1.
Displaying Your Results
Dr Tarek Amin
Professor of Public Health
Cairo University
amin55@myway.com

2.
Are you
Currently engaged in research?
Intention to publish in indexed
journals?

3.
M
istakes Could
H
appen!!!
 Confusing between data and information in the
results section.
 Inclusion of too many pieces of data which may
obscure the important stuff.
 Inclusion of the mean, median, standard deviation,
range, confidence interval, standard error and others for
every measured variable studied.
 Writing a manuscript around a significant P value.
 Relying on statistical jargon instead of E
nglish to
describe the results.

4.
Supported by CI
“precision of what you found”
E
ffect size
“what you found”
Cameo appearance of the carrierfading P value.
If needed, add adjusted analyses
“the exploration of alternative explanation”
P
repare the stage

5.
P
resenting Your Results
Statistics
T
ables
L
ist
Descriptive
Dichotomous
Categorical
Continuous
AnAlytic
Comparison
Subjects
characteristics
Comparison
M
ulti-variate
F
igures
P
hotographs
Cartoon
Numerical

6.
Statistics: Descriptive Results
Involve only one variable, either predictor or an outcome
types of Descriptive DAtA
Categorical
Dichotomous
B
inary data
Continuous data
L
imited number of
mutually exclusive
possibilities
Data having > 6
ordered values
F
ollow a logical
order or rank
Do not have a
logical sequence
Ordinal
Nominal

7.
1-Describing Dichotomous and Categorical Variables
P
ercentage
Standardize your data for easy
comparison
P
roportions
Risks, rates and Odds
Numerical expression compares one part of the study
units to the whole “expressed in fractions or decimals”
(male patients represented 2/ of our study subjects)
3
P
rovide both the numerator and denominator:
(4/ and 400/
10
1000) =
40%
Indicate precision using appropriate number of digits:
(4/ = 18.2%
22
not 18.0%)
Do not use % when the denominator is small:
(< 50 subjects).
W dichotomous variables only one value is needed:
ith
(after 3 years, 44% (86/
196) of the subjects
were still alive)
F categorical variables, provide all % within categories:
or
(we found that 12 % of the subjects had poor health, 23% had fair health

8.
Risks, Rates, and Odds
estimates of the frequency of a dichotomous outcome in a group of subje
who have been followed for a period of time.
A study of 5000 people who were followed for 2 years to see who
developed lung cancer, and among them 80 new cases occurred.
Risk
Number who develop outcome
Number at risk
Odds
80
Number who develop outcome
=
= 0.016
5000 Number at risk who do not develop outcome
In cross-sectional study = prevalence =
Number with a characteristic
T
otal number
R
ate
80
=
4920
= 0.0163
Used in case-control study /in performing logistic
regression.
Number who develop outcome
80
=
P
erson-time at risk
= 0.008 /
person4920 * 2 = 9940
Risk and Odds are roughly the same if the outcome occur in less 10 %, and
similar to rate multiplied by the average amount of follow up.

9.
Going little more deeper

10.
2- Describing Continuous Variables
Using Measures of average and spread
1- E
xamine your data
M
easures of
skewness
Using a graph
10
No. of
5
women
100
37.51-40.00
35.51-37.50
32.51-35.00
30.01-32.50
27.51-30.00
25.01-27.50
22.51-25.00
20.01-22.50
17.51-20.00
0
15.01-17.5
0
Number
50
of men
age of the mother
0 1 2 3 4 5 6 7 8 9
Triglyceride level
Non-normal distribution
Normal distribution

11.
M
easures of skewness or symmetry
Pearson’s skewness
Coefficient
Skewness = (mean-median)/
SD
0 = perfectly symmetrical
> + 0.2 or < - 0.2 indicate severe
skewness
F
isher’s measure
of skewness
Deviation of the mean to the third
power, done by computer.
A value close to 0 = normal
distribution
> + 1.96 or < - 1.96 indicate
significant skewness
2- Description
Normal distribution
Non-normal distribution
M
ean
Standard deviation
M
edian
Inter-quartile range
M
easures of average and spread: P
rovide information about the population
from which your sample was chosen, and to which your results may apply.

12.
Statistics: Analytic Results
Rules
Compare two or more variables or groups.
 F decide who should be compared “intention to treat”
irst
or “once randomized always analyzed”.
 Comparing “like with like”.
 M
aking comparison between groups rather within groups
“placebo versus study groups rather than change occurred
within study group after intervention”
 Compare independent sampling units “five episodes of
angiodema in a single patient should not be counted as a
five sampling units”
 Compare the effect size.

