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Introduction to biostatistics Lecture plan
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Transcript of Introduction to biostatistics Lecture plan
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Introduction to Introduction to biostatisticsbiostatisticsLecture planLecture plan
1.1. BasicsBasics2.2. Variable typesVariable types3.3. Descriptive statisticsDescriptive statistics::
Categorical dataCategorical data Numerical dataNumerical data
4.4. IInferential statisticsnferential statistics Confidence Confidence intervalintervalss HipotHipotheses testingheses testing
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DEFINITIONSDEFINITIONSSTATISTISTATISTICSCS can mean can mean 2 things:2 things:- the numbers we get when we measure and - the numbers we get when we measure and count things (data)count things (data)- a collection of procedures for describing and - a collection of procedures for describing and anlysing data.anlysing data.
BIOSTATISTIBIOSTATISTICSCS – – application of statistics application of statistics in nature sciences, when biomedical and in nature sciences, when biomedical and problems are analysed.problems are analysed.
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Why do we need statistics?Why do we need statistics?
????
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Basic parts of Basic parts of statististatisticcs:s:
DescriptiveDescriptive IInferentialnferential
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TerminologyTerminology
Population Sample
Variables
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Variable typesVariable types
Categorical Categorical ((qualitativequalitative))
Numerical Numerical ((quantitativequantitative))
CombinedCombined
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Categorical dataCategorical dataNominalNominal
2 categories2 categories >2 categories>2 categories
OrdinalOrdinal
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Numerical dataNumerical data
ContinuousContinuous DisDiscretecrete
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Description of categorical Description of categorical datadata
Arranging dataArranging data Frequencies, tablesFrequencies, tables Visualization (graphical Visualization (graphical
presentation)presentation)
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Frequencies and Frequencies and contingency tablescontingency tables
From those From those who were who were unsatisfied 4 unsatisfied 4 were males, were males, 6 were 6 were females.females.
TotalTotal MalesMales FemalesFemales
SatisfiedSatisfied 4040
80%80%1414
77,877,8%%
2626
81,3%81,3%
UnsatisfiedUnsatisfied 1010
20 %20 %44
22,222,2%%
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18,7%18,7%
TotalTotal 5050
100%100%1818
100%100%3232
100%100%
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GraGraphical presentationphical presentation
Lyčių struktūra Lietuvoje 1993 m.
vyrų
moterų
Lyčių struktūra Lietuvoje 1991 m.
vyrų
moterų
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GraGraphical presentationphical presentation
Lyčių struktūra Lietuvoje
44%45%46%47%48%49%50%51%52%53%54%
1993 m. 1996 m.
vyrų
moterų
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GraGraphical presentationphical presentationLyčių struktūra Lietuvoje
0%
20%
40%
60%
80%
100%
120%
1993 m. 1996 m.
moterų
vyrų
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GraGraphical presentationphical presentation
0%
20%
40%
60%
80%
100%
Kro
atija
Danija
Švedija
Suom
ija
Pra
ncūzija
Airija
Norv
egija
Rusija
Slo
vakija
Slo
venija
Lie
tuva
J01A Tetraciklinai J01C Penicilinai
J01D Kiti β-laktaminiai antibiotikai J01E Sulfonamidai ir trimetoprimas
J01F Makrolidai, linkozamidai, streptograminai J01M Chinolonai
J01X Kiti
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GraGraphical presentationphical presentation
•OtherOther::- Maps- Maps- - Chernoff facesChernoff faces- - Star plotStar plots, etcs, etc..
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Description of numerical Description of numerical datadata
Arranging dataArranging data Frequencies (relative and cumulative), Frequencies (relative and cumulative),
graphical presentationgraphical presentation Measures of central tendency and Measures of central tendency and
variancevariance Assessing normalityAssessing normality
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GroupingGrouping
Sorting dataSorting data GrGrooupups (5-17 gr.) according s (5-17 gr.) according
researcher’s criteria.researcher’s criteria.
To assess distribution, for graphical presentation in excelTo assess distribution, for graphical presentation in excel
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Frequencies, their comparison Frequencies, their comparison and calculationand calculation
197 students were asked about the amount of money (litas) they had in cash at the moment.
