Transcript STATISTICAL ANALYSIS FOR THE MATHEMATICALLY

STATISTICAL ANALYSIS FOR THE
MATHEMATICALLY-CHALLENGED
Associate Professor Phua Kai Lit
School of Medicine & Health Sciences
Monash University
(Sunway Campus, Malaysia)
December 2012
How do you select an appropriate
Statistical Test to analyse your data?
• Relax! This is easily done with the help of the
following table:
Note: This table has been adapted from Table 37.1 “Selecting a Statistical
Test” presented in the website http://www.graphpad.com
Measurement
(from an
underlying Normal
Distribution)
Rank or
Binomial (only two
Measurement
outcomes are
(from an
possible)
underlying
population which is
not a Normal
Distribution
Describe one
sample
Mean, standard
deviation, variance
Median,
interquartile range
Proportion
Compare a sample
to a hypothetical
value or
hypothetical
distribution
Student’s t-test for
one sample
(use the Z-test for a
large sample, i.e.
n > 29)
Wilcoxon signedrank test
Chi-square
goodness-of-fit test
Compare two
Student’s t-test for
unpaired or
unpaired samples
unmatched samples (use the Z-test for
samples > 29)
Mann-Whitney test Chi-square test of
association (Use
or the Wilcoxon
Fisher’s exact test
rank sums test
for small samples)
Note: This table has been adapted from Table 37.1 “Selecting a
Statistical Test” presented in the website http://www.graphpad.com
Measurement
(from an
underlying Normal
Distribution)
Rank or
Binomial (only two
Measurement
outcomes are
(from an
possible)
underlying
population which is
not a Normal
Distribution
Wilcoxon matched- McNemar’s test
pairs signed-rank
test
Compare two
paired/matched
samples
Student’s t-test for
two paired samples
Compare three or
more unmatched
samples
One-way ANOVA
(analysis of
variance)
Compare three or
more matched
samples
Repeated measures Friedman’s two way Cochrane Q test
ANOVA
analysis of variance
test
Kruskal-Wallis oneway analysis of
variance test
Chi-square test of
association
Note: This table has been adapted from Table 37.1 “Selecting a
Statistical Test” presented in the website http://www.graphpad.com
Measurement
(from an
underlying Normal
Distribution)
Measure
association
between two
variables
Pearson’s
correlation
coefficient
Predict value of one Simple linear
variable from
regression
another variable
Predict value of one Multiple linear
variable from
regression
several other
variables
Rank or
Binomial (only two
Measurement
outcomes are
(from an
possible)
underlying
population which is
not a Normal
Distribution
Contingency
Spearman’s rank
coefficients
correlation
coefficient
Nonparametric
regression
Simple logistic
regression
Multiple logistic
regression
After choosing your stats test ….
• Input your data and run the stats test – here is
an online site where you can run your stats
test
• www.graphpad.com/quickcalcs/index.cfm
How to interprete the output from
your chosen Stats Test (1)
• 1. Look at the p-value : if the p-value is less than 0.05, it is
statistically significant. You will then reject H0 and accept
H1. If the p-value is less than 0.01, it is highly statistically
significant. You will then reject H0 and accept H1.
• Note: H0 is the “null hypothesis” and H1 is the “research
hypothesis”. The null hypothesis is the hypothesis you wish
to reject. It is usually stated in a negative manner, e.g. “no
association between Variable X and Variable Y” (for the Chisquare test of association) or “no difference between
Population Mean X and Population Mean Y” (for the t-test
of difference between two means)
How to interprete the output from
your chosen Stats Test (2)
• 2. Look at the 95% Confidence Interval (if it is in
the output):
• For Relative Risk analysis or Odds Ratio analysis
(two kinds of stats tests used in epidemiology),
reject H0 and accept H1 if the 95% Confidence
Interval does not contain 1
• For the t-test of difference between two
population means, reject H0 and accept H1if the
95% Confidence Interval does not contain 0 (zero)
Additional Resources
(to help you understand Statistics)
• http://phuakl.tripod.com/biostatistics1.html
• http://phuakl.tripod.com/biostatistics2.html
• http://www.statsoft.com/textbook/elementar
y-statistics-concepts/button/1/
Helpful books …… some written by me
and my co-authors 
Thanks for watching !
(Love statistics, hate computers –
when they fail to run )