13.
M
ood changes of residents and interns on the day after being on call.
Characteristics
Alert in rounds
M
ood
H
appy
Neutral
Sad
Sleep (mean hr /
night)
Interns
(n=40)
Residents
(n=20)
P value
40 %
60%
0.020
20%
30%
50%
4.2
40%
30%
30%
6.8
0.030
0.012
0.001
E
ffect size:
Residents are 1.5 times as likely to be alert (60% /
40%=1.5) or
20% more likely to be alert.
Interns are 0.67 times as likely to be alert.
void writing the results section around a significant P value.

14.
Effect Size “approach”
¶ L the 5 or 10 most essential analytic ‘key’ results in
ist
your study “brevity is a virtue”.
¶ Decide which is the predictor (independent) variable,
and which is the outcome variable, for each.
¶ Decide whether predictor and outcome variables are
dichotomous, categorical, or continuous.
¶ Decide what sort of effect size to use, based on the
type of predictor, outcome variables and study design.

15.
E
ffect size measurements
P
redictor
variable
Outcome
variable
Dichotomous
Dichotomous
M (vs.
ale
female)
Antistroke drug
(vs. placebo)
H
ypertension
(SB > 160 or
P
DB >90)
P
‘Cross-sectional’
Stroke in the next
2 years
Clinical trial
E
ffect size
Relative
prevalence
= proportion of men “hypertensive”
proportion of women “hypertensive
Difference in
prevalence
= proportion of hypertensive men –
Relative risk
(risk ratio)
Risk difference
Use of
saccharine (vs.
non-use)
B
ladder cancer
(vs. control)
Vertebral
fracture (vs. no
vertebral
fracture)
* In cohort design:
F
ormula
proportion of hypertensive women
= risk of stroke in persons treated with drug
risk of stroke in placebo group
= risk of stroke in the treated – risk in placebo
B
ladder cancer in
the next 20 years
Cohort study
Odds ratio /RR*
= odds of cancer in users of saccharine
odds of cancer in non-users
Use of saccharine
in the previous 20
years
Case-control
Odds ratio
= odds of saccharine use in cases of cancer
odds of saccharine use in controls
Rate ratio
= hip fracture rate in those with vertebral
H fracture in the (relative
ip
fractures
next 5 years
hazard)
hip fracture rate in those w/ vertebral
o
Survival analysis
fractures
relative risk and Odds ratio could be used.
Rate difference
= rate of hip fracture in those with vertebral

16.
E
ffect size measurements
P
redictor
variable
Outcome
variable
Dichotomous
Continuous
W
hite (vs. non
white)
Systolic blood
pressure (SB )
P
Case-control /
Cohort
New drug (vs.
placebo)
Change in
diastolic blood
pressure (DB )
P
Clinical trial
Continuous
E
ffect size
M
ean difference
M
ean %
difference”
F
ormula
= mean SB in whites – mean SB in non
P
P
whites
= mean SB in white – mean SB in non
P
P
whites
mean SB in non white
P
Continuous
M
ean difference in
change
Creatinine
clearance
1, 25- vitamin D
level
Regression/
Slope
Serum lead
level
IQ
P
roportion of
variance explained
= mean change in DB in treatment group –
P
mean change in DB in placebo group
P
Change in 1, 25 Vitamin D level per change
in creatinine clearance
Correlation between lead level and IQ

17.
T conclude
o
Simple effect size for dichotomous predictor and
dichotomous outcome variables
Depends primarily on the study
design:
β Cross-sectional = prevalence
β Case-control = Odds ratios
β Cohort or randomized trial = risk,
rate, Odds, or risk or rate
differences.

18.
Risk ratio: how many times more likely an
event was to occur in one group than in
another: a risk ratio of 2.23 (123%) greater risk
(or 2.23 folds).
T conclude
o
Risk ratios (odds ratio and rate ratios) that
are less than 1 can be difficult to interpret.
Risk difference: how much more likely an
outcome is to happen in one group than in
another ‘a risk difference of 1 % means that of
100 subjects, one less event occurred in one of the
group’.
Number needed to treat= 1/risk difference.

19.
T conclude
o
Odds difference do not make sense ,
when comparing odds, only the odds
ratio is useful.
W
hen the outcome is rare (< 10%):
Odds ratios, risk ratios, and rate ratios
are similar.
W
hen the outcome is > 30 %: the
three measures are very different.

20.
M
ore complicated ways for dichotomy
Logistic regression
W
hen the time to the
outcome is not known or
does not matter.
Used to delineate the
possible predictor for the
outcome
It yields Odds ratios.
Cox proportional
hazard model
Used when the time to the
event
is known and matters.
Useful when the amount of
follow up varies among the
subjects “E
nrolled at different
times, dropped out or died of
unrelated causes”.
It yields rate (hazard) ratio.
Survival analysis
Nothing to do with living or
dying. Remaining free of
the outcome of interest
Used whether the outcome
is fatal or not
“disease free survival”.
Now, I know how you feel.