Frequency Cumulative frequencynumber of litas n % n %
1 1 0,5 1 0,52 2 1,0 1+2=3 1,53 4 2,0 3+4=7 3,64 8 4,1 7+8=15 7,65 15 7,6 15+15=30 15,26 24 12,2 30+24=54 27,47 29 14,7 54+29=83 42,18 31 15,783+31=114 57,99 29 14,7114+29=143 72,6
10 24 12,2143+24=167 84,811 15 7,6167+15=182 92,412 8 4,1182+8=190 96,413 4 2,0190+4=194 98,514 2 1,0194+2=196 99,515 1 0,5196+1=197 100,0
Total 197 100,0
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Gaphical presentation of Gaphical presentation of frequenciesfrequencies
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NormalNormal distributions distributions Most of them around centerMost of them around center Less above and lower central Less above and lower central
values, approximately the values, approximately the same proportionssame proportions
Most often Gaussian Most often Gaussian distributiondistribution
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Not normal distributionsNot normal distributions
More observations in one part.More observations in one part.
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2222Asymmetrical distribution
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How would you How would you describe/present your describe/present your
respondents if the data are respondents if the data are numeric?numeric?
2 groups of measures2 groups of measures::
1.1. Central tendency (central Central tendency (central value, average)value, average)
2.2. VarianceVariance
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MEASURES OF CENTRAL MEASURES OF CENTRAL TENDENCYTENDENCY
Means/averages (arithmetic, Means/averages (arithmetic, geometric, harmonic, etc.)geometric, harmonic, etc.)
ModeMode MedianMedian QuartilesQuartiles
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MEASURES OF CENTRAL MEASURES OF CENTRAL TENDENCYTENDENCY
AritArithhmetimetic meanc mean (X, (X, μμ))
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MEASURES OF CENTRAL MEASURES OF CENTRAL TENDENCYTENDENCY
MedianMedian (Me) – (Me) – the middle value or 5the middle value or 500thth procentilprocentilee ( (the value of the observationthe value of the observation, , that divides the sorted datathat divides the sorted data in almost in almost equal parts)equal parts)..It is found this wayIt is found this way
When When n n oddodd: median: median is the middle observation is the middle observationWhen When n n eveneven: median: median is the average of values is the average of values of two middle observationsof two middle observations
2
1n
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MEASURES OF CENTRAL MEASURES OF CENTRAL TENDENCYTENDENCY
ModModee (Mo) – (Mo) – the most common the most common valuesvalues Can be more than one modeCan be more than one mode
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MEASURES OF CENTRAL MEASURES OF CENTRAL TENDENCYTENDENCY
Quartiles Quartiles (Q(Q11, , QQ22, , QQ33, , QQ44) ) – – sample sample size is divided into 4 equal parts size is divided into 4 equal parts getting 25% of observations in each getting 25% of observations in each of them.of them.
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Is it enough measure of Is it enough measure of central tendency to central tendency to
describe respondents?describe respondents?
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MEASURES OF VARIANCEMEASURES OF VARIANCE
Min and maxMin and max RangeRange StandarStandard deviationd deviation – – sqrt of sqrt of
variance (SD)variance (SD) VarianceVariance - V= - V= ∑∑(x(xii - x) - x)22/n-1/n-1
InterInterquartile range quartile range (Q(Q3-Q1 or 3-Q1 or 75%-25%) IQRT75%-25%) IQRT
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What measures are to be used for What measures are to be used for sample description?sample description?
If distribution is NORMALIf distribution is NORMAL MeanMean Variance Variance ((oror standarstandard deviationd deviation))
If distribution is NOT NORMALIf distribution is NOT NORMAL MedianMedian IQRT or min/maxIQRT or min/max
Those measures are used also with numeric ordinal dataThose measures are used also with numeric ordinal data
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X, Mo, Me
Mean~Mean~MedianMedian~~ModModee,,SD ir SD ir empyric ruleempyric rule
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EMPEMPYRICAL RULEYRICAL RULE
Number of observationsNumber of observations (%) 1, 2 ir (%) 1, 2 ir 2.5 SD 2.5 SD from mean if distribution is from mean if distribution is normalnormal
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Example
X-2SD +2SD
X=8
SD=2,5
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Normality assessmentNormality assessmentSummarySummary
GraphicalGraphical Comparison of measures of central Comparison of measures of central
tendency; empyrical rule (mean and tendency; empyrical rule (mean and standard deviation)standard deviation)
SSkewnesskewness and and kurtosis kurtosis ((if Gaussian if Gaussian =0)=0)
KolmogorovKolmogorov--Smirnov testSmirnov test
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MedianMean( *)
75th Procentile
25th Procentile
75th Procentile
25th Procentile
Outliers
BoxplotBoxplot
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Boxplot exampleBoxplot example
44014,00
15,33
16,67
18,00
19,33
20,67
22,00
23,33
24,67
26,00
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Central limit theoremCentral limit theorem
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Inferential Inferential statististatisticscs
Confidence Confidence intervalintervalss HipotHipothheesesses testingtesting
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Confidence Confidence intervalintervalss
Interval Interval where the “true” value where the “true” value most likely could occur.most likely could occur.
