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8/13/2019 Bios Tast is Tics

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BIOSTATISICS


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B.K. Mahajan. Methods in Biostatistics, 6thedition, Jaypee

brothers P.S.S.Sundar Rao, J.Richard. An introduction to Biostatistics,3rd

edition, Prentice Hall of India.

James F Jekel, David L Katz, Joann G Elmore. Epidemiology,biostatistics and preventive medicine, 2ndedition, WB Saunders

Company

Research methodology-C.R.Kothari,

Foundations of clinical research-Portney & Watkins

www.google.com
http://www.google.com/http://www.google.com/


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Etymology:

Italian word statista-means statesman German word statistic - meanspolitical state.

Definitions:

Statistics-

Principles and methods for the collection, presentation,

analysis and interpretation of numerical data.

The science and art of dealing with variation in such a way as

to obtain reliable results.

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Statistics is an important & integral part of

research methodology.

It is a pervasive force on which the entire

spectrum of clinical decision making is dependent.

Tests of significance are one of the centralconcepts in statistics.

These are the mathematical methods by which the

probability of an observed difference occurring by

chance is found.

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John GrauntFather of health statistics

Bio statistics-

It is the method of collecting, organizing, analyzing,tabulating & interpreting the data related to living

organisms & human beings. Application of statistics to health problems.

Health statistics public/ community health.Medical statistics medicine.Vital statistics demography.Dental statistics dentistry.

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To define what is normal or healthy in a population. Ex:-

pulse rate/ min.To find:-

Statistical difference between means of two variables.Ex: mean blood pressure of two cricket teams after acricket match.

Co-relation between two variables.Ex; - Female literacy rate & Infant Mortality Rate.

usefulness of sera & vaccines in the field. % of deathsamong vaccinated compared to % of deaths among non-vaccinated.

To test the efficacy of different treatments eg. Medicalmanagement and surgical management of angina patients.


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To assess the state of oral health in the community and todetermine the availability and utilization of dental carefacilities.

To indicate the basic factors underlying the state of oralhealth by diagnosing the community and find solutions tosuch problems.

To determine success or failure of specific oral healthcare programs or to evaluate the programme action.

To promote health legislation and in creatingadministrative standards for oral health.


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Data

Qualitative dataQuantitative data

DiscreteContinuous

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Definition:A collective recording of observationseither numerical or other-wise.

two broad categories:

Ordinal

DichotomousNominal


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Def: A collective recording of observations either numeric

or otherwise is called data Types:

Qualitative Quantitative

sources Primary SecondaryMethods of collecting data

CensusSampling


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Interval scale No absolute zero

Eg. Centigrade scale of temperature

Ratio scale Has a true/ absolute zero

Kelvin temperature scale

Most common quantitative data


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Nominal data

Naming or categorical variables that have no

measurement scales

Examples Recording blood groups

a) O b) A c) B d) AB

Reasons for extraction of teeth

a) Caries b) periodontitis c) therapeutic d)

others


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Ordinal (ranked) data

Characterized in terms of more than two variables and

have a clearly implied direction but the data are notmeasured on a measurement scale

Examples

Severity of patient perceived pain

a) No pain b) mild pain c) moderate pain d) severe

Esthetic concerns of children

a) Satisfied b) neutral c) not satisfied

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Dichotomous data (Binary variables)

The variable can have only two values May or may not be directional Examples

Sex of the respondents Presence or absence of dental disease in a village

population

Nominal, ordinal and dichotomous data can be calledcategorical data

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Def: the total process of collecting,

compiling and publishingdemographic, economic and social

data pertaining at a specified time

or times, to allpersons in a country

or delimited territory


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The first regular census in India- 1881

Recent census in India- March, 2001

Census act- 1948

Functions-

Demographics, social & economic conditions of people.

Baseline data

Advantages-

Complete information

Disadvantages-

expensive, time consuming, needs more man-power, lesser

accuracy

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Objective of classification of data :

make the data simple,

concise, meaningful,

interesting and helpful in further analysis.

two main methods of presenting data:

Tabulation and

Diagrams


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classified on the following bases: Geographical. i.e , area-wise, e.g. cities, districts etc.

Chronological i,e, on the basis of time.

