displaying your results
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Are youCurrently engaged in research?Intention to publish in indexed journals?
Mistakes Could Happen!!!
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 English to describe the results.
Prepare the stage
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Cameo appearance of the carrier-fading P value.
Presenting Your Results
Statistics Figures Tables
Analytic Descriptive
List
Subjects characteristics
Multi-variate
Comparison Numerical
Cartoon
Photographs
DichotomousCategoricalContinuous
Comparison
Statistics: Descriptive ResultsInvolve only one variable, either predictor or an
outcome
Types of descriptive data
Follow a logical order or rank
Ordinal
DichotomousBinary data
CategoricalLimited number ofmutually exclusive
possibilities
Continuous dataData having > 6 ordered values
Do not have a logical sequence
Nominal
1-Describing Dichotomous and
Categorical Variables
PercentageStandardize your data for easy
comparison
Risks, rates and OddsProportions
Provide both the numerator and denominator: (4/10 and 400/1000) = 40%Indicate precision using appropriate number of digits: (4/22 = 18.2% not 18.0%)Do not use % when the denominator is small: (< 50 subjects).With dichotomous variables only one value is needed: (after 3 years, 44% (86/196) of the subjects were still alive)For categorical variables, provide all % within categories: (we found that 12 % of the subjects had poor health, 23% had fair health and 41% had good health).
Numerical expression compares one part of the studyunits to the whole “expressed in fractions or decimals”(male patients represented 2/3 of our study subjects)
Risks, Rates, and OddsAre estimates of the frequency of a dichotomous outcome in a group of subjects
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 80 = = 0.016Number at risk 5000
In cross-sectional study = prevalence = Number with a characteristic
Total number
Odds
Number who develop outcome 80 = = 0.0163Number at risk who do not develop outcome 4920
Rate
Number who develop outcome 80 = = 0.008 /person-yearPerson-time at risk 4920 *2 = 9940
Used in case-control study / in performing logistic regression.
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.
Going little more deeper
2- Describing Continuous
Variables
0
50
100
Number of men
0 1 2 3 4 5 6 7 8 9
Triglyceride level
0
5
10
No. of women
15.01-17.5
17.51-20.00
20.01-22.50
22.51-25.00
25.01-27.50
27.51-30.00
30.01-32.50
32.51-35.00
35.51-37.50
37.51-40.00
age of the mother
Using Measures of average and spread
1- Examine your data
Using a graphMeasures of
skewness
Non-normal distribution Normal distribution
Measures of skewness or
symmetry Pearson’s skewness
Coefficient Fisher’s measure
of skewness
Skewness = (mean-median)/SD0 = perfectly symmetrical> + 0.2 or < - 0.2 indicate severe 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 skewness2- Description
Normal distribution Non-normal distribution
Mean Standard deviation
Median Inter-quartile range
Measures of average and spread: Provide information about the population from which your sample was chosen, and to which your results may apply.
Statistics: Analytic Results
Rules Compare two or more variables or groups.
First decide who should be compared “intention to treat” or “once randomized always analyzed”.
Comparing “like with like”. Making 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.
Mood changes of residents and interns on the day after being on call.
Characteristics Characteristics Interns Interns (n=40)(n=40)
Residents Residents (n=20)(n=20)
P P value value
Alert in roundsAlert in rounds
MoodMood
HappyHappy
NeutralNeutral
Sad Sad
Sleep (mean hr Sleep (mean hr /night)/night)
40 %40 %
20%20%
30%30%
50%50%
4.2 4.2
60%60%
40%40%
30%30%
30%30%
6.86.8
0.0200.020
0.0300.030
--
0.0120.012
0.0010.001
Effect 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.
Avoid writing the results section around a significant P value.
Effect Size “approach”
¶ List the 5 or 10 most essential analytic ‘key’ results in 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.
