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

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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 ... – PowerPoint PPT presentation

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


1
Research Methods 2M.Sc. Physiotherapy/Podiatry/P
ain
  • 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
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4
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

5
High variance big overlap
Medium variance medium overlap
Low variance small overlap
6
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

7
The t-test
t statistic
t statistic is interpreted relative to the DF for
sample(s)
8
The t-test
9
The t-test
10
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?

11
Two tailed ? ? 0 or ?1 ? ?2
95
One tailed ? ? or ? 0 or ?1 ? or ? ?2
12
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?

13
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

14
Heteroscedastic
Homoscedastic
15
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

16
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17
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?

18
Test 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

19
p values and types of errors
  • Difference is significant if less than 5
    probability it occurred by chance
  • p lt 0.05

20
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 lt 0.05

21
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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