Qualitative i.e according to some attribute. Quantitative i,e in terms of magnitude.

The two elements of classification are The variable and

The frequency.


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Variable:

a name denoting a condition , occurrence or effect thatcan assume different values

Divided: subgroups ,classes. have lowest and highest values Class interval :difference between the upper and

lower limit of a class Eg: in the class 5 -14, 5 - lower limit and 14 - upper limit. class interval = 14 - 5 =9.Frequency: is the number of units belonging to eachgroup of the variable.

Frequency distribution table:way of presenting data in

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Title of the table named at the bottom

The no. of class intervals - between 5 and 20.

The class intervals - at equal width.

Clearly definedclass limits to avoid ambiguity.For e.g., 0-4.5-9. 10-14. Etc.

Clearly defined row and column with the headings.

Units of measurement should be specified.

If the data is not original, the source of the data should bementioned at the bottom of the table.

Frequency distribution table

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Extremely useful

attractive to the eyes,

give a bird's eye view of the entire data, have a lasting impression

facilitate comparison of data relating to

different time periods and regions.


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TYPES OF DIAGRAMS: Bar Diagram : qualitative data.

Multiple Bar: qualitative data Component Bar Diagram: qualitative data.

Frequency Polygon: qualitative data

Pie Diagram: qualitative data Line diagram: qualitative data

Proportional Bar Diagram

Histogram: quantitative data of continuous type. Cartograms or Spot Map: geographical distribution of

frequencies

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Basic rules :

self explanatory

simple and consistent with the data. values of the variables - on horizontal or X-axis and

the frequency - vertical line or Y-axis.

No too many lines on the graph, should not lookclumsy.

The scale of presentation right hand top cornerof the graph.

The scale of division of the two axes should beproportional.

the details of the variables and frequencies

presented on the axes. 25


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represent qualitative data. only one variable. width of the bar remains the same

the length varies according to the frequency ineach category. bars : vertical or horizontal.

Limitation : represent only one classification cannot be used for comparison

SIMPLE BAR DIAGRAM:


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compare qualitative data with respect toa single variable.

Eg: sex wise or with respect to time orregion.

each category of the variable have a setof bars of the same width correspondingto the different sections without any gap

in between the width and the lengthcorresponds to the frequency.


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represent qualitative data.

both, the number of cases in major groups as

well as the subgroups simultaneously

cases of the major group drawn

each rectangle is divided according to no. in the

subgroups.


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represent qualitative data.

compare only the proportion of sub-groupsbetween different major groups of observations,then bars are drawn for each group with the samelength, either as 1 or 100%. These are thendivided according to the sub-group proportion ineach major group.


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useful to study changes of values in the variable over

time simplest type X-axis, - hours, days, weeks, months or years Y-axis- value of any quantity pertaining to X-axis,


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quantitative data of continuous type.

bar diagram without gap between the bars.

represents a frequency distribution.

X-axis: the size of an observation is marked. Starting from

0, the limit of each class interval is marked, the width

corresponding to the width of the class interval in the

frequency distribution.

Y-axis :the frequencies are marked. A rectangle is drawn

above each class interval with height proportional to the

frequency of that interval.


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frequency distribution of quantitative data

compare two or more frequency distributions.

a point is marked over the mid-point of the class

interval, corresponding to the frequency.

points are connected by straight lines.

The first point and last point are joined to the midpoint

of previous and next class respectively. To compare two or more frequency distributions, lines of

different types are drawn on the same graph.


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Fig.--. Height and Weight of 20 students of CODS

0

10

20

30

4050

60

70

80

3 4 5 6 7

Height in feet

WeightinK

Gs

Weight

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show geographical distribution of frequencies of a

characteristic.


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The pictures representing the value of items

are called pictograms.

It is most useful way of representing data to

those people who cannot understand.


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Central Tendency

MeanMedian

Mode

SummaryMeasures

Variation

Variance

Standard Deviation

Range


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Should be easy to understand and compute.

should be based on each and every item in the series.

should not be affected by extreme observations

(either too small or too large values). should be capable of further statistical computations.

It should have sampling stability.


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simplest measure of central tendency.

