Bio-Statistics Guide for Dental Professionals

BIO-STATISTICSBIO-STATISTICS
INDIAN DENTAL ACADEMY
Leader in continuing dental education
www.indiandentalacademy.com

STATISTICSSTATISTICS
 It is a science ofIt is a science of
 Collection of dataCollection of data
 Presentation of dataPresentation of data
 Summarization of dataSummarization of data
 Analysis of data andAnalysis of data and
 Interpretation of data.Interpretation of data.
 The only science that enablesThe only science that enables
different experts using the samedifferent experts using the same
figure to draw different conclusionsfigure to draw different conclusions

Bio-statisticsBio-statistics
(Grant John)(Grant John)
 Application of statistics to healthApplication of statistics to health
problems.problems.
 Different names in different fields:Different names in different fields:
 Health statistics –public/ communityHealth statistics –public/ community
health.health.
 Medical statistics – medicine.Medical statistics – medicine.
 Vital statistics – demography.Vital statistics – demography.
 Dental statistics – dentistry.Dental statistics – dentistry.www.indiandentalacademy.com

General application of bio-statistics:General application of bio-statistics:
 To define what is normal or healthy in a population.To define what is normal or healthy in a population.
Ex:-pulse rate/ min.Ex:-pulse rate/ min.
 To find:-To find:-
 Statistical difference between means of two variables. Ex: meanStatistical difference between means of two variables. Ex: mean
plaque scores for two groups.plaque scores for two groups.
 Co-relation between two variables.Co-relation between two variables.
Ex; - sugar & Dental caries, Fluoride Conc. & Fluorosis.Ex; - sugar & Dental caries, Fluoride Conc. & Fluorosis.

usefulness of sera & vaccines in the field. % of deaths amongusefulness of sera & vaccines in the field. % of deaths among
vaccinated compared to % of deaths among unvaccinated.vaccinated compared to % of deaths among unvaccinated.
 To test the efficacy of different tooth pastes.To test the efficacy of different tooth pastes.
Ex: Colgate, close up.Ex: Colgate, close up.

Use of statistics in dentistry:-Use of statistics in dentistry:-
 To assess the state of oral health in theTo assess the state of oral health in the
community & to determine the availability &community & to determine the availability &
utilization of dental care facilities.utilization of dental care facilities.
 To indicate the basic factors underlying theTo indicate the basic factors underlying the
state of oral health by diagnosing thestate of oral health by diagnosing the
community & solutions to such problems.community & solutions to such problems.
 To determine success or failure of specific oralTo determine success or failure of specific oral
health care program or to evaluate thehealth care program or to evaluate the
programme action.programme action.
 To promote health legislation and in creatingTo promote health legislation and in creating
administrative standards for oral health.administrative standards for oral health.

Common statistical termsCommon statistical terms
 Data: -Data: - A set of values recorded on one or moreA set of values recorded on one or more
observational units.observational units.
 Sampling unitSampling unit :-each member of a population.:-each member of a population.
 Sample:-Sample:- part of a populationpart of a population
 Survey :-Survey :- planned & systematic process of collectingplanned & systematic process of collecting
statistical data.statistical data.
DATA
quantitative qualitative primary secondary
Ex:-ht, wt, DMFT
Ex:- oral hygiene status
Periodontal status
Ex:-brushing habits
feeding practices
Ex:- hospital records

METHODS OF DATA COLLECTIONMETHODS OF DATA COLLECTION
PRIMARY DATA
OBSERVATIONAL
METHOD
INTERVIEW QUESTIONNAIRE
THROUGH
SCHEDULE
OTHER
METHODS

METHODS OF DATA COLLECTIONMETHODS OF DATA COLLECTION
2.2.
SECONDARY DATA
PUBLISHED
DATA
UN PUBLISHED
DATA

SAMPLING AND SAMPLING METHODSSAMPLING AND SAMPLING METHODS
 IMPORTANCE OF SAMPLING:-IMPORTANCE OF SAMPLING:-
 The physical impossibility of checking all the items inThe physical impossibility of checking all the items in
the population.the population.
 The destructive nature of goods.The destructive nature of goods.
 Adequacy of sampling results.Adequacy of sampling results.
 Cost of study in the entire populationCost of study in the entire population
 Saving the time.Saving the time.

