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Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain

Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain . Inferential Statistics. Why ?. Differences between samples/data sets Differences in means or medians of samples Different enough? Different by chance? Different due to treatment? Differences in  ?. Testing the differences.

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Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain

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  1. Research Methods: 2M.Sc. Physiotherapy/Podiatry/Pain Inferential Statistics

  2. Why ? • Differences between samples/data sets • Differences in means or medians of samples • Different enough? • Different by chance? • Different due to treatment? • Differences in ?

  3. Testing the differences • Differences between sample • Relative to (Xi – )2 n Differences in the sample Measure(s) of Centrality Relative to the variance of the samples

  4. High variance = big overlap Medium variance = medium overlap Low variance = small overlap

  5. Inferential statistical tests Put a value on this relationship; overlap versus difference Test that value against expected norms State probability of that degree of difference with that degree of overlap

  6. The t-test t statistic = t statistic is interpreted relative to the DF for sample(s)

  7. t statistic = (Standard Error of the Difference) The t-test

  8. The t-test

  9. The t-test • Look up t statistic in tables of the t distribution • Is t significant = is the difference between the two data sets significant ? • One or two tailed test?

  10. Two tailed:   0 or 1  2 95% One tailed:   or  0 or 1  or  2

  11. Assumptions; t-tests t statistic is only representative of the level of difference if data is Parametric Interval or Ratio and Normally distributed Only compares two samples, three or more…?

  12. Assumptions; 1 way ANOVA Three or more samples One-way Analysis of Variance = One-Way ANOVA Parametric Data which is Homoscedastic; SPSS; Levenes test for Homogeniety of Variance

  13. Heteroscedastic Homoscedastic

  14. Non-Parametric tests • Test differences in medians or rank order • Non Parametric equivalents of t-tests; Mann-Whitney U-test or Wilcoxon • Non Parametric equivalent of the One-way ANOVA; Kruskal Wallis Test or Friedmans

  15. Parametric or Non-Parametric ? • Parametric = Interval or Ratio Normally Distributed • Non-Parametric = Interval or Ratio not Normally Distributed and Nominal and Ordinal data • So…….. Test for normality?

  16. Test of Normality of Distribution • Normal Probability Plots; Shapiro-Wilk, Anderson Darling, Kolmogorov Smirnov, n-Score etc • Calculate a test statistic • SPSS: n < 50 Shapiro-Wilk; n > 50 Kolmogorov Smirnov p > 0.05 normal p < 0.05 not normal

  17. p values and types of errors • Difference is significant if less than 5% probability it occurred by chance p < 0.05

  18. p values and types of errors Type I (Alpha) error; There is no significant difference but you think there is. Protection by setting high “Alpha exclusion value” p < 0.05

  19. p values and types of errors Type II (Beta) error There is a significant difference and you miss it; Study has a low “power” Protection by using a large n

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