Title: Research Methods: 2 M.Sc. Physiotherapy/Podiatry/Pain
1Research Methods 2M.Sc. Physiotherapy/Podiatry/P
ain
2Why ?
- Differences between samples/data sets
- Differences in means or medians of samples
- Different enough?
- Different by chance?
- Different due to treatment?
- Differences in ? ?
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4Testing 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
5High variance big overlap
Medium variance medium overlap
Low variance small overlap
6Inferential 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
7The t-test
t statistic
t statistic is interpreted relative to the DF for
sample(s)
8The t-test
9The t-test
10The 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?
11Two tailed ? ? 0 or ?1 ? ?2
95
One tailed ? ? or ? 0 or ?1 ? or ? ?2
12Assumptions 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?
13Assumptions 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
14Heteroscedastic
Homoscedastic
15Non-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
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17Parametric 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?
18Test of Normality of Distribution
- Normal Probability Plots Shapiro-Wilk, Anderson
Darling, Kolmogorov Smirnov, n-Score etc - Calculate a test statistic
- SPSS
- n lt 50 Shapiro-Wilk n gt 50 Kolmogorov Smirnov
- p gt 0.05 normal p lt 0.05 not normal
19p values and types of errors
- Difference is significant if less than 5
probability it occurred by chance - p lt 0.05
20p 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 lt 0.05
21p 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