SAMPLING METHODSSAMPLING METHODS
 PROBABILITY SAMPLINGPROBABILITY SAMPLING
Simple random samplingSimple random sampling
Stratified random samplingStratified random sampling
Systematic random samplingSystematic random sampling
Cluster random samplingCluster random sampling
Multistage random samplingMultistage random sampling
Multiphase random sampling.Multiphase random sampling.
 NON PROBABILITYNON PROBABILITY
SAMPLINGSAMPLING
Judgement samplingJudgement sampling
Quota samplingQuota sampling
Convenience samplingConvenience sampling

PROBABILITY SAMPLING TECHNIQUEPROBABILITY SAMPLING TECHNIQUE
SIMPLE RANDOM SAMPLING :SIMPLE RANDOM SAMPLING :
(unrestricted random sampling )(unrestricted random sampling )
-- a procedure of selecting a sample in which every-- a procedure of selecting a sample in which every
item in a population has an equal chance of beingitem in a population has an equal chance of being
included in a sample.included in a sample.
-- applicable when population is very small,-- applicable when population is very small,
homogeneous and readily available.homogeneous and readily available.
Advantages:-Advantages:- No harm due to personal bias.No harm due to personal bias.
Disadvantages:-Disadvantages:- Selection of sample costlySelection of sample costly
and time consuming.and time consuming.

Stratified random samplingStratified random sampling
If population is heterogeneous, simple random sampling is not useful.If population is heterogeneous, simple random sampling is not useful.
Purpose of this sampling is to increase the efficiency of sampling byPurpose of this sampling is to increase the efficiency of sampling by
dividing heterogeneous into homogenous.dividing heterogeneous into homogenous.
These homogenous groups are termed as strata.These homogenous groups are termed as strata.
Ex: Areas, classes, ages, sexes etc.,Ex: Areas, classes, ages, sexes etc.,
 ADVANTAGES:-ADVANTAGES:-
There is a greater precision of results.There is a greater precision of results.
It gives better results when population is scattered.It gives better results when population is scattered.
 DISADVANTAGES:-DISADVANTAGES:-
It is too technical methodIt is too technical method
Time consuming.Time consuming.

Systematic Random sampling:Systematic Random sampling:
It is applied to field studies when the population is large, scattered &It is applied to field studies when the population is large, scattered &
non homogenous.non homogenous.
K=N/nK=N/n
K - sample interval or sample ratioK - sample interval or sample ratio
N - population sizeN - population size
n - Sample size.n - Sample size.
Ex:- If 150 patients are to be included in the sample from aEx:- If 150 patients are to be included in the sample from a
population of 3000.population of 3000.
I.e. K=3000/150=20.I.e. K=3000/150=20.
Systematic design is simple, convenient to adopt.Systematic design is simple, convenient to adopt.
The time & labor in collection of sample is relatively small.The time & labor in collection of sample is relatively small.
It gives accurate results when population is largeIt gives accurate results when population is large

Cluster samplingCluster sampling::
When population is vast & scattered over a wide area,When population is vast & scattered over a wide area,
cluster sampling is applicable.cluster sampling is applicable.
In this sampling the population is divided into groups, then aIn this sampling the population is divided into groups, then a
required no of groups or clusters are selected by simplerequired no of groups or clusters are selected by simple
random sampling.random sampling.
Ex:-City is divided into wards, required no of wards areEx:-City is divided into wards, required no of wards are
selected randomly.selected randomly.
Wards ---- I stageWards ---- I stage
Blocks ---- II stage.Blocks ---- II stage.
II stagesII stages  multistage sampling.multistage sampling.

