statistics

9TH IOS PG
CONVENTION
www.indiandentalacademy.com

APPLICATION
OF
BIOSTATISTICS
IN
ORTHODONTICS

STATISTICS
STATISTICS AS A SINGULAR NOUN IS “A
SCIENCE OF FIGURES”
WHERE AS PLURAL NOUN IT MEANS
“FIGURES” OR NUMERICAL DATA OR
INFORMATION.

BIOSTATISTICS
BIOSTATISTICS CAN BE DEFINED AS ART
AND SCIENCE OF COLLECTION,
COMPILATION, PRESENTATION, ANALYSIS
AND LOGICAL INTERPRETATION OF
BIOLOGICAL DATA AFFECTED BY
MULTIPLICITY OF FACTORS“An ounce of truth produces tons of statistics”

STATISTICS
THE WORD STATISTIK IS DERIVED FROM
AN ITALIAN WORD STATISTA MEANING
STATESMAN.
GOTTFRED CHENWALL, A PROFESSOR AT
MARLBOROUGH USED THIS WORD FOR
THE FIRST TIME.
ZIMMERMAN INTRODUCED THE WORD
STATISTICS INTO ENGLAND.

DURING THE OUTBREAK OF PLAGUE IN
ENGLAND, IN 1532 THEY STARTED
PUBLISHING THE WEEKLY DEATH
STATISTICS.THIS PRACTICE CONTINUED AND
BY 1632, THESE BILLS OF MORTALITY, LISTED
BIRTHS AND DEATHS BY SEX
HISTORY OF
STATISTICS

IN 1662, CAPT.JOHN GRAUNT USED 30
YEARS OF THESE BILLS TO MAKE
PREDICTIONS ABOUT THE NUMBER
OF PEOPLE WHO WOULD DIE FROM
VARIOUS DISEASES AND
PROPORTIONS AF MALE AND FEMALE
BIRTHS THAT COULD BE EXPECTED.
HISTORY OF
STATISTICS..

KNOWLEDGE OF STATISTICAL
METHODS
1.ENABLES US TO MAKE INTELLIGENT USE OF
THE CURRENT LITERATURE.
2.OPENS UP NEW PATHS OF EXPERIMENTAL
PROCEDURES
3.ENABLES A RESEARCH WORKER TO COLLECT,
ANALYZE AND PRESENT HIS DATA IN THE
MOST MEANINGFUL AND EXPEDITIOUS
MANNER.
4.ALLOWS A BIOINFORMATICS PROFESSIONAL
USE STATISTICAL SOFTWARES IN Awww.indiandentalacademy.com

LIMITATIONS
STATISTIC LAWS ARE NOT EXACT LAWS LIKE
MATHEMATICAL OR CHEMICAL LAWS BUT
ARE ONLY TRUE IN MAJORITY OF CASES.
EX: WHEN WE SAY THAT THE AVERAGE
HEIGHT OF AN ADULT INDIAN IS 5’ 6’’ , IT
INDICATES THE HEIGHT NOT OF INDIVIDUAL
BUT OF A GROUP OF INDIVIDUALS.www.indiandentalacademy.com

SUBDIVISIONS OF
STATISTICS
THEY CAN BE SEPERATED INTO TWO
BROAD CATEGORIES:
1.DESCRIPTIVE STATISTICS
2.INFERENTIAL STATISTICS

Norm Sample
size
Mean Std.
Deviation
Std. Error
95% C I for Mean
Min
Max
Lower
bound
Upper
bound
LED 40 sec
10 9.659 0.615891 0.19476168 9.218418476 10.099581 8.34 10.7
LED 20 sec
10 7.596 0.816921 0.25833312 7.011609886 8.1803901 6.36 8.95
Argon Laser 10 sec
10 7.568 1.741518 0.5507163 6.322193174 8.8138068 3.6 9.47
Argon Laser 5 sec
10 5.824 1.636773 0.51759315 4.653122953 6.9948770 4.37 8.93
Halogen Light 40 sec
10 10.374 1.688939 0.53408946 9.165805693 11.582194 8.21 12.97
DESCRIPTIVE
STATISTICS