Ungrouped data:Mean = Sum of all the observations of the data

Number of observations in the data

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0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14

Mean = 5 Mean = 6


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strong measure of central tendency

Not affected by extreme values

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14

Median = 5 Median = 5

In an ordered array, the median is the middle number

If n or N is odd, the median is the middle numberIf n or N is even, the median is the average of the two

middle numbers


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Value that occurs most often Not affected by extreme values Used for either numerical or categorical data

There may may be no mode There may be several modes

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mode = 90 1 2 3 4 5 6No Mode


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me n

.


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medi n


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mode


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Variation

VarianceStandardDeviationPopulationVariance

SampleVariance

PopulationStandardDeviation

Sample

Standard

Deviation

Range

Interquartile

Range


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Measure of variation Difference between the largest and

the smallest observations:

Ignores the way in which data aredistributed

Largest SmallestRange X X

7 8 9 10 11 12

Range = 12 - 7 = 5

7 8 9 10 11 12

Range = 12 - 7 = 5


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Shows variation about the mean EX,Dr A = 2,4,3,4,6,6,2,5

Dr B = 4,5,4,3,4,5,3,4Dr C = 3,3,8,3,3,3,4,5

mean for Dr A = 32/8=4 daysmean for Dr B = 32/8=4 daysmean for Dr C = 32/8=4 days

2

2 1

1

n

i

i

X X

Sn

Sample variance: (For sample more than 30)


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(x-x)

Dr A = -2,0,-1,0, 2,2,-2,1 = 0 Dr B = 0,1,0,-1,0,1,-1,0 = 0 Dr C = -1, -1, 4,-1,-1,-1,-1,0 = 0

(x-x)2 Dr A = 18, Dr B = 4 , Dr C = 22Thus, Dr A =18/8 = 2.25

Dr B = 4/8 = 0.5

Dr C = 22/8 = 2.75

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Mean = 15.5

s = 3.33811 12 13 14 15 16 17 18 19 20 21

11 12 13 14 15 16 17 18 19 20 21

Data B

Data A

Mean = 15.5

s = .9258

11 12 13 14 15 16 17 18 19 20 21

Mean = 15.5

s = 4.57

Data C


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Summarizes the deviations , of a large distribution Indicates whether the variation from mean is by

chance or real

Helps in finding standard error

Helps in finding the suitable size of sample

Standard deviation is only interpretable as asummary measure for variations having

approximately symmetric preparations


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Compare relative variability

Variation of same character in two or more series

compare the variability of one character in two different

groups having different magnitude of values or to compare two characters in the same group by

expressing in percentage

C V = S.D x 100

mean

Higher the C.V greater variability


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area under the curve between any 2 pts which

correspond to the number of observations betweenany 2 values of the variant - in terms of a relationshipbetween the mean and the SD:

a) Mean 1 S.D. covers 68.3% of the observations;

b) Mean 2 S.D. covers 95.4% of the observations;c) Mean 3 S.D. covers 99.7% of the observations.This relationship is used for fixing confidence interval.

Normal distribution law forms the basis for varioustests of significance.


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Describes how data is distributed

Measures of shape Symmetric or skewed

Mean =Median =ModeMean


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relative frequency or probable chances of

occurrence with which an event is expected tooccur on an average

Expressed as p Ranges from 0-1 when p= 0, no chance of event happening When p=1 , 100% chances of event happening

no of events occurring

total no of trialsq = negative probability


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Methods to estimate the difference b/w estimates of samples

two hypothesis are made:

Null hypothesis or hypothesis of no difference

Alternative hypothesis of significant difference

1.Null hypothesis or hypothesis of no difference [Ho]

Asserts that there is no real difference in sample & general

population

The difference found is accidental & arises out of sampling

variations


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States that sample result is different than thehypothetical value of population

To minimize errors the sampling distribution or areaunder normal curve is divided into two regions orzones

1.Zone of acceptance :samples in the area of mean1.96 SE, null hypothesis accepted

2.Zone of rejection: sample in the shaded area isbeyond the mean 1.96 SE, null hypothesis-rejected


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T I


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Type I error: null hypothesis is rejected { when it is true}

The null hypothesis is rejected even it falls inthe zone of acceptance serious error

Type II error


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Type II error null hypothesis is wrongly accepted error the null hypothesis is accepted even it falls in the zoneof rejection not serious error, needs only confirmation of result by

changing the level of significance

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Defined as number of independent numbers in

sample

Eg:

When there are 10 values , 9 choices or degrees offreedom

In unpaired t test of difference between 2 means

df = n1+n2-2

Where;n1& n2 are no observations.