Multistage samplingMultistage sampling
As the name implies this method refers to theAs the name implies this method refers to the
sampling procedures carried out in several stagessampling procedures carried out in several stages
using random sampling technique.using random sampling technique.
CountryCountry
StatesStates 1st stage1st stage
DistrictsDistricts 2nd stage2nd stage
TaluksTaluks 3rd stage3rd stage
VillagesVillages 4th stage4th stage
WardsWards 5th stage5th stage

Multiphase sampling:Multiphase sampling:
In this method part of the information is collected from theIn this method part of the information is collected from the
whole sample & part from the subsample.whole sample & part from the subsample.
Ex:Ex: T.B. PatientsT.B. Patients..
Physical examination or Mantoux test.Physical examination or Mantoux test.
X-rayX-ray
Sputum examination.Sputum examination.
Number of subsample in 2nd & 3rd phase willNumber of subsample in 2nd & 3rd phase will
become successively smaller and smallerbecome successively smaller and smaller
Less costly & more purposeful.Less costly & more purposeful.
Less laborious.Less laborious.

Non Probability samples:Non Probability samples:
JUDGEMENT SAMPLING:-JUDGEMENT SAMPLING:-
Selection of samples is left to the Judgement of investigator.Selection of samples is left to the Judgement of investigator.
In this sampling accuracy of results depends upon investigator.In this sampling accuracy of results depends upon investigator.
 ADVANTAGESADVANTAGES
Employed mainly when population is small.Employed mainly when population is small.
Employed to conduct pilot studyEmployed to conduct pilot study
 LIMITATIONSLIMITATIONS
Accuracy of results depends upon the knowledge of theAccuracy of results depends upon the knowledge of the
investigator.investigator.
If investigator is biased it affects the acceptance or rejection ofIf investigator is biased it affects the acceptance or rejection of
an hypothesisan hypothesis

QUOTA SAMPLINGQUOTA SAMPLING
Each investigator is allotted quota ofEach investigator is allotted quota of
persons which are to be interviewed.persons which are to be interviewed.
Investigators are given instructions toInvestigators are given instructions to
interview persons within the quota withinterview persons within the quota with
some specified characteristics.some specified characteristics.
Ex: -Ex: - Persons within the quota of 10 housePersons within the quota of 10 house
wives, 6 professionals.wives, 6 professionals.

Convenience / Chunk SamplingConvenience / Chunk Sampling
/ incidental sampling/ incidental sampling
Chunk is a fraction of population which is selectedChunk is a fraction of population which is selected
for investigator because it is conveniently available.for investigator because it is conveniently available.
Ex: In order to estimate oral hygiene status in theEx: In order to estimate oral hygiene status in the
city the investigator may select a few areas nearcity the investigator may select a few areas near
by his house.by his house.
Results of this sampling are rarely representativeResults of this sampling are rarely representative
because they are generally biased.because they are generally biased.

Methods of Presentation:Methods of Presentation:
 GRAPHS AND DIAGRAMS:-GRAPHS AND DIAGRAMS:-
Advantages:Advantages:
powerful impact on imagination of people.powerful impact on imagination of people.
better retained in memory than tables.better retained in memory than tables.
Disadvantages:Disadvantages:
details of original data may be lost.details of original data may be lost.
GENERAL RULE OF GRAPHING:GENERAL RULE OF GRAPHING:
Y axis ( vertical ) : represent frequency of scores.Y axis ( vertical ) : represent frequency of scores.
X axis ( horizontal ) : represent the variables.X axis ( horizontal ) : represent the variables.

TYPES OF GRAPHTYPES OF GRAPH
Bar graphBar graph
HistogramHistogram
Frequency polygon.Frequency polygon.
Frequency curve.Frequency curve.
Line chart.Line chart.
Scatter or dot diagram.Scatter or dot diagram.
Box whisker plot .Box whisker plot .
Pictogram.Pictogram.
Map diagram.Map diagram.
Pie diagram.Pie diagram.

