Biostatistics /certified fixed orthodontic courses by Indian dental academy

BIOSTATISTICS..
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 Statistic or datum means a measured or
counted fact or piece of information stated
as a figure such as height of one person ,
birth of a baby ,etc.

 Biostatistics:-
It can be defined as an art and
science of collection , compilation,
presentation, analysis and logical
interpretation of biological data affected
by multiplicity of factors.
It is the term used when the tools of
statistics are applied to data that is derived
from biological sciences such as medicine
or dentistry.

 Biostatistics can also be called as :-
 Quantitative medicine
 Science of variations
 For such studies we need mathematical
techniques called as statistical methods.

 Depending upon the field of application
there can be :-
 Health statistics
 Medical statistics
 Vital statistics
 These terms are overlapping and not
exclusive of each other.

Applications..
 Physiology and anatomy
 Pharmacology
 Medicine
 Community medicine
 Community dentistry
 Public health
 Research field

Common statistical terms..
 Variable:-
a characteristic that takes on
different values in different persons ,place
or things . It is denoted by X and notation
for orderly series as X1, X2,X3…..Xn
 Constant:-
a character that do not vary.e.g
mean , standard deviation etc

 Observation:-
An event and its measurement. e.g.
blood pressure .
 Observational unit:-
the source that gives observations
such as object, person , etc.
 Data :-
a set of values recorded on one or
more observational units.

 Population:-
It is an entire group of people or study
elements – person ,things or
measurements for which we have an
interest at a particular time .it may be
finite or infinite.
 Sample :-
It is defined as a part of the population
 Sampling unit:-
each member of the population

 Parameter:-
it is the summary value or constant of
the variable that describes the population
such as mean variance , correlation
coefficient ,proportion ,etc. e.g. mean
height ,birth rate

 Parametric test:-
one in which population constants are
used such as mean , variance etc and data
tend to follow one assumed or established
distribution such as normal, binomial
,Poisson, etc
 Non- parametric tests:-
no constants are used ,data do not follow
any specific distribution and no assumptions
are made . E.g. to classify good, better and
best you allocate arbitrary no. to each
category.

Types of data..
A. Qualitative / Enumeration data
Quantitative / measurement data
B. Discrete Data
Continuous Data
C. Grouped Data
Ungrouped Data

D. Primary data
Secondary data
E. Nominal data
Ordinal data

Sources of data…
 Census
 Registration of vital events
 Sample Registration System (SRS)
 Notification of diseases
 Hospital records
 Epidemiological Surveillance
 Surveys
 Research Findings

Methods of presentation
of data...

Principles of data presentation:-
The data should be :-
 arranged in such a way that it will arouse
interest in reader.
 Made sufficiently concise without loosing
important details.

 Presented in simple form to enable the
reader to form quick impression and to
draw some conclusions directly or
indirectly.
 Facilitate further statistical analysis.
 Able to define a problem and suggest its
solution.

Tables..
Sample of putty No. of impressions made
Sample A 30
Sample B 40
Sample C 25
Sample D 25

Charts and diagrams for
Qualitative data..

Bar diagram..

Pie or sector diagram..
Patients reported to department in 1 yr
Complete dentures
FPD
RPD
others

Venn diagram..
Implants
FPD
RPD

Pictogram..
Number of dentures delivered
2004
2005
2006

Shaded Maps,Spot Maps or Dot Maps
• Represents the
places where
implant research
centers can be
established

Charts and diagrams for
Quantitative data..

Histogram

Frequency polygon

Frequency curve

Epidemic curve

Line diagram

Cumulative frequency diagram/
Ogive

Scatter or Dot diagram

Box plot

Central tendency..

 It should be rigidly defined
 Its computation should be based on all
observations
 It should lend itself for algebraic treatment
 It should be least affected by the extreme
observations.

