research methods: 2 m.sc. physiotherapy/podiatry/pain inferential statistics
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Research Methods: 2M.Sc.
Physiotherapy/Podiatry/Pain
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
x
x
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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
groups of Variance
meansin Differencet statistic =
t statistic is interpreted relativeto the DF for sample(s)
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The t-test
21
21
-
-
xxSE
xxt statistic =
(Standard Error of the Difference)
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The t-test
)1(var
)1(var
-
2
2
1
1
21
nn
xxt
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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
One tailed: or 0 or 1 or 2
95%
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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 < 50 Shapiro-Wilk; n > 50 Kolmogorov
Smirnovp > 0.05 normal p < 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 < 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 < 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