Bar graphBar graph
Length of the bars indicate frequency of character.Length of the bars indicate frequency of character.
ADVANTAGES:ADVANTAGES:
Easy to prepare.Easy to prepare.
enable values to be comparedenable values to be compared
visually.visually.
TYPES :TYPES :
simple bar graphsimple bar graph
multiple bar graph:multiple bar graph:
two or more bars may be grouped.two or more bars may be grouped.
component bar graph :component bar graph :
bars may be divided into two orbars may be divided into two or
more parts, each part representingmore parts, each part representing
a certain item.a certain item.

SIMPLE BAR GRAPHSIMPLE BAR GRAPH

MULTIPLE BAR GRAPHMULTIPLE BAR GRAPH
0
5
10
15
20
25
30
35
1 2 3 4 5
Series1
Series2

COMPONENT BAR GRAPHCOMPONENT BAR GRAPH
0
10
20
30
40
50
60
1 2 3 4 5
Series2
Series1

HISTOGRAMHISTOGRAM
 Frequency of each group will form aFrequency of each group will form a
column or rectangle - histogram.column or rectangle - histogram.
 X-axis – variables.X-axis – variables.
 Y-axis – frequency.Y-axis – frequency.

FREQUENCY POLYGONFREQUENCY POLYGON
 Area diagram of frequency distributionArea diagram of frequency distribution
joining the mid points of intervals at thejoining the mid points of intervals at the
height of frequencies.height of frequencies.
 It gives a polygon i.e. a figure with manyIt gives a polygon i.e. a figure with many
angles.angles.

FREQUENCY CURVEFREQUENCY CURVE
 When the number of observations is veryWhen the number of observations is very
large & group interval is reduced thelarge & group interval is reduced the
frequency polygon tends to lose itsfrequency polygon tends to lose its
angulations giving place to a smoothangulations giving place to a smooth
curve known as frequency curvecurve known as frequency curve

LINE CHARTLINE CHART
 This is a frequencyThis is a frequency
polygon presentingpolygon presenting
variations by line.variations by line.
 It shows the trend ofIt shows the trend of
an event occurringan event occurring
over period of timeover period of time
rising, falling orrising, falling or
showing fluctuations.showing fluctuations.

SCATTER OR DOT DIAGRAMSCATTER OR DOT DIAGRAM
 It is graphic presentation to showIt is graphic presentation to show
the nature of correlation betweenthe nature of correlation between
two variables character X & Y intwo variables character X & Y in
the same person (S) or group (S)the same person (S) or group (S)
such as height and weight in mensuch as height and weight in men
aged 20 years, hence it is alsoaged 20 years, hence it is also
called correlation diagram.called correlation diagram.
 The characters are read on theThe characters are read on the
base (ht) & vertical (wt) axis & thebase (ht) & vertical (wt) axis & the
perpendicular drawn from theseperpendicular drawn from these
readings meet to give one scatterreadings meet to give one scatter
point.point.
 Varying frequencies of theVarying frequencies of the
characters give a number of suchcharacters give a number of such
points or dots that show scatter.points or dots that show scatter.
 A line is drawn to show the natureA line is drawn to show the nature
of correlation at a glance.of correlation at a glance.

BOX WHISKER PLOTBOX WHISKER PLOT
 If the number of points are large , a dot plot can beIf the number of points are large , a dot plot can be
replaced by box whisker plot.replaced by box whisker plot.
 The maximum and minimum values , if they are variableThe maximum and minimum values , if they are variable
are indicated by the extremities (whisker ) of theare indicated by the extremities (whisker ) of the
diagram.diagram.
 The median value is the central vertical line and upperThe median value is the central vertical line and upper
and lower limits are indicated by corresponding verticaland lower limits are indicated by corresponding vertical
ends of the box.ends of the box.