In paired t- test df = n-1


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Standard error of mean = SD of means of severalsample from same population

SE = SD of observation in the sample

No of observation in the sample

Variation in biological observation


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Whenever 2 sets of observation have beencompared, it becomes essential to findwhether the diff observation b/w the 2

groups is because of sampling variation/ anyother factor Method Tests of Significance

Tests of significance


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Tests of significance

Parametric tests:Their model specifies certain conditions about theparameters of the population from which the researchsample is drawn.

Used for quantitative data.

Nonparametric tests or distribution free tests:

Their model does not specify conditions about the

parameters of the population from which the researchsample is drawn.Used for qualitative data.

Non parametric tests :Parametric tests :


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Non parametric tests :

Chi Square test

Wilcoxon signed rank test

Mann-Whitney U test

Spearmans correlation test

Mc Nemars test

Fishers exact probability test

Parametric tests :

Large sample tests:

Z-test

Small sample test :

Chi Square test

t-test

Independent sample t-test

Paired t test

F-test [ANOVA]


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To compare sample mean with population Means of two samples Sample proportion with population Proportion of two samples Association b/w two attributes


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One-sided tests have onerejection region,i.e. youcheck whether theparameter of interest islarger (or smaller) than a

given value. Two-sided tests are used

when we test a parameterfor equivalence to a certain

value. Deviations from thatvalue in both directions arerejected.


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Large samples ( > 30) Difference observed b/w sample estimate and that of

population is expressed in terms of SE Score of value of ratio b/w the observed difference &

SE is called Z Z = diff in means / SE of mean


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e.g. Oral hygiene instructions &

development of new cavities.

Group 0-

1

2-3 4-5 Total

No. who receivedinstructions

30 15 5 50

No. who did not

receiveinstructions

20 15 15 50

Total 50 30 20 100

Number of new cavities


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Drawbacks : Tells us about the association but fails

to measure the strength of association.

Test is unreliableifthe expectedfrequency in any one cell is less than 5.

Correction is done by subtracting 0.5from |0-E| Yatess correction

Not applicablewhen there is 0 or 1 in any

of the cells [ Resort to Fishers exactprobability test]

Paired samples:


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Wilcoxon signed rank test [Matched pairs test] :

Find the differences between each pair ofvalues & assign rankto the differences fromthe smallest to the largest without regard to

sign.In case there are ties, then we wouldassign each of the tied observation the meanof the ranks which they jointly occupy.

The actual signs of each difference are


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gthen put to the corresponding ranks &the test statistic T is calculated which

happens to be the smaller of the twosums. [The sum of the negative ranks& the sum of the positive ranks]

Calculated value must be equal toor smaller than the table value inorder to be considered significant.

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Unpaired samples:


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Mann-Whitney test [U test]:

Used to determine whether twoindependent samples have been drawnfrom the same population.

Applies under very general conditions.

Rank the data jointly taking them as

belonging to a single sample in eitheran ascending or descending order.

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Fi h x t p b bilit t t :


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Fisher s exact probability test :

Used in place of2test if

There are 0 or 1 in any of the cells

or any expected value is < 1

Any cell frequency is < 5or more than

20% of the expected frequencies are


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m f f g f

Tests are only useful aidsfor decisionmaking not decision making itself. Do not explain the reasonswhy does

the difference exist. Results are based on probabilities& as such

can not be expressed with full certainty. Inferences based on them cannot be said

to be entirely correct evidencesconcerningthe truth of the hypothesis

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Compare more than two samples Compares variation between the classes as well as

within the classes For such comparisons there is high chance of error

using t or Z testOne-way used to compare more than 3 means from

independent groups.Is the age different between White, Black, Hispanicpatients?

Two-way used to compare 2 or more means by 2 or morefactors.Is the age different between Males and Females,With and Without Pnuemonia?


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Pearsons correlation coefficient r = (X x) (Y-y)

(X x) (Y- y) Does not prove whether one variable alone can cause

the change in other.


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Thank you

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