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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: 2M.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 • Differences between sample • Relative to (Xi – )2 n Differences in the sample Measure(s) of Centrality Relative to the variance of the samples
High variance = big overlap Medium variance = medium overlap Low variance = small overlap
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
The t-test t statistic = t statistic is interpreted relative to the DF for sample(s)
t statistic = (Standard Error of the Difference) The t-test
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?
Two tailed: 0 or 1 2 95% One tailed: or 0 or 1 or 2
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…?
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
Heteroscedastic Homoscedastic
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
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?
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
p values and types of errors • Difference is significant if less than 5% probability it occurred by chance p < 0.05
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
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