Predictor Predictor variable variable
Outcome Outcome variablevariable
Effect size Effect size Formula Formula
DichotomoDichotomous us
Dichotomous Dichotomous Relative Relative prevalence prevalence
Difference in Difference in prevalence prevalence
= proportion of men “hypertensive”= proportion of men “hypertensive”
proportion of women proportion of women “hypertensive“hypertensive
= proportion of hypertensive men – = proportion of hypertensive men –
proportion of proportion of hypertensive womenhypertensive women
Male (vs. Male (vs. female) female)
Hypertension Hypertension
(SBP > 160 or (SBP > 160 or DBP >90)DBP >90)
‘‘Cross-Cross-sectionalsectional’’
Antistroke Antistroke drug (vs. drug (vs. placebo)placebo)
Stroke in the Stroke in the next 2 years next 2 years
Clinical trial Clinical trial
Relative risk Relative risk (risk ratio)(risk ratio)
Risk Risk difference difference
= risk of stroke in persons treated = risk of stroke in persons treated with drugwith drug
risk of stroke in placebo group risk of stroke in placebo group
= risk of stroke in the treated – risk = risk of stroke in the treated – risk in placebo in placebo
Use of Use of saccharine saccharine (vs. non-(vs. non-use)use)
Bladder Bladder cancer (vs. cancer (vs. control)control)
Vertebral Vertebral fracture (vs. fracture (vs. no vertebral no vertebral fracture)fracture)
Bladder Bladder cancer in the cancer in the next 20 years next 20 years
Use of Use of saccharine in saccharine in the previous the previous 20 years 20 years
Hip fracture in Hip fracture in the next 5 the next 5 years years
Survival Survival analysisanalysis
Cohort studyCohort study
Odds ratio / Odds ratio / RR*RR*
Case-controlCase-control
Odds ratio Odds ratio
Rate ratio Rate ratio (relative (relative hazard)hazard)
Rate Rate difference difference
= odds of cancer in users of = odds of cancer in users of saccharinesaccharine
odds of cancer in non-usersodds of cancer in non-users
= odds of saccharine use in cases of = odds of saccharine use in cases of cancercancer
odds of saccharine use in odds of saccharine use in controlscontrols
= hip fracture rate in those with = hip fracture rate in those with vertebral fracturesvertebral fractures
hip fracture rate in those w/o hip fracture rate in those w/o vertebral fracturesvertebral fractures
= rate of hip fracture in those with = rate of hip fracture in those with vertebral fracture – rate of hip vertebral fracture – rate of hip fracture in those w/o vertebral fracture in those w/o vertebral
fracture.fracture.
Effect size measurements
*In cohort design: relative risk and Odds ratio could be used.
Predictor Predictor variable variable
Outcome Outcome variablevariable
Effect size Effect size Formula Formula
DichotomoDichotomous us
Continuous Continuous Mean Mean differencedifference
Mean % Mean % difference” difference”
Mean Mean difference in difference in change change
= mean SBP in whites – mean SBP = mean SBP in whites – mean SBP in non whitesin non whites
= mean SBP in white – mean SBP in = mean SBP in white – mean SBP in non whitesnon whites
mean SBP in non whitemean SBP in non white
= mean change in DBP in treatment = mean change in DBP in treatment group – group –
mean change in DBP in placebo mean change in DBP in placebo group group
White (vs. White (vs. non white)non white)
New drug New drug (vs. (vs. placebo) placebo)
Systolic blood Systolic blood pressure pressure (SBP)(SBP)
Case-control / Case-control / CohortCohort
Change in Change in diastolic blood diastolic blood pressure pressure (DBP)(DBP)
Clinical trialClinical trial
ContinuouContinuous s
Continuous Continuous
Regression/Regression/Slope Slope
Proportion of Proportion of variance variance explained explained
Change in 1, 25 Vitamin D level per Change in 1, 25 Vitamin D level per change in creatinine clearancechange in creatinine clearance
Correlation between lead level and Correlation between lead level and IQ IQ
Creatinine Creatinine clearanceclearance
Serum lead Serum lead level level
1, 25- vitamin 1, 25- vitamin D level D level
IQ IQ
Effect size measurements
Simple effect size for dichotomous predictor
and dichotomous outcome variables
Depends primarily on the study design:
Cross-sectional = prevalence Case-control = Odds ratios Cohort or randomized trial =
risk, rate, Odds, or risk or rate differences.
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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).
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.
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Odds difference do not make Odds difference do not make sensesense, , when comparing odds, when comparing odds, only the odds ratio is useful.only the odds ratio is useful.When the outcome is rare (< When the outcome is rare (< 10%):10%): Odds ratios, risk ratios, Odds ratios, risk ratios, and rate ratios are similar. and rate ratios are similar. When the outcome is > 30 %:When the outcome is > 30 %: the three measures are very the three measures are very different.different.