21.
T conclude
o
E
ffect size for Dichotomous predictors and
Continuous outcome variable
Distribution
Normal
Compare means
M
ean difference is the effect size
Absolute or % difference could be used
Non-normal
Compare medians
Or use non-parametric tests

22.
E
ffect size for Continuous predictor and
Continuous outcome
L
inear regression
Correlation
Or others
T conclude
o

23.
Indicating the precision of your estimates
with Confidence Intervals.
• It is the range of values that are consistent with
your estimate.
• 95% CI= repeating of bias-free study many
times, 95 % of all the CI for the point estimate
“ your finding” will contain the true value of
the population.
• The wider a CI, the less precise is the point
estimate.

24.
Relation between CI and P value
T concept of NO E F CT
he
FE .
E
ffect size measured as
No effect “insignificant P value”
Difference in prevalence
Risk difference
Rate difference
Number needed to treat
M
ean difference
M
ean % difference
M
ean change
M
ean % change
Slope
Correlation
P
revalence ratio
Risk ratio
Odds ratio
Rate ratio
0
0
0
ზ
0
0
0
0
0
0
1
1
1
1

25.
E
xamples
• M
ean difference in serum bicar. level
between 2 groups is 5 meq/ (95% CI of
L
2-8) = the difference is significant
because it does not include the NO
E F CT ‘0’.
FE
• T relative risk of osteosarcoma in
he
smokers is 2.0 (95% CI, 1.0-4.0)= P
value is > o.o5.
• Odds ratio is 1.4 (95 % CI= 1.1-3.9)=
the P value is significant because it does
not include the no effect= 1.

26.
W
here the P value come from?
• Statistical tests of significance:
• W
hat, when, why and how?
Next table.
• Actual P value should be provided: (P
=
0.034 rather P < 0.05) or (P = 0.098
rather P > 0.05 or NS).
• Do not compare the P value.
• Use the P value wisely: not more than 1015.

27.
Road map for statistical tests of significance
T
ype of Data
Goal of the
test
Measurement
(continuous)
Rank, Score, or
M
easurement (nonnormal)
B
inomial
(T P
wo ossible
Outcomes)
Survival T
ime
Describe one group
M
ean, SD
M
edian, interquartile
range
P
roportion
K
aplan M
eier survival
curve
Compare one group to
a hypothetical
value
One-sample t test
W
ilcoxon test
Chi-square
or
B
inomial test * *
Compare two unpaired
groups
Unpaired t test
M
ann-W
hitney test
F
isher's test
(chi-square for
large samples)
L
og-rank test or M
antelH
aenszel*
Compare two paired
groups
P
aired t test
W
ilcoxon test
M
cNemar's test
Conditional
proportional
hazards
regression*
Compare three or more
unmatched groups
One-way ANOVA
K
ruskal-W
allis test
Chi-square test
Cox proportional
hazard
regression* *
Compare three or more
matched groups
Repeated-measures
ANOVA
F
riedman test
Cochrane Q* *
Conditional
proportional
hazards
regression* *
Quantify association
between two
variables
P
earson correlation
Spearman correlation
Contingency
coefficients* *
P
redict value from
another measured
variable
Simple linear regression
or
Nonlinear
regression
Nonparametric
regression* *
Simple logistic
regression*
Cox proportional
hazard regression*
P
redict value from
M
ultiple linear
M
ultiple logistic
Cox proportional

28.
PARAM T
E RIC AND NONP
ARAM T
E RIC T ST
E S
You should definitely choose a
parametric test if you are sure
that your data are sampled from
a population that follows a
Gaussian “normal” distribution
(at least approximately)

29.
Select a nonparametric test in three
situations:
Ω T outcome is a rank or a score and the
he
population is clearly not Gaussian. E
xamples
include class ranking of students, Apgar score,
visual analogue score for pain, and star* * *
scale.
Ω Some values are "off the scale" that is, too high
or too low to measure. E
xcess extremes.
Ω T data ire measurements, and you are sure
he
that the population is not distributed in a
Gaussian manner “biological fluids or markers”

30.
P
ARAM T
E RIC AND NONP
ARAM T
E RIC T ST T E
E S: H
H
ARD W
AY.
A formal statistical test
(K
olmogorov-Smirnoff test) can be
used to test whether the distribution
of the data differs significantly from
a Gaussian distribution.

31.
Conclusions:
• Identify the type of your variables.
• Define which are the predictors and which
are the outcomes.
• Use the effect size in description of your
results.
• E
stimate the 95% confidence intervals for
your estimates for better precision.
• Use the P value wisely and do not let it
steal the show.

32.
Thank you