DAT
A
WHENEVER AN OBSERVATION IS MADE, IT
WILL BE RECORDED AND A COLLECTIVE
RECORDING OF THESE OBSERVATIONS,
EITHER NUMERICAL OR OTHERWISE, IS
CALLED A DATA.
EX: RECORDING THE SEX OF A PERSON IN A
GROUP OF PERSONSwww.indiandentalacademy.com

VARIABLE
IN EACH OF CASES A CERTAIN
OBSERVATION IS MADE FOR A
CHARACTERISTIC AND THIS
CHARACTERISTICS VARIES FROM ONE
OBSERVATION TO OTHER OBSERVATION
AND IS CALLED A VARIABLEwww.indiandentalacademy.com

TYPES OF DATA
I. QUALITATIVE / QUANTITATIVE
II. DISCRETE / CONTINUOUS
III. GROUPED / UNGROUPED
IV.PRIMARY / SECONDARY
V. NOMINAL / ORDINAL

TYPES OF CLINICAL DATA THAT
CAN BE SUPPORTED BY
STATISTICS
STATISTICS CAN BE USED TO HELP THE
READER MAKE A CRITICAL EVALUATION OF
VIRTUALLY ANY QUANTITATIVE DATA.
IT IS IMPORTANT THAT THE STATISTICAL
TECHNIQUES USED ARE APPROPRIATE FOR
THE GIVEN EXPERIMENTAL DESIGN.

NEED FOR ORGANISING THE
DATA
DATA ARE NOT NECESSARILY
INFORMATION, AND HAVING MORE DATA
DOES NOT NECESSARILY PRODUCE
BETTER DECISIONS.
THE GOAL IS TO SUMMARISE AND PRESENT
DATA IN USEFUL WAYS TO SUPPORT

METHODS OF PRESENTATION OF
DATA
•TABULATION
•CHARTS AND DIAGRAMS

GUIDELINES PRESENTATION OF
TABLES
1.TABLE MUST BE NUMBERED
2.TITLE-BRIEF AND SELF EXPLANATORY –
SHOULD BE GIVEN
3.THE HEADINGS OF COLUMNS AND ROWS
MUST BE CLEAR, SUFFICIENT, CONCISE
AND FULLY DEFINED

4.THE DATA MUST BE PRESENTED ACCORDING
TO SIZE OF IMPORTANCE -
CHRONOLOGICALLY, ALPHABETICALLY OR
GEOGRAPHICALLY
5.FULL DETAILS OF DELIBERATE EXCLUSIONS IN
COLLECTED SERIES MUST BE GIVEN.
6.IF DATA INCLUDES RATE OR PROPORTION
MENTION THE DENOMINATOR I.E. NUMBER OF
TABLES..

6.TABLE SHOULD NOT BE TOO LARGE.
8. FIGURES NEEDING COMPARISON SHOULD
BE PLACED AS CLOSE AS POSSIBLE
9. ARRANGEMENT SHOULD BE VERTICAL.
10. FOOT NOTES SHOULD BE GIVEN
WHEREVER NECESSARY.
TABLES..

Norm
Sample
size
Mean
SD S.E.
95% C I for
Mean
Min
Max
Lower
bound
Upper
bound
LED 40sec 10 9.659 0.6158 0.1947 9.2184 10.09 8.34 10.7
Table-11Descriptive Statistics of Shear bond strength
TABLES..

