Advanced Quantitative Methods

Advanced Quantitative Methods

William L. Holzemer, RN, Ph.D., FAANProfessor, School of NursingUniversity of California, San Franciscobill.holzemer@nursing.ucsf.edu

2

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.

3

Assignments

• PhD Students -individual assignments

• MS Students – group assignment– Mini-literature review

• Outcomes Model• Substruction• Synthesis Tables• Summary

4

Nursing = Nursing Science?

Definition of Nursing

American Nurses Association:

“Nursing is the assessment , diagnoses, and treatment of human responses”

5

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.”

6

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.”

7

Common Elements:Definitions of Nursing

• Person (individual, family, community)

• Health (Wellness & Illness)

• Environment

• Nursing (care, interventions, treatments)

8

Nursing Science

The body of knowledge that supports

evidence-based practice

9

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

10

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

11

Outcomes Model for Health Care Research(Holzemer, 1994)

Inputs1970’s

Processes 1980’s

Outcomes

1990’s

Client

Provider

Setting

12

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)

13

Outcomes Model: Nursing Process

Inputs Processes Outcomes

Client Problem Outcome

Provider Intervention

Setting

14

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

15

Outcomes Model: Your assignment(Think about a project or program of research)

Inputsz

Processes x

Outcomes

y

Client

Provider

Setting

16

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

17

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

18

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.”

19

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.”

20

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?

21

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.

22

Uses of Substruction

• Critique a published study

• Plan a new study

23

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

24

Substruction

Theory

(Theoretical system)

Construct

Concept

Deductive

(qualitative)

Methods

(Operational System)

Measures

Scaling/Data

analysis

(quantitative)

Inductive

25

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

26

Statements of Relationships

Construct:

Postulate:Statement of relationship between a construct and concepts

Pain consists of three concepts

Concepts:

Intensity

Location

Duration

27

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

28

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

29

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?

30

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

31

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?

32

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

33

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?

34

Literature Review

• What is known?

• What is not known?

• Resources– The Cochran Library – Library Data Bases

• PubMed• CINYL

35

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

36

Literature Review

S tud y 1 S tud y 2 S tud y 3

T o p ic

37

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.

38

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)

39

Table 3. Instruments

Studies

Instrument # items

Validity Reliability Utility

Smith (1999) McGill Pain Questionnaire

Jones (2003)

40

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)

41

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?

42

Research Designs

43

Research Design: Qualitative

• Ethnography

• Phenomenology

• Hermeneutics

• Grounded Theory

• Historical

• Case Study

• Narrative

44

Rigor in Qualitative Research

• Dependability

• Credibility

• Transferability

• Confirmability

45

Types of Quantitative Research Designs

• We will focus on RIGOR:

– Experimental

– Non-experimental

46

X,Y, Z notation

• Z = covariate • Severity of illness

• X = independent variable (interventions)• Self-care symptom management

• Y = dependent variable (outcome)• Quality of life

47

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?

48

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)

49

Literature Review Study Aims

Study Aims Study Question

Study Question Study Hypothesis

50

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.

51

Experimental Designs

52

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

53

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

54

Classic Experimental Design

O1exp X O2exp

R

O1con O2con

(pretest) (posttest)

The RCT is the Gold Standard for Evidence-Based Practice

55

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

56

Goal:

Statement of Causal Relationship

57

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.

58

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

59

Dimensions of Research Designs: Groups & Time

O1exp X O2exp

Groups (n=2 experimental & control)O1con O2con

-----------------------------------------------

Time (n=2) (repeated measures)

60

Dimensions of Research Designs: Groups & Time

Groups = between factors

Time = within factors

61

Types of Designs

• O - descriptive, one time

• O1 O2 O3 - descriptive, cohort, repeated measures)

• O1 X O2 (not an experimental design!) - pre-post-test

62

Types of Designs

• O1 X O2

O1 O2

RCT randomized controlled trial

63

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)

64

Types of Design

O1 X1 O2

R O1 X2 O2

O1 O2

# of groups? ___

# points in time? ___

65

Types of Designs

Post-test only design:

X O2

O2

What is the biggest threat to this post-test only design?