PICTOGRAMPICTOGRAM
 The pictures representing the value ofThe pictures representing the value of
items are called pictograms.items are called pictograms.
 It is most useful way of representing dataIt is most useful way of representing data
to those people who cannot understand.to those people who cannot understand.

MAP DIAGRAMMAP DIAGRAM
 They are mainly employed to depict theThey are mainly employed to depict the
regional distribution of a variable orregional distribution of a variable or
variables. Ex: India map.variables. Ex: India map.

PIE DIAGRAMPIE DIAGRAM
 The frequency of theThe frequency of the
group is shown in a circle.group is shown in a circle.
 Degree of angle denotesDegree of angle denotes
the frequency.the frequency.
 Instead of comparing theInstead of comparing the
length of bar , the areaslength of bar , the areas
of segments areof segments are
compared.compared.

MEASURES OF CENTRAL TENDENCYMEASURES OF CENTRAL TENDENCY
 Three common typesThree common types
MEANMEAN
MEDIANMEDIAN
MODEMODE

MEANMEAN
 Obtained by summing up all theObtained by summing up all the
observations and dividing the total by no. ofobservations and dividing the total by no. of
observations.observations.
 It is expressed by X .It is expressed by X .
X =X = Sum of observationsSum of observations
No of observationsNo of observations
X =X = X1+X2+X3……………..+XnX1+X2+X3……………..+Xn
nn

MEANMEAN
 MERITSMERITS
Easy to understand & easy to calculate.Easy to understand & easy to calculate.
It is based upon all the observations.It is based upon all the observations.
It is affected as little as fluctuations of sampling.It is affected as little as fluctuations of sampling.
It is capable of further mathematical treatment.It is capable of further mathematical treatment.
 DEMERITSDEMERITS
It is affected much by extreme values.It is affected much by extreme values.
If one observation is missing mean can’t beIf one observation is missing mean can’t be
calculated.calculated.
It can’t be calculated by inspectionIt can’t be calculated by inspection

MEDIANMEDIAN
 When all the observations of a variable are arranged in eitherWhen all the observations of a variable are arranged in either
ascending or descending order of magnitude. The middle value isascending or descending order of magnitude. The middle value is
median.median.
 If two nos. are there in the middle then total the two numbers andIf two nos. are there in the middle then total the two numbers and
take the average.take the average.
 E.g.1.:E.g.1.: DMFT of seven subjects are arranged in ascending orderDMFT of seven subjects are arranged in ascending order
3, 4, 4, (5), 5, 6, 7.3, 4, 4, (5), 5, 6, 7.
the fourth observation (5) is median in this seriesthe fourth observation (5) is median in this series
E.g.2.:E.g.2.:
3, 4, 5, 6, 7, 8, 9, 10.3, 4, 5, 6, 7, 8, 9, 10.
6+7= 136+7= 13
median is 13/2= 6.5median is 13/2= 6.5www.indiandentalacademy.com

MEDIANMEDIAN
 Merits:Merits:--
Easy to understand and calculateEasy to understand and calculate
Not affected by extreme values.Not affected by extreme values.
Can be located graphically.Can be located graphically.
 Demerits :-Demerits :-
It is not based upon all the observations.It is not based upon all the observations.
Not amenable to algebraic treatment.Not amenable to algebraic treatment.
Affected much by fluctuations of sampling.Affected much by fluctuations of sampling.

MODEMODE
 It is most frequently occurring observation in a series.It is most frequently occurring observation in a series.
 Mode is rarely used in medical studies.Mode is rarely used in medical studies.
 Merits:Merits:
Easy to understand & calculate.Easy to understand & calculate.
Can be calculated graphically.Can be calculated graphically.
Not affected by sampling fluctuations.Not affected by sampling fluctuations.
 Demerits:Demerits:
It is not based upon all observationsIt is not based upon all observations
In some cases mode is ill defined.In some cases mode is ill defined.
It is not adaptable to algebraic treatment.It is not adaptable to algebraic treatment.
in small no. of cases there may be no mode at all becausein small no. of cases there may be no mode at all because
no values may be repeated.no values may be repeated.
If mode is ill-defined in that case use the followingIf mode is ill-defined in that case use the following
relation.relation.
 Mode = 3 median – 2 mean.Mode = 3 median – 2 mean.