PRESENTATION THROUGH
CHART / DIAGRAM /
GRAPH

LINE CHART

BAR
DIAGRAM
0
5
10
15
20
25
30
35
40
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

MULTIPLE BAR
COMPONENT
BAR
BAR DIAGRAM…

HISTOGRAM
FREQUENCY POLYGON

PIE
DIAGRAM

SCATTER
DIAGRAMS

BOX PLOT

VENN
DIAGRAM

PICTORGRAM

SHADED MAPS / SPOT MAPS / DOT
MAPS

STEPS IN STATISTICAL
METHODS
1.COLLECTION OF DATA
2.CLASSIFICATION
3.TABULATION
4.PRESENTATION BY GRAPHS
5.DESCRIPTIVE STATISTICS
6.ESTABLISHMENT OF RELATIONSHIP
7.INTERPRETATION

TYPES OF
STUDIES
DESCRIPTIVE
•CORRELATIONAL
•CASE STUDIES
-CASE REPORTS
-CASE SERIES
•CROSS SECTIONAL
SURVEYS
ANALYTICAL
•OBSERVATIONAL
- CASE CONTROL
- COHORT
•INTERVENTIONAL
-CLINICAL TRIALS
-ANIMAL EXPERIMENTS

RESEARCH
DESIGNS
EXPLORATIVE
DESCRIPTIVE
DIAGNOSTIC
EXPERIMENTAL

DESIGN OF THE
INVESTIGATION
1.RETROSPECTIVE SURVEYS
2.PROSPECTIVE SURVEYS
3.FOLLOW UP STUDIES
4.CROSS SECTIONAL
SURVEYS
5.PROPHYLACTIC TRIALS
6.THERAPEUTIC TRIALSwww.indiandentalacademy.com

COHORT
STUDY
SUBJECTS ARE DIVIDED INTO GROUPS
DEPENDING ON PRESENCE OR ABSENCE OF
A RISK FACTOR AND THEN FOLLOWED UP
FOR A PERIOD OF TIME TO FIND OUT
WHETHER THEY DEVELOP THE DISEASE OR
NOT. THIS IS PROSPECTIVE RESEARCH.

THE STUDY IS DESIGNED TO INVESTIGATE
THE ASSOCIATION BETWEEN A FACTOR AND
A DISEASE.THESE STUDIES ARE KNOWN AS
TROHOC STUDY. SINCE THESE FORM A
RETROSPECTIVE INVESTIGATION i.e.
OPPOSITE OF A COHORT STUDY.
TROHOC STUDY

INTERVENTIONAL
STUDIES
THESE ARE ALSO KNOWN AS EXPERIMENTAL
STUDIES OR CLINICAL TRIALS. IN THESE
STUDIES THE INVESTIGATOR DECIDES
WHICH SUBJECT GETS EXPOSED TO A
PARTICULAR TREATMENT (OR PLACEBO).
THESE STUDIES MAY BE COHORT OR CASE-
CONTROL.
EX-ANIMAL EXPERIMENTS,ISOLATED TISSUE
EXPERIMENTS,IN VITRO EXPERIMENTS.www.indiandentalacademy.com

INTERVENTIONAL STUDIES
•RANDOMIZED CONTROLLED TRIALS/CLINICAL
TRIALS-WITH PATIENTS AS UNIT OF STUDY
•FIELD TRIALS/COMMUNITY INTERVENTION
STUDIES-WITH HEALTHY PEOPLE AS UNIT OF
STUDY
•COMMUNITY TRIALS-WITH COMMUNITIES AS
UNIT OF STUDY

STUDY DESIGNS
1.CASE REPORT
2.CASE SERIES REPORT
3.INCIDENCE PREVALENCE STUDIES
4.TROHOC STUDY
5.COHORT STUDY
6.RANDOMIZED CONTROLLED TRIALS
7.META ANALYSIS

SAMPLING
SAMPLING IS THE SELECTION OF THE PART
OF AN AGGREGATE TO REPRESENT THE
WHOLE
SAMPLE A FINITE SUBSET OF STATISTICAL
INDIVIDUALS IN A POPULATION
SAMPLE SIZE THE NUMBER OF INDIVIDUALS IN

