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 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)

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

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 One tailed:   or  0 or  1  or   2 95%

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 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