1) Arithmetic mean
2) Median
3) Mode
4) Quartiles
5) Geometric Mean
6) Harmonic mean
7) Weighted mean

Average (arithmetic mean)
 A.M = sum of observations
number of observations
Sample of putty No. of impressions made
Sample A 30
Sample B 40
Sample C 25
Sample D 25
AM = 30+40+25+25 = 30
4
Thus on an average 30 impressions can be made out of a box of putty

 Merits:-
 Easy to calculate and understand
 Based on all observations
 Familiar to common man and rigidly
defined
 Capable of further mathematical
calculations
 Least affected by sampling fluctuations.
More stable

 Demerits:-
 Only for quantitative data
 Unduly affected by extreme values
 Cannot be calculated when frequecy
distribution is with open end classed
 Sometimes AM is not among the
observation
 Cannot be determined graphically

Median..
 When all observations are arranged in
ascending or descending order, the middle
observation is known as median.
1. Ungrouped data
Median = value of [ (n+1)/2] , if n is odd
[ (n+1)/2] + [n/2] , if n is even
2
year No. of cases
treated by P.Gs
2003 289
2001 350
2004 400
2005 410
2002 450
2000 500
2006 650
Year No. of cases
treated by P.Gs
2000 500
2001 350
2002 450
2003 289
2004 400
2005 410
2006 650

ii. Grouped data:-
median = I + N/2 – c.f. x h
f
where,
N = total frequency
f = frequency
h = class width
c.f = less than cumulative frequency of
the class previous to the median class
I = lower boundary of the median class

Weight of infants in kg No. of infants
2.0 – 2.4 37
2.5-2.9 117
3.0-3.4 207
3.5-3.9 155
4.0- 4.4 48
4.5 and above 26
Weight of infants
in kg
No. of infants Cumulative
frequency
1.95– 2.45 37 37
2.45-2.95 117 154
2.95-3.45 207 361
3.45-3.95 155 516
3.95- 4.45 48 564
4.45 and above 26 590
Median = 2.95 + 295- 154 x 3.29 = 3.29
207
3.29 kg is the median weight

 Merits:-
 Easy to calculate and understand
 Can be computed for distribution with open
end classes
 Not affected by extreme observations
 Applicable for both quantitative and
qualitative data
 Can be determined graphically

 Demerits:-
 Not based on all observations
 Not rigidly defined
 Not capable of further mathematical
treatment

Mode..
 The observation that occurs most frequently in a
series is known as mode
i. Ungrouped data:-
Diastolic blood pressure of 9 individual
86 90 92 70 86 98 86 80 86
Therefore the mode is 86

ii. grouped data:-
mode = I + fm –f 1 x h
2 fm – f1 –f2
Where ,
I = lower boundary of the modal class
fm = frequency of modal class
f1 = frequency of pre modal class
f2 = frequency of post modal class
h = width of the class

 Merits:-
 Can be computed for distribution with open
end classes
 Not affected by extreme observations
 Applicable for both quantitative and
qualitative data
 Can be determined graphically

 Demerits:-
 Not based on all observations
 Not rigidly defined
 Not capable of further mathematical
treatment
 It is indeterminate when the maximum
frequency is at one end of the distrbution.

Quartiles..
 The values which divide the given data in
four equal parts when the observations are
arranged in order of magnitude are known
as quartiles.
 There will be three quartiles Q1 , Q2 and
Q3

Geometric mean..
 When values are given in geometric
progression the G.M is taken
GM = antilog [ sum ( f. log x) ]
N
N= sum (f)

Harmonic means..
 It is reciprocal of arithmetic mean of
reciprocal observations.
 For ungrouped data
HM = n
[ 1/x]
 For frequency distribution
HM = N
Σ (f/x)

Weighted mean..
 While computing sometimes we need to
prefer or give more importance to certain
values than others… and thus weighted
mean is calculated.
WM = sum ( w. x)
sum (w)

Dispersion..

 The variations or dispersion gives the
information as to how individual
observations are scattered or dispersed
from the mean of a large series.
 Deviation = observation - mean

Measure of dispersion..