SAMPLE SELECTION-GUIDELINES
1.WELL CHOSEN
2.SUFFICIENTLY LARGE (TO MINIMIZE SAMPLING ERROR)
3.ADEQUATE COVERAGE

METHODS OF
SAMPLING
1.NON RANDOM SAMPLING
2.PROBABILITY SAMPLING

PROBABILITY
SAMPLING
1.SIMPLE RANDOM SAMPLING- WITH OR WITHOUT
REPLACEMENT
2.SYSTEMATIC SAMPLING
3.STRATIFIED SAMPLING
4.CLUSTER SAMPLING
5.SUB SAMPLING/ MULTISTAGE SAMPLING
6.MULTIFACE SAMPLING

FACTORS INFLUENCING SAMPLE
SIZE
1.DIFFERENCE EXPECTED
2.POSITIVE CHARACTER
3.DEGREE OF VARIATION AMONG
SUBJECTS
4.LEVEL OF SIGNIFICANCE DESIRED- p
VALUE
5.POWER OF THE STUDY DESIREDwww.indiandentalacademy.com

DETERMINATION OF SAMPLE
SIZE
QUANTITATIVE DATA
4 SD2
L 2
N=
SD= STANDARD
DEVIATION
L = ALLOWABLE ERROR

SIZE
P = POSITIVE
CHARACTER
L = ALLOWABLE ERROR
Q = 1- p
QUALITATIVE DATA
4 pq
L 2
N=

SIZE
THE SAMPLE SIZE WAS DETERMINED FROM THE
PARAMETER OF ARCH LENGTH WITH THE LIKELY
CHANGE IN ARCH LENGTH BEING HALF OF THE
DECIDUOUS INCISORS(3MM) WITH A SD OF
2.8MMS, A POWER OF .85 WITH SIGNIFICANCE AT
THE LEVEL OF .05 WOULD REQUIRE A SAMPLE
SIZE OF 35
Journal of orthodontics Vol 31:2004,107-114

PRECISION
INDIVIDUAL BIOLOGICAL VARIATION,
SAMPLING ERRORS AND MEASUREMENT
ERRORS LEAD TO RANDOM ERRORS LEAD TO
LACK OF PRECISION IN THE MEASUREMENT.
THIS ERROR CAN NEVER BE ELIMINATED BUT
CAN BE REDUCED BY INCREASING THE SIZE
OF THE SAMPLE

PRECISION
PRECISION= square root of sample size
standarad deviation
STANDARD DEVIATION REMAINING THE
SAME, INCREASING THE SAMPLE SIZE
INCREASES THE PRECISION OF THE
STUDY.

STRATEGIES TO ELIMINATE
ERRORS
1.CONTROLS
2.RANDOMIZATION OR RANDOM
ALLOCATION
3.CROSS OVER DESIGN
4.PLACEBO
5.BLINDING TECHNIQUE -SINGLE/ DOUBLE BLINDINGwww.indiandentalacademy.com

EXPERIMENTAL VARIABILITY
ERROR/ DIFFERENCE /
VARIATION
THERE ARE THREE TYPES
1.OBSERVER-subjective / objective
2.INSTRUMENTAL
3.SAMPLING DEFECTS OR ERROR OF BIAS

BIAS IN THE SAMPLE
THIS IS ALSO CALLED AS SYSTEMATIC
ERROR. THIS OCCURS WHEN THERE IS A
TENDENCY TO PRODUCE RESULTS THAT
DIFFER IN A SYSTEMATIC MANNER FROM
THE TRUE VALUES. A STUDY WITH SMALL
SYSTEMATIC ERROR IS SAID TO HAVE
HIGH ACCURACY.ACCURACY IS NOT
AFFECTED BY THE SAMPLE SIZE.