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The variance of samples The variance of samples and their measuresand their measures
μ, σ, p0
X1, SD1; p1
X2, SD2; p2X3, SD3; p3
X4; SD4; p4
X
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The variance of samples and The variance of samples and confidence confidence intervalintervalss
μ, p0
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Confidence intervalConfidence interval
Statistical definition:Statistical definition:
If the study was carried out 100 times, If the study was carried out 100 times, 100 100 reresultssults ir ir 100 C100 CII were got, 95 were got, 95 times of 100times of 100 the the “true” value will be in that interval. But it will “true” value will be in that interval. But it will not appear in that interval 5 times of 100.not appear in that interval 5 times of 100.
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Confidence Confidence intervalintervalss((generalgeneral, , most common most common
calculationcalculation))
95% CI 95% CI :: X X ±± 1.96 1.96 SE SE XXminmin;; X Xmaxmax
Note: for normal distribution, when n is largeNote: for normal distribution, when n is large
95% CI 95% CI :: pp ±± 1.96 1.96 SESE ppminmin ;; p pmaxmax
Note: whenNote: when p ir p ir 1-p > 5/n1-p > 5/n
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StandarStandard errord error (SE) (SE)
Numeric dataNumeric data
((X X ))Categorical dataCategorical data
(p)(p)
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Width of confidence inervalWidth of confidence inerval
depends ondepends on::
a)a) Sample sizeSample size;;
b)b) Confidence levelConfidence level ( (guaranty - usually 95%, guaranty - usually 95%, but available any %)but available any %);;
c)c) dispersiondispersion..
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HipotHipotheses testingheses testing
HH00: : μμ11==μμ22; p; p11=p=p22; (RR=1, OR=1, ; (RR=1, OR=1, differencedifference=0)=0)
HHAA: : μμ11≠≠μμ22; p; p11≠p≠p22 (two sided, one (two sided, one sided)sided)
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Significance level Significance level αα (agreed (agreed 0 0..005).5).
TesTestt for for P P valuevalue (t-test, (t-test, χχ22 , etc, etc..).).
P P value is the probability to get the value is the probability to get the difference (association)difference (association),, if the null if the null hypothesis is truehypothesis is true..
OROR P P value is the probability to get the difference value is the probability to get the difference (association) due to chance alone, when the null (association) due to chance alone, when the null hypothesis is truehypothesis is true..
HipotHipotheses testingheses testing
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Statistical agreementsStatistical agreements
If If P<0P<0.05, we say, that results can’t .05, we say, that results can’t be explained by chance alone, be explained by chance alone, therefore we reject Htherefore we reject H00 and accept Hand accept HAA..
If If PP≥≥00.05, we say.05, we say, , that found that found difference can be due to chance difference can be due to chance alone, therefore we don’t reject Halone, therefore we don’t reject H0.0.
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TestTestssTest depends onTest depends on
Study designStudy design,, Variable typeVariable type distribution,distribution, Number of groups, etc.Number of groups, etc.
Tests (probability distributions): z test t test (one sample, two independent, paired) Χ2 (+ trend) F test Fisher exact test Mann-Whitney Wilcoxon and others.
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P value tells, if there is statistically P value tells, if there is statistically significant difference (association).significant difference (association).
CI gives interval where true value can CI gives interval where true value can be.be.
Inferential statisticsInferential statisticsSummarySummary
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Inferential statisticsInferential statisticsSummarySummary
Neither P value, nor CNeither P value, nor CI I give other give other explanations of the result (bias and explanations of the result (bias and confounding). confounding).
Neither P value, nor CNeither P value, nor CI I tell anything tell anything about the biological, clinical or public about the biological, clinical or public health meaning of the resultshealth meaning of the results..