 Median is a better indication of central valueMedian is a better indication of central value
when one or more of the lowest or the highestwhen one or more of the lowest or the highest
observations are wide apart or not so evenlyobservations are wide apart or not so evenly
distributed.distributed.
 Out of the three measures of central tendencyOut of the three measures of central tendency
mean is better utilized more often because itmean is better utilized more often because it
uses all the observations in the data & is furtheruses all the observations in the data & is further
used in the tests of significance.used in the tests of significance.

STANDARD DEVIATIONSTANDARD DEVIATION
 It is the square root of the mean of theIt is the square root of the mean of the
squares of all the deviations. Deviationssquares of all the deviations. Deviations
being measured from the mean of thebeing measured from the mean of the
observations.observations.
 Root – Means – Square – Deviation .Root – Means – Square – Deviation .
 It is usually denoted byIt is usually denoted by ΣΣ (sigma) or S.D.(sigma) or S.D.
 S.D. =S.D. = ΣΣ (X- X)(X- X)22
nn

 When the sample size is more than 30,When the sample size is more than 30,
the above basic formula may be used withthe above basic formula may be used with
out modification.out modification.
 For smaller samples, substitute theFor smaller samples, substitute the
denominator (n-1) for n.denominator (n-1) for n.
 Modified formula isModified formula is
S.D. =S.D. = ΣΣ ( X- X )( X- X )22
n -1n -1

STEPS IN DETERMINING S.D.STEPS IN DETERMINING S.D.
 Calculate mean i., X=Calculate mean i., X= ΣΣx/n.x/n.
 Find deviation i e., (x-x ) = xFind deviation i e., (x-x ) = x
 Find square of deviation i.e., (x-x )Find square of deviation i.e., (x-x )22
 Find sum of square of deviationsFind sum of square of deviations
i.e.,i.e., ΣΣ ( x - x )( x - x )22
Divide sum by n-1 or n i.e.,Divide sum by n-1 or n i.e., ΣΣ ( x - x )( x - x )22
/ n./ n.
Take the square root i.e.,Take the square root i.e., ΣΣ ( x - x )( x - x )22
/ n./ n.

USES OF S.D.USES OF S.D.
 When the statistics having the greatest stabilityWhen the statistics having the greatest stability
is sought .is sought .
 when the extreme deviations should exercise awhen the extreme deviations should exercise a
proportionally greater effect upon the variability.proportionally greater effect upon the variability.
 When the co-efficient and correlation and otherWhen the co-efficient and correlation and other
statistics are subsequently to be computed.statistics are subsequently to be computed.

 Merits:Merits:
It is based upon all the observationsIt is based upon all the observations
Amenable to algebraic treatmentAmenable to algebraic treatment
It is affected by fluctuations of sampling.It is affected by fluctuations of sampling.
 DemeritsDemerits
It is an absolute measure of dispersion.It is an absolute measure of dispersion.
It is little bit difficult to understand & calculate.It is little bit difficult to understand & calculate.
It is affected by extreme value.It is affected by extreme value.

NORMAL DISTRIBUTION OR NORMALNORMAL DISTRIBUTION OR NORMAL
CURVECURVE
 In a normal curve –In a normal curve –
 The area between one S.D. on either side of meanThe area between one S.D. on either side of mean
( x ± 1( x ± 1σσ
) will include approx. 68.3% of the values.) will include approx. 68.3% of the values.
 The area between two S.D. on either side of meanThe area between two S.D. on either side of mean
( x ± 2( x ± 2σσ
) will cover most of the values. i.e., 95.4 %.) will cover most of the values. i.e., 95.4 %.
 The area between ( x ± 3The area between ( x ± 3σσ
) will include 99.7% of the) will include 99.7% of the
values.values.
- Confidence limits .- Confidence limits .