BIAS IN THE
SAMPLE..
ACCURACY IS NOT AFFECTED BY THE
SAMPLE SIZE. THERE ARE AS MANY AS 45
TYPES OF BIASES, HOWEVER THE
IMPORTANT ONES ARE:
1.SELECTION BIAS
2.MEASUREMENT BIAS
3.CONFOUNDING BIAS

ERRORS IN SAMPLING
SAMPLING ERRORS NON SAMPLING ERRORS
Faulty sampling design Coverage error
-due to non response or non
cooperation of the informant
Small size of the sample Observational error
-due to interviewers bias,imperfect
exptl. design,or interaction
Processing error
-due to errors in statistical analysis

DAHLBERG’S
FORMULA
DAHLBERG IN 1940 USED THIS FORMULA TO
CALCULATE THE METHOD ERROR
Method error=√Σd2
2n
WHERE d=DIFFERENCE BETWEEN TWO
MEASUREMENTS OF A PAIR
n = NUMBER OF SUBJECTS

DISTRIBUTION
S
WHEN YOU HAVE A COLLECTION OF
POINTS YOU BEGIN THE INITIAL ANALYSIS
BY PLOTTING THEM ON A GRAPH TO SEE
HOW THEY ARE DISTRIBUTED

DISTRIBUTION-
TYPES
1.NORMAL-GAUSSIAN
2.BINOMIAL
3.POISSON
4.RECTANGULAR OR UNIFORM
5.SKEWED
6.LOG NORMAL
7.GEOMETRIC

UNIFORM OR
RECTANGULAR
BIMODAL
DISTRIBUTION-TYPES..

NORMAL OR GAUSSIAN DISTRIBUTION

CHARACTERISTICS OF NORMAL
DISTRIBUTION
1.THE CURVE HAS A SINGLE PEAK, THUS IT
IS UNI MODAL
2.IT HAS A BELL SHAPE
3.MEAN, MEDIAN AND MODE ARE THE SAME
VALUES.
4.TWO TAILS EXTEND INDEFINITELY AND
NEVER TOUCH THE HORIZONTAL AXIS (THIS
MEANS THAT INFINITE NUMBER OF VALUES ARE POSSIBLE)

CONFIDENCE
LIMITS
POPULATION MEAN+1 SE LIMITS INCLUDE
68.27% OF THE SAMPLE MEAN VALUES
POPULATION MEAN+1.96 SE LIMITS
INCLUDE
95% OF THE SAMPLE MEAN VALUES
INCLUDE
99% OF THE SAMPLE MEAN VALUESwww.indiandentalacademy.com

INCLUDE
99.9% OF THE SAMPLE MEAN VALUES
THESES LIMITS ARE CALLED CONFIDENCE
LIMITS AND THE RANGE BETWEEN THE
TWO IS CALLED THE CONFIDENCE
INTERVAL
CONFIDENCE
LIMITS

NORMAL DISTRIBUTIONS WITH
SAME MEAN AND VARIED STANDARD
DEVIATION

BINOMIAL DISTRIBUTION
THE BINOMIAL DISTRIBUTION IS USED FOR
DESCRIBING DISCRETE NOT THE
CONTINUOUS DATA. THESE VALUES ARE AS
A RESULT OF AN EXPERIMENT KNOWN AS
BERNOULLI’S PROCESS.THEY ARE USED TO
DESCRIBE
1.ONE WITH CERTAIN CHARACTERISTIC
2.REST WITHOUT THIS CHARACTERISTIC
THE DISTRIBUTION OF THE OCCURRENCE OF
THE CHARACTRERISTIC IN THE POPULATIONwww.indiandentalacademy.com

THE POISSON
DISTRIBUTION
IF IN A BINOMIAL DISTRIBUTION THE VALUE OF
PROBABILITY OF SUCCESS AND FAILURE OF
AN EVENT BECOMES INDEFINITELY SMALL AND
THE NUMBER OF OBSERVATION BECOMES
VERY LARGE, THEN BINOMIAL DISTRIBUTION
TENDS TO POISSON DISTRIBUTION.
THIS IS USED TO DESCRIBE THE OCCURRENCE
OF RARE EVENTS IN A LARGE POPULATION.www.indiandentalacademy.com

