Principles of statistical testing
(1) simple lie
(2) treacherous lie
(3) Statistics
Benjamin Disraeli
What is statistics?
 the way data are collected, organised, presented,
analysed and interpreted
 statistics helps to decide
– descriptive
 basic characteristics of the data
– inductive
 characterisation of the sample or population studied, which make
possible to interfere characteristics of the whole population (entire
“sample”)
Why do we need statistics?  variability!
repeated measurements
of temperature
18.2°C
18.5°C
19.1°C
18.7°C
variability of height
in population
180 cm
175 cm
165 cm
157 cm
diversity in biological
populations
inter-population or ethnical
differences
= BIODIVERZITY
temporal changes/
fluctuations
time
statistics is about variability !!!
Type of data
 data, measures
– qualitative = descriptive
 nominal, binary
e.g. blood groups A, B, 0, AB or Rh+, Rh
ordinal, categorical
e.g. grades NYHA I, II, III, IV or TNM system (cancer)
– quantitative = measurable on scale
 directly measured values
 interval (how much more?)
 ratios (how many times?)
Raw data – not too clear
DNA DN_kod UREA KREATININ glom_filt sRAGE
HER0087 3 7.6 97 1.172 9660.3
HER0037 3 7.6 139 0.574 5843
HER0009 3 6 118 1.502 5753.5
HER0012 3 17.3 274 0.442 5400
HER0118 3 22.6 156 0.463 5386.7
HER0094 3 10.8 234 0.812 5312.4
HER0144 3 5200
KRUS002 3 25.9 309 0.393 4947.8
HER0006 3 7.5 118 1.028 4944.5
HER0007 3 4.7 84 0.764 4917.8
HER0122 3 28.4 295 0.308 4627.1
HER0128 3 7.2 123 1.048 4503.5
KRUS50 3 37.8 525 0.284 4446
HER0035 3 7.1 111 0.739 4404
HER0001 3 14.2 188 0.557 4395.1
HER0057 3 21.8 281 0.703 4389.2
HER0015 3 7.2 75 2.703 4263.3
HER0111 3 13.7 131 0.954 4188.9
KRUS042 3 4.4 104 0.983 4127
HER0047 3 26 333 0.244 4101.9
HER0062 3 22.8 169 0.42 3852.7
HER0002 3 6.9 135 0.999 3815.3
HER0115 3 18.3 152 0.396 3741.2
KRUS045 3 4.4 85 1.7 3693.3
KRUS001 3 20.5 178 0.861 3621.5
M__0136 2 3606.9
HER0086 3 24.7 300 0.237 3577.7
HER0132 3 13 154 0.608 3409.8
HER0010 3 6.4 64 1.4 3398
HER0032 3 7.3 73 1.839 3325.5
HER0005 3 3.9 89 2.074 3318.7
KRUS016 2 6 105 2.38 3243.2
HER0071 3 7.3 120 0.769 3234.5
KRUS009 3 10.8 188 0.89 3212.6
M__0164 1 7.3 59 3203.9
OLS0008 2 3203.9
HER0061 3 18.2 241 0.277 3080.6
HER0065 3 7.2 116 0.953 3072.3
HER0058 3 16.8 158 0.668 3066
HER0014 3 14.6 187 0.0765 3047.4
Graphical data description
Examples of real data
Data description
 position measures (central tendency measures)
– mean ()
– median (= 50% quintile)
 frequency middle
– quartiles
 upper 25%, median, lower 75%
– mode
 the most frequent value
 variability measures
– variance (2)
– standard deviation (SD, )
– standard error of mean (SEM)
– coefficient of variance (CV= /)
– min-max (= range)
– skewness
– kurtosis
 distribution
Data description
 frequency (polygon, histogram)
original ordered histogram
data data
115 <100: 0
135 100-110: 1
120 111-120: 0
140 121-130: 2
125 131-140: 4
130 141-150: 8
150 151-160: 4
145 161-170: 11
. >171: 0
.
.
0
2
4
6
8
10
12
100-110
111-120
121-130
131-140
141-150
151-160
161-170
171-180
Distribution
 continuous
– normal
– asymmetrical
– exponential
– log-normal
 discrete
– binomial
– Poisson
Mean vs. median vs. mode(s)
 numbers:13, 18,
13, 14, 13, 16, 14,
21, 13
 x = (13 + 18 + 13 +
14 + 13 + 16 + 14 +
21 + 13) ÷ 9 = 15
 median = (9 + 1) ÷
2 = 10 ÷ 2 = 5. číslo
= 14
 mode = 13
 range = 21 – 13 = 8
Normal (Gaussian)  Student  symmetrical
distribution
 not every symmetrical distribution has
to be normal !!