 Gives information on how individual
observations are scattered or dispersed
from the mean of a large series.
 Different measures of dispersion are:-
1) Range
2) Quartile deviation
3) Coefficient of Quartile deviation
4) Mean deviation
5) Standard deviation
6) Variance
7) Coefficient of variance

Mean deviation..
 Based on all observations
 Mean deviation = Sum I x – x I
n

Standard deviation
 σ = √ Sum (x – x )2
n -1
 The problem of negative variable is solved
here and we can estimate the scatter in the
population

Variance
 Nothing else but square of standard deviation
and denoted by σ2

Day of reporting with
complaint
No. of patient reported
1 10
2 25
3 35
4 05
5 10
6 10
7 15
Mean = 110/7 = 15.7
SD = √ 668.34 = 10.5
6
Day of reporting
with complaint
No. of patient
reported
Ix- x I2
1 10 32.49
2 25 86.49
3 35 372.49
4 05 110.49
5 10 32.49
6 10 32.49
7 15 1.4
Total 668.34

Uses of Standard deviation:-
a) Summarizes the deviation of a large
distribution from mean in one figure used
as a unit of variation
b) Indicates weather the variation is real or
due to special reason
c) Helps in comparing two samples
d) Helps in finding the suitable sample size
for valid conclusion

Merits of SD:-
 Rigidly defined
 Based on all observations
 Doesn’t ignore the algebraic sign of
deviation
 Capable of further mathematical
treatment
 Not much effected by sample fluctuation

Demerits of SD:-
 Difficult to understand and calculate
 Cannot be calculated for qualitative data
and distribution with open end classes
 Unduly affected by extreme deviations

Sampling..

 Sampling method is a scientific and
objective procedure of selecting units from
a population and provides a sample that is
expected to be representative of the
population as a whole.
 Results are generalized for the entire
population which might not be completely
correct ,thus sampling errors are there.

 Thus :-
Sample should be well chosen
Sample must be sufficiently large
There must be adequate coverage of the
sample.

Method of sampling..

A. Non-random sampling:-
sample is chosen without
conscious bias and may not represent the
population.
 Not useful and gives only the feel of the
population
 Also called as “Chunks” , “Accidental”,
“incidental" or “samples of convenience”

 For example we pick a group of 30 people out
of a population without seeing there age ,
sex, social status etc for presence of a fixed
prosthesis in their mouth.

Another type in same is judgment type
sample:-
 Quota samples:-
the investigator is interested in
getting some predetermined no. of units for
the sample. E.g. in terms of sex, education
 Purposive sampling:-
Selected because the investigator
believes that they represent the population
under study.
e.g. literacy rate

B. Probability sampling:-
each individual in the population has
a probability of getting selected
 Gives a better picture of the population
and results can be generalized

 Types of sampling:-
1) Simple random sampling
2) Systematic sampling
3) Stratified sampling
4) Cluster sampling
 If probability sampling is done in more
than one stage then there can be two
stage or multistage sampling

Simple random sampling..
 Selection solely based on chance
 Done for a small homogenous population
 E.g. choosing samples from a dental unit for
efficacy of soft liners
 Can be of two types:-
 Without replacement ( when population is infinite)
 With replacement ( when population is finite)
Hence prepare a sample frame , decide
the sample size and then randomly pick
the sample size that is needed.www.indiandentalacademy.com

Systemic sampling..
 Only first unit is selected randomly and rest are
chosen in a pre-determined pattern
automatically as complete list of population is
available
 Due to simplicity and low cost this is a preferred
method and helps establishing control over the
field of work.
 E.g. choosing a sample from the population in
Dhankawadi for presence of a dental prosthesis.

Stratified sampling..
 Population is divided into groups or strata
and then the desired sample size is picked
from these homogenous groups
 Lesser the differences with in the strata
more is the difference in between the
strata, which means greater gain.
 Proportional Allocation

 It is more precise
 Nature and size of the strata can be
known, hence better application of the
results for the population.
 E.g. oral health status of population living
in Katraj.We can divide this population
into strata

Cluster sampling..
 The population is divided into smallest
possible groups or clusters and then these
clusters are chosen by simple random
sampling method
 Useful when the list of elements in sample
is not available.
 Necessary prerequisite is that every cluster
should correspond to only one cluster so
that there are no repetitions or omissions.

 Large number of small clusters are preferred
over small number of large clusters.
 Disadvantage is that the clusters might
contain same type of elements.
 E.G. we divide the population of Pune in
clusters according to the area and then do a
study for prosthetic needs of the population

 Sub Sampling
 Random Digit Dial
 Sampling by computers

Errors…

Non-Sampling Errors..
 Discrepancy between the survey value and
the true value is called as observational or
response error.
 Present right from the planning of the
survey to the analysis of the data.