DISPERSION
?
DATA
SET
OBSERVATIONS TOTAL .MEAN
I 00 10 20 25 70 125 25
II 23 24 25 26 27 125 25
IT IS NECESSARY TO STUDY THE VARIATION.
THIS VARIATION IS ALSO KNOWN AS
DISPERSION.IT GIVES US INFORMATION, HOW
INDIVIDUAL OBSERVATIONS ARE SCATTERED
OR DISPERSED FROM THE MEAN OF LARGEwww.indiandentalacademy.com

DIFFERENT MEASURES OF
DISPERSION
1.RANGE
2.QUARTILE DEVIATION
3.COEFFICIENT OF QUARTILE DEVIATION
4.MEAN DEVIATION
5.STANDARD DEVIATION
6.VARIANCE
7.COEFFICIENT OF VARIATION

STANDARD DEVIATION
1.STANDARD DEVIATION INDICATES HOW
CLOSE THE INDIVIDUAL READINGS TO THE
MEAN.
2.THE SMALLER THE STANDARD DEVIATION,
THE MORE HOMOGENEOUS IS THE
SAMPLE.
3.A LARGER SD IMPLIES THAT THE
INDIVIDUAL SUBJECTS MEASUREMENTSwww.indiandentalacademy.com

COEFFICIENT OF
VARIATION
WHEN YOU WANT TO COMPARE TWO OR
MORE SERIES OF DATA WITH EITHER
DIFFERENT UNITS OF MEASUREMENTS
OR EITHER MARKED DIFFERENCE IN
MEAN, A RELATIVE MEASURE OF
DISPERSION, COEFFIENT OF VARIATION
IS USED.
C.V. = ( S X100)
X

Population means are best used as bases for comparison,not as treatment
goals.
STANDARD ERROR OF THE
MeanSTANDARD ERROR OF THE MEAN= STANDARD DEVIATION
SQUARE ROOT OF NUMBER OF SUBJECTS
A LARGE STANDARD ERROR IMPLIES THAT WE
CANNOT BE VERY CONFIDENT THAT OUR
SAMPLE STATISTICS ARE REALLY GOOD
ESTIMATES OF POPULATION PARAMETERS
A SMALL STANDARD ERROR ALLOWS US TO
FEEL MORE CONFIDENT THAT OUR SAMPLE
STATISTICS ARE REPRESENTATIVE OF
POPULATION PARAMETERS.

“P” VALUE-
SIGNIFICANCE
IT REPRESENTS THE PROBABILITY.
TO DETERMINE IF THE TREATMENT GROUP
IS DIFFERENT FROM CONTROL GROUP
IF IT IS LESS THAN .05, IT MEANS THERE ARE
FEWER THAN 5 CHANCES OUT OF 100 THAT
THE DIFFERENCE WE OBSERVE ARE DUE TO
RANDOM CHANCE ALONE.
LESS THAN .01
LESS THAN .001 www.indiandentalacademy.com

CRITICAL RATIO, Z SCORE
It indicates how much an observation is bigger or
smaller than mean in units of SD
Z ratio = Observation – Mean
Standard Deviation
The Z score is the number of SDs that the simple
mean depart from the population mean.
As the critical ratio increases the probability of
accepting null hypothesis decreases.

