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PTP 560
• Research Methods
Week 8
Thomas Ruediger, PT
Systematic Review and Meta Analysis
Systematic review
• Structured approach
• Analysis of myriad information
• With detailed description of methods and criteria
• As opposed to classical review
If there are
• Sufficient data for further analysis, you can…
• Use quantitative index
• Develop single estimate of intervention effect
• This is now Meta-analysis=statistical analysis of a
systematic review
Figure 16.1
Levels of evidence
• Useful for categorizing
• Not owned by Systematic Review and Meta Analysis
•
•
•
•
•
1 (a,b,c) =
2 (a,b) =
3 (a,b) =
4
=
5
=
RCT, systematic review of RCT, CPRs
Cohort Study(ies), systematic reviews
Case Control Study(ies), systematic reviews
Case series, case control
Expert opinion or bench (basic) research
Table 16.1
Evaluating Methodologic Quality
• Study Bias
•
•
•
•
Selection - How comparison groups are formed
Performance
- Differences in provision of care
Attrition - Differential subject loss
Detection - Outcomes assessment differ
• Rating Scales
• Jadad Scale
• Instrument to Measure the Likelihood of Bias
• Physiotherapy Evidence Database (PEDro)
• Wide use in PT literature (Table 16.3)
• QUADAS Scale
• Qualitative Assessment of Diagnostic Accuracy Studies
Systematic Review or
Meta-Analysis?
• Meta-Analysis Powerful
• Must have statistical data sufficient for analysis
• Adds:
•
•
•
•
Statistical Power by increasing sample size
Improves effect size estimates
Resolves conflicting results
Improves generalizability
• Effect size
• The samples not pooled together
• Rather, each sample effect size index contributes
• Effect size index calculation =
mean difference between groups/pooled SD
Presenting Meta-analysis results
• Weighted Effect size
• As all studies not equal
• Larger the sample size, more precise estimate of effect
• Forest Plot
• Individual studies
• Cumulative result
• Let’s look at Hooked on Evidence
Descriptive Statistics
• Characterize
• Shape
• Central Tendency
• Variability
• Parameters are population characteristics
• When they are from a sample, statistics
Frequency Distributions
• Could look at all the data
• Scatterplot excellent for this
• Frequency Distribution
• 3 – 1s, 4 – 2s, 2 – 5s etc
• Grouping may be useful
• Graphing
• Stem and Leaf
• Leaf is the rightmost digit
• Stem are the rest
• Histogram of scores or classes (groups)
Skewed distributions
Central Tendency
• What is an average?
• Mean
• μ for population
• X for sample
• Median
• Mode

How is it calculated?

Sum/n

Middle # (or middle two/2)
Most frequent value

With Nominal data – Only mode is useful
With Ordinal Data – May use mode and/or median
Ratio/interval Data – All three measures may be used
Percentiles
• A measure of Variability
• 100 equal parts
• Relative position
• 75th percentile
• 75% below this
• 24% above this
• Quartiles a common grouping
• 25th (Q1), 50th (Q2), 75th (Q3) , 100th (Q4)
• Inter-quartile Range
• Distance between Q3-Q1
• Middle 50%
• Semi-inter-quartile Range
• Half the inter-quartile range
• Useful variability measure for skewed distributions
Population Variability
• How measurements differ from each other
• In total these always sum to zero
• Variance handles this
• Sum of squared deviations
• Divided by the number of measurements
• σ2 for population variance
• Standard deviation
• Square root of variance
• σ for population variance
Sample Variability
• How measurements differ from each other
• In total these always sum to zero
• Variance handles this
• Sum of squared deviations
• Divided by (the number of measurements – 1)
• s2 for sample variance
• Standard deviation
• Square root of variance
• s for sample standard deviation
Other Measures of Variability
• Range
•
•
•
•
Difference between highest and lowest
Usually described as
“Mean of 15 years, with a range of 11 to 23 years”
Here the range is 12
• Coefficient of Variation (CV = s/X * 100)
• Ratio of standard deviation to the mean, as %
• It is independent of units
• Good for comparing relative variation
• It accounts for differences in magnitude
• Excellent PT example in P & W
Statistical Inference
• Allow us to test theories and generalize
• Inference
• Specific to general in logic
• Sample to population in research
• Probability
• “Likelihood that any one event will occur, given ALL possible
outcomes
Probability and Distributions
• From P & W
• All men,
• μ = 69 inches,
• σ =3 inches
• What is the probability (p)
• that the next man selected• will be between 66 and 72 inches tall?-68%
• Greater than 78 tall?
• Less than ½ percent, only on one size. (.3%/2=.15%)
Sampling Error
• Difference between the population and sample
• Sampling error of the mean
• X -μ
• Sampling distribution of means consistently normal
• Reflects the Central Limit Theorem
• Standard Error of the Mean (σ x)
• Standard deviation of a sampling distribution (theoretical)
• Is an estimate of population standard deviation
• s x = s/√n (it is a function of the size of the sample)
• We can describe the range of values
• within a certain probability,
• of having a single sample,
• with the mean we find
95% probability, in a single random sample of finding
Confidence Intervals (CI)
• Range of scores in which the population mean (μ) lies
• Constructed around sample mean, X
• X is the Point estimate of μ
• CI = X ± (z) s x
Confidence Intervals (CI)
• Range of scores in which the population mean (μ) lies
• Constructed around sample mean, X
• X is the Point estimate of μ
• CI = X ± (z) s x
“When you see z, think standard deviation.”
1.96 is the most common z in the CI; reflects 95% of the total sampling distribution
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