Transcript Principles of Investigation B.Sc. (Hons) Physiotherapy Year 1

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
t statistic =
Differencein means
Varianceof groups
t statistic is interpreted relative
to the DF for sample(s)
The t-test
t statistic =
x1 - x 2
SE x 1 - x 2 
(Standard Error of the Difference)
The t-test
t 
x1 - x 2
var1
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, nScore 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