 Smooth bell shaped curve.Smooth bell shaped curve.
 Symmetrical.Symmetrical.
 Highest frequency in the middle.Highest frequency in the middle.
 Fall of frequencies on either side is equal.Fall of frequencies on either side is equal.

CHARACTERISTICS OF THE NORMALCHARACTERISTICS OF THE NORMAL
CURVECURVE
 Symmetrical around its vertical axis.Symmetrical around its vertical axis.
 The mean , median , and the mode of theThe mean , median , and the mode of the
distribution have the same value.distribution have the same value.
 No boundaries on either direction.No boundaries on either direction.
 Curve of probability , not of certainty.Curve of probability , not of certainty.

NULL HYPOTHESISNULL HYPOTHESIS
 It is a hypothesis which reflects no change or noIt is a hypothesis which reflects no change or no
difference usually denoted by Ho.difference usually denoted by Ho.
 E.g., patients with diabetes have raised B.P. or oralE.g., patients with diabetes have raised B.P. or oral
contraceptives may cause breast cancer –contraceptives may cause breast cancer – STUDYSTUDY
HYPOTHESISHYPOTHESIS..
 Converse of study hypothesis is theConverse of study hypothesis is the null hypothesis.null hypothesis.
e.g.,e.g., patients with diabetes do not have raised B.P. orpatients with diabetes do not have raised B.P. or
oral contraceptives do not cause breast cancer.oral contraceptives do not cause breast cancer.
negatively phased , hence termed null.negatively phased , hence termed null.

TEST OF SIGNIFICANCETEST OF SIGNIFICANCE
 chi – square test.chi – square test.
 t – test .t – test .

Chi – square test (xChi – square test (x22
))
( test of goodness of fit )( test of goodness of fit )
 X is a Greek letter written as chi & pronounced as Kye.X is a Greek letter written as chi & pronounced as Kye.
 XX22
test was developed bytest was developed by Karl Pearson.Karl Pearson.
 It involves calculations of a quantity called XIt involves calculations of a quantity called X22
. It is applied to rule out. It is applied to rule out
chance or to estimate the probability of chance occurrence of a difference.chance or to estimate the probability of chance occurrence of a difference.
 Compares experimentally obtained results with those to be expectedCompares experimentally obtained results with those to be expected
theoretically on some hypothesis.theoretically on some hypothesis.
USES :USES :
-It is used to find the significance in two or more than two-It is used to find the significance in two or more than two
proportions.proportions.
-It is used as a test of association between two events in binomial or-It is used as a test of association between two events in binomial or
multinomial samples.multinomial samples.
-The chi square statistics (X-The chi square statistics (X22
) measures the discrepancy between) measures the discrepancy between
observed & expected frequencies by adding together all values ofobserved & expected frequencies by adding together all values of
(Observed number – expected number)(Observed number – expected number)22
Expected numberExpected number

t – testt – test
 W.S. Gosset.W.S. Gosset.
 To test the significance of difference between 2 means in small sample.To test the significance of difference between 2 means in small sample.
 Student’s t-test:-Student’s t-test:-
-paired t-test.-paired t-test.
-unpaired t-test.-unpaired t-test.
Paired t-test:- 2 sets of observations on the same individual, before and afterPaired t-test:- 2 sets of observations on the same individual, before and after
exposure to some factor. E.g. –changes after orthodontic treatmentexposure to some factor. E.g. –changes after orthodontic treatment
t =d/SE =mean difference/(SD/ n) where SD=Standard deviation oft =d/SE =mean difference/(SD/ n) where SD=Standard deviation of
difference, n=no. of pairs.difference, n=no. of pairs.
Unpaired t-test:- Observations made on 2 different groups & differenceUnpaired t-test:- Observations made on 2 different groups & difference
between them is compared. E.g.- Comparing sales in 2 different cities.between them is compared. E.g.- Comparing sales in 2 different cities.
t =x1-x2 / SE of difference.t =x1-x2 / SE of difference.
x1=mean of first group, x2= mean of second group.x1=mean of first group, x2= mean of second group.

