PTP 560

1. PTP 560 • Research Methods Week 8 Thomas Ruediger, PT

2. 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

3. Levels of evidence • Useful for categorizing • Not owned by Systematic Review and Meta Analysis • 1 (a,b,c) = RCT, systematic review of RCT, CPRs • 2 (a,b) = Cohort Study(ies), systematic reviews • 3 (a,b) = Case Control Study(ies), systematic reviews • 4 = Case series, case control • 5 = Expert opinion or bench (basic) research Table 16.1

4. 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

5. 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

6. 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

7. Descriptive Statistics • Characterize • Shape • Central Tendency • Variability • Parameters are population characteristics • When they are from a sample, statistics

8. 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)

9. Skewed distributions Mean “pulled” to the tail by extreme measurements

10. Central Tendency • How is it calculated? • Sum/n • Middle # (or middle two/2) • Most frequent value • What is an average? • Mean • μ for population • X for sample • Median • Mode 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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%)

17. 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 (σx) • Standard deviation of a sampling distribution (theoretical) • Is an estimate of population standard deviation • sx = 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

18. 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

19. 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