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

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Research Methods 2M.Sc. Physiotherapy/Podiatry/P
ain

• Inferential Statistics

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Why ?

• 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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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

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

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

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Two tailed ? ? 0 or ?1 ? ?2
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One tailed ? ? or ? 0 or ?1 ? or ? ?2
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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?

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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

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Heteroscedastic
Homoscedastic
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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

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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?

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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

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p values and types of errors

• Difference is significant if less than 5
  probability it occurred by chance
• p lt 0.05

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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

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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