 Faults at planning level. E.g. incomplete
coverage , faulty method of selection or
estimation
 Faults in carrying out the instructions by
the enumerator
 Faults by the respondents
 There can also be Non-Response Errors
where data could not be collected due to
any reason. E.g. subject unavailable.

 It is better to omit a lost sample or
element than to substitute with another
one
 Omission creates small biased samples
while substitution creates large biased
samples.

Sampling Errors..
 These errors are by chance and concern
incorrect rejection or acceptance of the
Null Hypothesis
 Can be of two types :-
 Type I
 Type II

Type I:-
 Also called as Alpha error or error of first
kind
 if null hypothesis is false then noType I
error
 Some studies take an alpha error of 5% as
cut off limit for rejecting null hypothesis.
 Repeated testing or multiple comparisons
increases the likelihood of type I error

Type II:-
 Error Of Second type or Beta error
 Occurs when null hypothesis is accepted
when actually it is false
 If null hypothesis is true then there is no
Type II error

Sample size..
 A sample size can be calculated by using the
standard formulae should have :-
 Required level of statistical significance of the
expected result
 Acceptable chance of missing a real effect
 Magnitude of the effect under investigation
 Prevalence of disease
 Relative sizes of groups being concerned

 Smaller the sample size….lesser is the
precision
precision = √n
s
where n = sample size
s = SD for the sample

Bias in sample..
 Also called as systemic error
a. Selection bias:-
distortion in manner of selection
b. Measurement bias:-
distortion in the measurement

c. Confounding bias:-
associated with both exposure and
outcome. Cause problem when unequally
distributed between the sample and the
control group.
Can be controlled by randomization,
restriction and matching at designing
stage and stratification and statistical
modeling at analysis stage.

Probability..
 Chance of an event occurring
 Trial
 Events:- various outcome of a trial
 Exhaustive event:- total no. of possible
outcomes
 Favorable events:-no. of cases favorable to
an event

 Mutually exclusive events:- when
happening of one event precludes the
other.
 Equally likely events
 Independent events
 Sample space:- totality of all possible
outcomes

 probability = favorable no. of events
exhaustive no. of events
p + q = 1

 Subjective probability:-
probability based on personal evaluations
or believes.
E.g. when a dental surgeon feels that one
companies' material is better than other though
there be no scientific prove.
 Conditional probability:-
when there are conditions to be followed in
a trial.
E.g. when we compare the oral health care
facilities provided by the dental hospitals, now
difference lies in the area or condition they work

Normal distribution..
 Binominal distribution
 Uniform distribution
 Skewed distribution
 Normal / Gaussian distribution
 Log normal distribution
 Poisson distribution
 Geometric distribution
 Others:- multinominal ,exponential etc
distribution

Normal distribution
Y axis
X axis

 For comparison we also use standard normal
curve in which the population mean is taken
as zero and the Standard deviation as 1

Test of significance..

 Tests a hypothesis
 Null hypothesis:-
a hypothesis which assumes that there
is no difference between the population
means. Denoted by Ho
 Alternative hypothesis:-
a hypothesis that differs from the null
hypothesis. Denoted by H1

 Degree of freedom:-
the number of independent
observations which are used in statistics.
 Level of significance (α):-
the probability of committingType I
error
 Power of the test:-
the probability of committingType II
error. Denoted by β and 1-β.this is the
probability of taking a correct decision.

 Critical regions:-
Regions of acceptance and
rejection
a. one tailed test
b. two tailed test
 Confidence limit

Procedure for testing a hypothesis..
1. Set up a null hypothesis
2. Set up an alternate hypothesis.This gives
an idea weather it is a one or two tailed
test.
3. Choose the appropriate level of
significance
4. Compute the value of test statistic ”z”

Procedure for testing a hypothesis..
z = observed difference
standard error
5. Obtain the table value at given level of
significance
6. Compare the value of z with that of table
value
7. Draw the conclusion

Z test
 Also called as Large Sample test or Normal
test
 Statistical value of particular importance is
called as proportion and is obtained by
dividing the individual events by total no.
of events

 If IzI > 3 then Ho is always rejected
or else may be accepted
 if IzI> 1.96, Ho is rejected, 5% level of
significance or else may be accepted
 if IzI> 2.58, Ho is rejected, 1% level of
significance or else may be accepted
One tail test
Two tail test

Can be:-
 Test for qualitative data
 Test for quantitative data

 E.g :-
in Department of Prosthodontics , out of
120 cases treated 35 were of implant. Check
whether the proportion of implant cases is
40%.

