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

10. Central Tendency 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  How is it calculated?  Sum/n  Middle # (or middle two/2)  Most frequent value

11. Percentiles A measure of Variability 100 equal parts Relative position 75 th percentile 75% below this 24% above this Quartiles a common grouping 25 th (Q1), 50 th (Q2), 75 th (Q3), 100 th (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 σ 2 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) s 2 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 (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

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