– there are several conditions that have
to be fulfilled
 interval density of frequencies
 distribution function
 skewness = 0, kurtosis = 0
– data transformation
 mathematical operation that makes
original data normally distributed
 Student distribution is an
approximation of the normal
distribution for smaller sets of data
 test of normality
– Kolmogorov-Smirnov
– Shapiro-Wilks
 null hypothesis: distribution tested is not
different from the normal one
2
)(
2
1
2
1
)(
z
ezf



Normal distribution
Relationship between variables
 Correlation = relationship
(dependence) between the two variables
– correlation coefficient = degree of (linear)
dependence of the two variables X and Y
 Pearson (parametric)
 Spearman (non-parametric)
 Regression = functional relationship
between variables (i.e. equation)
– one- or multidimensional
– linear vs. logistic
– interpretation: assessment of the value
(or probability) of one parameter (event)
when knowing the value of the other one
Examples
Principles of statistical thinking
 inferences about the whole population
(sample) based on the results obtained from
the limited study sample
– whole population (sample)
 e.g. entire living human population
 we want to know facts applying to this whole
population and use them (e.g. in medicine)
– selection
 no way we van study every
single member of the whole
population or sample
 we have to select “representative”
sub-set which will
serve to obtain results valid
for the whole population
– random sample
 every subject has an equal
chance to be selected
Statistical hypothesis
 our personal research hypothesis
– e.g. “We think that due to the effects of the newly described drug
(…) on blood pressure lowering our proposed treatment regimen –
tested in this study – will offer better hypertension therapy
compared to the current one”.
 statistical hypothesis = mathematical formulation of our
research hypothesis
– the question of interest is simplified into two competing claims /
hypotheses between which we have a choice
 null hypothesis (H0): e.g. there is no difference on average in the effect
of an “old” and “new” drug
1 = 2 (equality of means)
1 = 2 (equality of variance)
 alternative hypothesis (H1): there is a difference
1  2 (inequality of means)
1  2 (inequality of variance)
 the outcome of a hypothesis
testing is:
– “reject H0 in favour of H1”
– “do not reject H0”
Hypothesis testing
Statistical errors
 to perform hypothesis testing
there is a large number of
statistical tests, each of which
is suitable for the particular
problem
– selection of proper test
(respecting its limitation of
use) is crucial!!!
 when deciding about which
hypothesis to accept there are
2 types of errors one can
make:
– type 1 error
 α = probability of incorrect
rejection of valid H0
 statistical significance P =
true value of α
– type 2 error
 β = probability of not being
able to reject false H0
 1 – β = power of the test
True state of the
null hypothesis
Statistical
decision made
H0 true H0 false
Reject H0 type I
error
correct
Don’t reject H0 correct type II
error
Statistical significance
 In normal English, “significant” means
important, while in statistics “significant”
means probably true (= not due to the
chance)
– however, research findings may be true without
being important
 when statisticians say a result is “highly significant” they
mean it is very probably true, they do not (necessarily)
mean it is highly important
 Significance levels
show you how likely
a result is due to
chance
Statistical tests for quantitative (continuous)
data, 2 samples
test unpaired paired
PARAMETRIC
(for normally or
near normally
distributed data)
1. two-sample t-test 1. one-sample t-test
dependent
NON-PARAMETRIC
(for other than
normal distribution)
1. Mann-Whitney Utest
(synonym Wilcoxon
two-sample)
1. Wilcoxon one-
sample
2. sign test
comparison of parametrs
between 2 independent
groups (e.g. cases 
controls)
comparison of parametrs in
the same group in time
sequence (e.g. before 
after treatment)
Statistical tests for quantitative (cont.) data,
multiple samples
test unpaired paired
PARAMETRIC
(normal
distribution, equal
variances)
1. Analysis of
variance (ANOVA)
1. modification of
ANOVA
NON-PARAMETRIC
(other than
normal distribution)
1. Kruskal-Wallis test
2. median test
1. modification of
ANOVA (Friedman
sequential ANOVA)
H0: all of n compared samples have equal
distribution of variable tested
Statistical tests for binary and categorical data
 binary variable
– 1/0, yes/no, black/white, …
 categorical variable
– category (from – to) I, II, III
 contingency tables n  n or n 
m. resp.
– Fisher exact testy
– chi-square
30
Thank you for your attention