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More complicated ways for
dichotomy Logistic regression Cox proportional
hazard model Survival analysis
When 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.
Used when the time to the eventis known and matters.Useful when the amount of follow up varies among the subjects “Enrolled at different times, dropped out or died of unrelated causes”.
It yields rate (hazard) ratio.
Nothing to do with living or dying. Remaining free of the outcome of interestUsed whether the outcome is fatal or not
“disease free survival”.
Now, I know how you feel.
Effect size for Dichotomous predictors and Continuous outcome
variable Distribution
Normal Non-normal
Compare meansMean difference is the effect sizeAbsolute or % difference could be used
Compare medians
Or use non-parametric tests
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Effect size for Continuous predictor
and Continuous outcome
Linear regressionCorrelationOr others
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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.
Relation between CI and P value
Effect size measured asEffect size measured as No effect “insignificant P No effect “insignificant P value”value”
Difference in prevalenceDifference in prevalence
Risk differenceRisk difference
Rate differenceRate difference
Number needed to treatNumber needed to treat
Mean differenceMean difference
Mean % differenceMean % difference
Mean changeMean change
Mean % changeMean % change
SlopeSlope
CorrelationCorrelation
Prevalence ratioPrevalence ratio
Risk ratioRisk ratio
Odds ratioOdds ratio
Rate ratioRate ratio
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The concept of NO EFFECT.
ExamplesExamples • Mean difference in serum bicar. level Mean difference in serum bicar. level
between 2 groups is 5 meq/L (95% CI between 2 groups is 5 meq/L (95% CI of 2-8) = of 2-8) = the difference is significant the difference is significant because it does not include the NO because it does not include the NO EFFECT ‘0’.EFFECT ‘0’.
• The relative risk of osteosarcoma in The relative risk of osteosarcoma in smokers is 2.0 (95% CI, 1.0-4.0)= smokers is 2.0 (95% CI, 1.0-4.0)= P P value is > o.o5value is > o.o5..
• Odds ratio is 1.4 (95 % CI= 1.1-3.9)= Odds ratio is 1.4 (95 % CI= 1.1-3.9)= the P value is significant because it the P value is significant because it does not include the no effect= 1. does not include the no effect= 1.
Where the P value come from?
• Statistical tests of significance:• What, 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
10-15.
Road map for statistical tests of significance Type of Data
Goal of the test Measurement (continuous)
Rank, Score, or Measurement (non-normal)
Binomial(Two Possible
Outcomes)
Survival Time
Describe one group
Mean, SD Median, interquartile range
Proportion Kaplan Meier survival curve
Compare one group to a hypothetical value
One-sample t test Wilcoxon test Chi-squareorBinomial test **
Compare two unpaired groups
Unpaired t test Mann-Whitney test Fisher's test(chi-square for large samples)
Log-rank test or Mantel-Haenszel*
Compare two paired groups
Paired t test Wilcoxon test McNemar's test Conditional proportional hazards regression*
Compare three or more unmatched groups
One-way ANOVA Kruskal-Wallis test Chi-square test Cox proportional hazard regression**
Compare three or more matched groups
Repeated-measures ANOVA
Friedman test Cochrane Q** Conditional proportional hazards regression**
Quantify association between two variables
Pearson correlation
Spearman correlation
Contingency coefficients**
Predict value from another measured variable
Simple linear regressionorNonlinear regression
Nonparametric regression**
Simple logistic regression*
Cox proportional hazard regression*
Predict value from several measured or binomial variables
Multiple linear regression*orMultiple nonlinear regression**
Multiple logistic regression*
Cox proportional hazard regression*
PARAMETRIC AND NONPARAMETRIC TESTS
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)
Select a nonparametric test in three situations:
Ω The outcome is a rank or a score and the population is clearly not Gaussian. Examples 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. Excess extremes.
Ω The data ire measurements, and you are sure that the population is not distributed in a Gaussian manner “biological fluids or markers”
PARAMETRIC AND NONPARAMETRIC
TESTS: THE HARD WAY.
A formal statistical test (Kolmogorov-Smirnoff test) can be used to test whether the distribution of the data differs significantly from a Gaussian distribution.
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.• Estimate the 95% confidence
intervals for your estimates for better precision.
• Use the P value wisely and do not let it steal the show.
Thank you