 Let p be the sample proportion of implant cases done
p = 35 = 0.29
120
P = 0.40
Ho : the proportion is 40 %
H1 : the proportion is not 40%
Z = p-P = 0.29-0.40 = -2.46
SE √
Reject the null hypothesis at 5% and since
the value is greater than 1.96
Thus the proportion of implant cases is
not 40%
0.40 x 0.60
120

Small sample test..
 When the sample size is less than 30
 T- test
 Unpaired t- test
 Paired t-test
 Chi- Square test

t-test
 W.S Gosset,1908
 Also called as student’s t test
 Assumptions:-
1) Sample must be random
2) Population standard deviation is not
known
3) The distribution of population from
which the sample is drawn is normal

 Test regarding single mean:
 For testing the significance of difference between
sample mean and population mean
t = x – μ
s/ √n
where, S2 = sum ( x- x )2
n-1
Values are seen with the table for this test and then
decide the significance

 E.g
Nine individuals are chosen from a population
and their mouth openings were fond out to be
( in mm) as 40,45,30,35,50,52,47,39,40.
discuss the mean mouth opening is
40mm
Solution:-
Ho : the mean mouth opening is 40 mm
H1 : the mean mouth opening is not 40 mm

X X-X (X-X)2
40 -2 4
45 3 9
30 -12 144
35 -7 49
50 8 64
52 10 100
47 5 25
39 -3 9
40 -2 4
Total 378 408
X= 378 = 42
9
S2= 408 = 51
8
t = 42-40 = 0.8
7.14/ 3

At degree of freedom of 8 the value of t is
3.355 at 1% l.o.s
Conclusion:-
therefore the mean mouth opening may be
40 mm.The difference occurred due to
sample fluctuation

Unpaired t test
 Two equivalent independent samples are
studied
 The two samples should be random from
normal population having unknown or same
variance
t = observed difference
SE

Paired t test
 When the two samples are dependent and
sample size is same
 E.G. increase in flexural strength of acrylic
denture before and after using glass fibers
1. Set up the null hypothesis
2. Set up the alternative hypothesis
3. Obtain the difference of paired observation,
d = x- y
4. Compute the mean of difference d = sum (d)/n

Paired t test
5. Find the SD of difference and calculate SE
SD of d (S) = √ sum ( d – d)2
n-1
SE of difference = SD of difference
√n

6. Work out the value of t
t = d √n
S
7. Find out the value from the t table
8. Reject or accept

 E.g:
In the trial for the impact strength for 10 acrylic resin
bars with and without reinforcement with glass fibers
the readings were
before ( in kg load)
10, 12, 7, 9, 13 ,17,8,12,10,15
after
16, 19,12,14,15,18,18,17,16,10
Test the efficacy of fiber reinforcement
Ho: glass fiber reinforcement is not effective
H1: glass fiber reinforcement is effective

Sample no. Before After d = Ix1-x2I (d-d)2
1 10 16 -6 0.64
2 12 19 -7 3.24
3 7 12 -5 0.4
4 9 14 -5 0.4
5 13 15 -2 10.4
6 17 18 -1 17.6
7 8 18 -10 23.04
8 10 17 -7 3.24
9 12 16 -4 1.44
10 15 10 5 0.4
Total 52 60.80
Mean = 52/10=5.2
SD(d)= √60.8/9= 2.6
SE = 2.6 = 0.86
√9
t = 5.2/0.86= 6.04

the value of t at 1% l.o.s is 1.83 for a degree of
freedom of 9
Conclusion:-
Thus the glass reinforcement is highly effective

Chi Square test
 Plays an important role in the problem where
information is obtained by counting or
enumerating instead of measuring.
 Use to test:-
a) Independence of attributes
b) Goodness of fit of the distribution

