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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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