Research Methods 2 M.Sc. PhysiotherapyPodiatryPain

							   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 x

• Relative to (Xi – x )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

                Difference in means
t statistic =
                Variance of groups

     t statistic is interpreted relative
     to the DF for sample(s)
                The t-test
                  x1 - x 2
t statistic =
                SE  x 1 - x 2 

 (Standard Error of the Difference)
        The t-test


           x1 - x 2
t 
       var 1        var 2
               
      (n1  1)   (n 2  1)
                  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




           95%




      One tailed:
  or  0 or 1  or  2
         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 Shapiro-Wilk; 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