p-value (probability value)p-value (probability value)
 Used to assess degree of dissimilarity between 2 sets ofUsed to assess degree of dissimilarity between 2 sets of
measurements.measurements.
 Actually a probability value to ascertain whetherActually a probability value to ascertain whether
dissimilarity is entirely due to variation in measurementsdissimilarity is entirely due to variation in measurements
or in subjects response i.e., result of chance alone.or in subjects response i.e., result of chance alone.
 Measures the strength of evidence by indicatingMeasures the strength of evidence by indicating
probability that a result observed would occur by chance.probability that a result observed would occur by chance.
 Derived from statistical tests.Derived from statistical tests.

 The smaller the p- value, the more significant is theThe smaller the p- value, the more significant is the
result.result.
 Some findings may be statistically or clinically significant.Some findings may be statistically or clinically significant.
 Other findings are neither.Other findings are neither.

When samples are very large,When samples are very large, small differences may besmall differences may be
statistically significant.statistically significant.

ANOVA TEST (Analysis of variance)ANOVA TEST (Analysis of variance)
 Used to compare means of more than 2 samples.Used to compare means of more than 2 samples.
 E.g.:- Whether occupation plays any part in theE.g.:- Whether occupation plays any part in the
causation of B.P.causation of B.P.
 Take B.P. of randomly selected 10 officers,10 clerks, 10Take B.P. of randomly selected 10 officers,10 clerks, 10
lab technicians and 10 attenders. Find mean of BP of 4lab technicians and 10 attenders. Find mean of BP of 4
classes of employees.classes of employees.
 If occupation plays no role- 4 groups will not differIf occupation plays no role- 4 groups will not differ
significantly.significantly.
 If occupation plays a role- 4 groups will differIf occupation plays a role- 4 groups will differ
significantly.significantly.
 To test whether 4 means differ- ‘F’ test / Analysis ofTo test whether 4 means differ- ‘F’ test / Analysis of
variance test applied.variance test applied.

 Start with Ho.Start with Ho.
 Calculate the sum of squares of all the observations.Calculate the sum of squares of all the observations.
Split this into 2 components-Split this into 2 components-
1.sum of squares between the classes1.sum of squares between the classes
2.sum of the squares within the classes2.sum of the squares within the classes
Sum of sqs. between the classes={(∑x1)2 /n1+ (∑X2)2 /n2 +Sum of sqs. between the classes={(∑x1)2 /n1+ (∑X2)2 /n2 +
(∑X3)2 /n3+ (∑x4)2 / n4} - (∑x2) /n(∑X3)2 /n3+ (∑x4)2 / n4} - (∑x2) /n
Sum of sqs within the classes =total sum of squares – (sum of squaresSum of sqs within the classes =total sum of squares – (sum of squares
between the classes)between the classes)
If the mean BP of the 4 groups differs significantly, then reject the Ho.If the mean BP of the 4 groups differs significantly, then reject the Ho.

List of ReferencesList of References
 Biostatistics- MahajanBiostatistics- Mahajan
 Community Dental Health- Antony W.JongCommunity Dental Health- Antony W.Jong
 Community Medicine – Park & ParkCommunity Medicine – Park & Park
 Essentials of Preventive & CommunityEssentials of Preventive & Community
Dentistry – Soben PeterDentistry – Soben Peter

Thank YouThank You

QuestionsQuestions
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Thank youThank you
For more details please visitFor more details please visit
www.indiandentalacademy.comwww.indiandentalacademy.com

Bio-Statistics Guide for Dental Professionals

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