VARIANCE RATIO OR FISCHER “F”
TEST
FOR COMPARISON OF VARIANCE (SD2
)
BETWEEN THE GROUPS (OR SAMPLES SD1
2
AND SD2
2
) VARIANCE RATIO TEST IS
UTILISED. THIS TEST INVOLVES A
DISTRIBUTION KNOWN AS “F” DISTRIBUTION.
THIS WAS DEVELOPED BY FISHER AND
SNEDECOR WITH DEGREES OF FREEDOM OF

IF THE CALCULATED F VALUES ARE
GREATER THAN THE VALUE TABULATED F
VALUE AT 0.05% OR AT 1% LEVEL THAN THE
VARIANCES ARE SIGNIFICANTLY DIFFERENT
FROM EACH OTHER. IF THE F VALUE
CALCULATED IS LOWER THAN THE
TABULATED THAN THE VARIANCES BY BOTH
SAMPLES ARE SAME AND ARE NOT
SIGNIFICANT
TEST

LEVENE’S TEST FOR EQUALITY
F Significance
SB with LED 40sec
10.35895 0.004764SB with Halogen40sec
TEST

NULL HYPOTHESIS
IT IS A HYPOTHESIS WHICH ASSUMES THAT
THERE IS NO DIFFERENCE BETWEEN TWO
VALUES SUCH AS POPULATION MEANS OR
POPULATION PROPORTIONS.
WHEN YOU ARE SUBJECTING TO NULL
HYPOTHESIS CERTAIN TERMINOLOGIES
SHOULD BE CLEAR.www.indiandentalacademy.com

1.ALTERNATE HYPOTHESIS
2.TEST STATISTIC
3.DEGREES OF FREEDOM
4.SAMPLING ERRORS
5.LEVEL OF SIGNIFICANCE
6.POWER OF THE TEST
7.REGIONS OF ACCEPTANCE AND
REJECTION
NULL HYPOTHESIS…..

PROCEDURE FOR
TESTING THE
HYPOTHESIS
STEP-1 SET UP THE NULL HYPOTHESIS
STEP-2 SET UP THE ALTERNATE HYPOTHESIS
STEP-3 CHOOSE THE APPROPRIATE LEVEL OF
SIGNIFICANCE
STEP-4 COMPUTE THE VALUE OF TEST STATISTIC
Z VALUE = OBSERVED DIFFERENCE
STANDARD ERROR

STEP-5 OBTAIN THE TABLE VALUE AT THE
GIVEN LEVEL OF
SIGNIFICANCE
STEP-6 COMPARE THE VALUE OF Z WITH
THAT OF TABLE VALUE
STEP-7 DRAW THE CONCLUSION
PROCEDURE FOR
TESTING THE
HYPOTHESIS…

POPULATION
CONCLUSION BASED ON
SAMPLE
NULL HYPOTHESIS
REJECTED
NULL
HYPOTHESIS
ACCEPTED
NULL HYPOTHESIS
TRUE
TYPE I ERROR CORRECT
DECISION
NULL HYPOTHESIS
FALSE
CORRECT
DECISION
TYPE II ERROR
NULL HYPOTHESIS…..

AREA OF ACCEPTANCE,
REJECTION

Parametric Non Parametric
1 Student paired T test 1 Wilcoxan signed rank test
2 Student unpaired T test 2 Wilcoxan rank sum test
3 One way Anova 3 Kruskal wallis one way anova
4 Two way Anova 4 Friedman one way anova
5 Correlation coefficient 5 Spearman’s rank correlation
6 Regression analysis 6 Chi-square test
TESTS OF
SIGNIFICANCE

STUDENT’S ‘t’ TEST
THIS TEST IS A PARAMETRIC TEST
DESCRIBED BY W.S.GOSSETT WHOSE PEN
NAME WAS “STUDENT”. IT IS USED FOR
SMALL SAMPLES, I.E. LESS THAN 30.
T Test can be:
Paired t test
Unpaired t test

PAIRED ‘T’ TEST IS USED FOR A GROUP
WHICH IS ITS OWN CONTROL
Ex Effect of bionator on mandibular length
UNPAIRED ‘T’ TEST FOR COMPARING TWO
DIFFERENT GROUPS, ONE OF WHICH MAY BE
CONTROLLED AND THE OTHER TEST GROUP.
Ex:Assessment of arch width of maxilla in thumbsuckers and
normal subjects
STUDENT’S ‘t’ TEST