66

Types of Research Design

• Experimental (true)

• Quasi-Experimental (quasi)– No random assignment to groups

67

Design Validity

– Statistical conclusion validity

– Construct validity of Cause & Effect (X & Y)

– Internal validity

– External

68

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?

69

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?

70

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?

71

Design Validity

External Validity– Threat of low generalizability to people,

places, & time

– Can we generalize to others?

72

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.

73

Sampling[Sample selection, not assignment]

74

Terms

• Population

• Sample

• Element

- All possible subjects

-A subset of subjects

- One subject

75

What do we sample?

• People (e.g. subjects)

• Places (e.g. hospitals, units, cities)

• Time (e.g. season, am vs. pm shift )

76

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

77

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

78

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)

79

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

80

Sampling Error

Population (n=1000) Mean Age: 36.5 years Samples (n=50) Mean Age: 34.6 yrs 37.1 yrs 36.4 yrs.

81

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)

82

Sample Size and Sampling Error

small Sampling Error large

small large Sample Size

83

Sample Size Calculations

• Type of design

• Accessibility of participants

• Statistical tests planned

• Review of the literature

• Cost (time and money)

84

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

85

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.

86

Power Analysis Programs

• SPSS Pakcage

• nQuery Adviser Release 4.0 (most recent?)http://www.statsolusa.com

87

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.

88

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

89

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

90

Effect Size

Meanexp – Meancon

Effect Size = SD e & c

91

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.

92

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

93

Hypothesis Testing: Is it true or false?

• Null hypothesis: H0

– Mean (experimental) = Mean (control)

• Alternative hypothesis: H1

– Mean (experimental) =/= Mean (control)

94

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)

95

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?

96

Sample Loss in RCT

N=243

N=91

N=105

N=118

N=89

N=110

N=122

6 months

1 month

Randomization

97

Measurement “If it exists, it can be measured”

R. Cronbach

98

What we measure:

• Knowledge, Attitudes, Behaviors (KAB)

• Physiological variables

• Symptoms

• Skills

• Costs

99

Classical Measurement Theory:

Measurement: Reliability Observation = Truth (fact) +/- Error Validity

100

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

101

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.

102

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

103

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

104

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.

105

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?

106

Instrument Reliability

Question: can you trust the data?

• Stability – change over time

• Consistency – within item agreement

• Rater reliability – rater agreement

107

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

108

Cronbach’s alpha

11

2

n

Xmn

nSD =

2

1

21

1 SD

itemsSD

n

n

n

alpha =

109

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?

110

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

111

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

112

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

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?

114

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

115

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

117

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: _<25

_ 25-35

_ 36-45

_ >45

123

Dichotomous Variables

Do not do this:1 = Male2= Female Do this!1 = male0 = 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 yearsSD= 4.2Range: 22-45)

129

Formulas

N

Xn

n1

Mean =

SD =

11

2

n

Xmn

n

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 mean=median=mode?

131

Normal Curve: very robust!

M +1 +2-1-2

34% 34%

2.5% 2.5%

132

Normal Curves

133

Normal Curve(Mean=Median=Mode)

50% 50%

MeanMedianMode

Frequency

134

Non-Normal Curves

Y-A

xis

X-AxisY

-Axi

s

X-Axis

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

Y-A

xis

X-AxisY

-Ax

is

X-AxisY

-Ax

is

X-Axis

r = ?r = ?

r = ?

146

Variance

Area under the curve = SD2

Variance

147

Shared variance r2

If r = 0.80, r2 = 0.64

64%

148

Shared variance r2

If r = 1, 100%

If r = 0, 0%

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 ΔX ΔY?• 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 FactorTime: 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

Mc Me

BetweenVariance

WithinVariance

157

Examining Variance: No difference between the means

McMe

158

Examining Variance: Big difference between means

Mc Me

159

Examining Variance: Three groups

Mc Me2 Me1

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 > 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

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

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 (0.05/10=0.005)

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 = X1+X2+X3

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

Health Status

Smoking

Gender

Age

Gender 4%

Smoking 40%

Age 25%

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, 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.

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

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

186

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

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 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)

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

Best Wishes