 General procedure :-
1. Write down the null hypothesis
2. Obtain the expected frequencies
3. Compute the value of chi square test
X2=Sum ( observed – expected )2
Expected
4. Find out the degree of freedom
5. Obtain the value from the table
6. Compare the value

 E.gSex O group A group B group Ab
group
total
Male 105 50 45 15 215
Female 115 60 40 10 225
Total 220 110 85 25 440
Expected frequency= RT x CT
GT
Sex O group A group B group Ab group
Male 107.5 53.57 46.42 12.22
Female 112.5 56.25 48.58 12.78

 Ho: blood group is independent of sex
 H1: blood group is not independent of sex
X2 = 3.42
Degree of freedom = (r-1) (c-1)= 3
Value of X2 for 3 degree of freedom is 7.81 at 5%
l.o.s
Conclusion:-
Blood group is independent of the sex

Correlation..
 Joint relation of two variables
 Positive Correlation
 Negative Correlation
 Easiest method of studying it is the graphical
method
 E.G: correlation between size of edentulous
arch and retention of the denture

 Correlation Coefficient
 By Prof. Karl Pearson
r = n (Sum xy)- n ( x y )
√ [Sum x2 – n x 2 ] √ [Sum y2 – Sum n y 2]
 also known as product moment correlation
coefficient
 - 1 ≤ r ≤ 1
 When no correlation then r=0

Linear regression..
 Regression means to step back
 To predict unknown value of a variable when value of
one is known
 Can be :-
 Simple regression
 Multiple regression
E.g. lets suppose we have data about the attrition
seen in complete dentures in 5 yr and we want to
know the attrition that would have been seen in 3
yrs.

Y = a+ b X
b= ∆y / ∆x
Y a = y intercept
∆x
x+∆xx

Analysis Of Variance
 ANOVA is a collection of statistical
models, and their associated procedures,
in which the observed variance is
partitioned into components due to
different explanatory variables, usually
called factors in Design of experiments

 sometimes known as Fisher's ANOVA or
Fisher's analysis of variance, due to the use
of Fisher's F-distribution as part of the test
of statistical significance.

 There are three conceptual classes of such
models:
 Fixed-effects model assumes that the data
come from normal populations which may
differ only in their means.
 Random-effects models assume that the data
describe a hierarchy of different populations
whose differences are constrained by the
hierarchy
 Mixed effects models describe situations
where both fixed and random effects are
present.

 One-wayANOVA is used to test for
differences among three or more
independent groups.
 Another-wayANOVA for repeated
measures is used when the subjects are
subjected to repeated measures; this
means that the same subjects are used for
each treatment. Note that this method
can be subject to carryover effects.

 FactorialANOVA is used when the
experimenter wants to study the effects of
two or more treatment variables.The most
commonly used type of factorialANOVA is
the 2x2 (read: two by two) design, where
there are two independent variables and
each variable has two levels or distinct
values.

 Multivariate analysis of variance
(MANOVA) is used when there is more
than one dependent variable.
 Both main effects and interactions
between the factors may be estimated

 Variance ratio :-
F = estimate of variance based on the variation between the groups
estimate of variance based on the variation within the groups
Degree of freedom = no. of observations - 1

Non parametric test
 Distribution free method of analysis
 Observations should be continuous but not
necessarily defined as required in other tests
 No assumptions are made for the population
 Sample observations have to be independent
 Easier to conduct and understand but less
powerful than the parametric tests

1. The sign test
2. Wilcoxon signed rank test
3. Mann -Whitney U test
4. Wilcoxon Rank Sum test
5. Kruskal –Wallis test
6. Kolmogrov- Smirnov test

Conclusion..

 Statistics has been a enigma to us, which we
feared unanimously.
 Conducting a study and not understanding
the analysis and interpretations cannot entitle
us to the word RESEARCHERS in true sense

 It is the call of the day that we step ahead
and understand biostatistics… accept it as
a part of our field of Prosthodontics and
use it for the betterment of our materials
techniques and most important of
all…..satisfaction of the patient.

Thank you…!!
For more details please visit

Biostatistics /certified fixed orthodontic courses by Indian dental academy

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