analysis
119
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

120
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.

121
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.

122
Coding Variables

• Capture data in its most continuous form
  possible.
• Age 35 years - get the actual value
• vs.
• Check one _lt25
• _ 25-35
• _ 36-45
• _ gt45

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Dichotomous Variables

• Do not do this
• 1 Male
• 2 Female
• Do this!
• 1 male
• 0 female
• Why? Add function

124
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

125
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.

126
Missing Data

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

127
Measures

• Central Tendency
• Relationships
• Effects

128
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)

129
Formulas
Mean
130
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 meanmedianmode?

131
Normal Curve very robust!
132
Normal Curves
133
Normal Curve(MeanMedianMode)
134
Non-Normal Curves
135
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)

136
Degrees of Freedom

• Statistical correction so one does not over
  estimate

137
Degrees of Freedom for ball 1?
138
Degrees of Freedom for ball 2?
139
Degrees of Freedom for ball 3?
140
Degrees of Freedom

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

141
Relationships or Associations
142
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.

143
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

144
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

145
Estimate the value of the correlation
146
Variance
147
Shared variance r2
148
Shared variance r2
149
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 ?X ? ?Y?
• Does a change in X cause a change in Y?
• Testing group differences (t or F tests)

150
Testing Effects of Interventions
151
Testing Group Differences

• t tests
• F tests (Analysis of Variance or ANOVA)
• (t tests are F tests with two groups)

152
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

153
Classic Experimental Design

• O1exp X O2exp
• ?
• R
• ?
• O1con O2con
• (pretest) (posttest)
• Group Between Factor
• Time Within Factor

154
Tests of Significance
3 4

1 O1 X O2

2 O1 O2

155
Testing Group Differences

• Between Variance
• F (or t)
• Within Variance

156
Examining Variance
157
Examining Variance No difference between the
means
158
Examining Variance Big difference between means
159
Examining Variance Three groups
160
Types of Designs

• O1 O2 O3
• change within group over time, repeated measures
  design

161
Types of Designs

• O1e X O2e
• O1c O2c
• change within group from O1e to O2e
• change between groups O2e and O2c

162
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.

163
Post-test only design

• X O2e
• O2c
• Unpaired t test
• Null hypothesis
• H0 O2e O2c
• Alternative directional hypothesis
• H1 O2e gt O2c

164

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

165
Standard Error of the Mean Average of sample SDs
166
Conceptual

• MeanE MeanC
• t
• standard error of the mean

167
Assumptions of ANOVA

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

168
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)

169
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

170
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?)

171
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
172
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
  (0.05/100.005)

173
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).

174
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

175
Multiple Regression Analysis

• Attempts to make causal statements of
  relationship
• Y X1X2X3
• Y dependent variable (health status)
• X1-3 predictors or independent variables
• Health Status Age Gender Smoking

176
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?

177
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.

178
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
179
Multiple Regression Shared Variance
Smoking 40
Age 25
Gender 4
180
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.

181
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

182
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

183
Regression Analysis

• Multiple regression one Y, multiple Xs.
• Logistic regression Y is dichotomous, popular
  in epidemiology, Ydisease or no disease odds -
  risk ratio (not explained variance)
• Canonical variate analysis multiple Y and
  multiple X variables Y1Y2Y3X1X2X3
• -linking physiological variables with
• psychosocial variables.

184
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.

185
Multiple Dependent Independent Path Analysis
Modeling
186
Structural Equation Modeling
187
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

188
Conceptual Types of Factor Analysis

• Exploratory see what is in the data set
• Confirmatory see if you can replicate the
  reported structure.

189
Factor Analysis

• Principal Components
• (principal factor
• or
• principal axes)

190
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
191
Factor Analysis

• An iterative process
• Factor extraction

192
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
193
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.

194
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, lets 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)

195
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

196
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.

197
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

198
Ethical Principles that Guide Research

• Confidential
• names kept guarded
• vs.
• Anonymous
• no identifiers

199

• Best Wishes