ANALYSIS OF VARIANCE (ANOVA)
THIS TEST IS USED TO COMPARE THE
MEANS OF THREE OR MORE GROUPS
TOGETHER. THIS IS USED WHEN-
•SUBGROUPS TO BE COMPARED ARE
DEFINED BY JUST ONE FACTOR
•SUBGROUPS ARE BASED ON TWO
FACTORS.
•DATA ARE NORMALLY DISTRIBUTED.www.indiandentalacademy.com

THE SHEAR BOND STRENGTH OF ADHESIVE
CURED USING FOUR DIFFERENT LIGHT
CURING UNITS ARE TO BE COMPARED.
SBS BELONGING TO THE FOUR LIGHT
CURING UNITS ARE TAKEN AND MEAN SBS
FOR EACH CURING LIGHT IS DETERMINED.
THESE MEANS ARE COMPARED TOGETHER
TO ASCERTAIN ANY DIFFERENCE BETWEEN
ANALYSIS OF VARIANCE (ANOVA)
…

Source of
variation
Sum of
Squares df
Mean
Square F Sig.
Between groups 132.6448 4 33.1612 17.2515 <0.00000012
Within groups
86.4999 45 1.92222
The mean difference is significant at the .05 levels
ANOVA and POST HOC TEST-
MULTIPLE TEST OF
BONFERRONI
CONTROL OTHER GROUPS SIGNIFICANCE
LED 40 seconds
LED 20 seconds
Argon Laser 10 seconds
Argon Laser 5 seconds
Conventional Halogen
40 seconds
0.01754
0.01540
1.6575
1

IF F1>F0.05 >F0.01
THEN THE PROBABILITY OF SIGNIFICANCE IS
P<0.05 P<0.01 RESPECTIVELY
F1<F0.05
THEN THE PROBABILITY OF SIGNIFICANCE IS
P>0.05(not significant)
RESULTS OF
ANOVA

TWO WAY ANALYSIS CAN BE USED IN THE
ABOVE SITUATION IF THE INFLUENCE OF TIME
APART FROM THE CURING LIGHT IS ALSO TO
BE TAKEN INTO CONSIDERATION.
IN THIS CASE THE DATA ARE CLASSIFIED
BY TWO FACTORS I.E. CURING LIGHT
AND TIME.
TWO WAY ANALYSIS OF
VARIANCE

MANOV
A
Comparison of skeletal and dental changes between 2 point and 4 point rapid palatal expanders AJO:2003 123;321-328
VARIABLE Before appliance
insertion
End of active
expansion
Immediately after
removal of appliance
Molar cusp width
36.325± 3.169 42.754± 3.030 42.302± 2.926
Molar gingival width
29.119± 2.446 Not measured 35.063± 2.230
Canine cusp width
29.725± 2.886 32.943± 2.913 32.759± 2.476
Canine gingival width
23.411± 3.247 26.637± 3.200 26.526± 2.914
Diastema width
0.719± 0.814 3.095± 1.447 Not measured
Maxillary perimeter
73.256± 4.133 77.137± 4.224 76.157± 4.759
Screw separation
Not measured 5.790± 1.141 Not measured
Anterior suture expansion
Posterior suture
expansion

DETERMINATION OF “r”
VALUE
WHEN THE DEGREE OF LINEAR (STRAIGHT LINE)
ASSOCIATION BETWEEN TWO VARIABLES IS
REQUIRED, CORRELATION COEFFICIENT IS
CALCULATED.
Ex: MEASURE THE CHANGES IN FMA AND THE
CHANGES THAT OCCURRED IN POGONION
POSITION AND PLOT THE DETERMINED VALUES
ON GRAPH PAPER.

A LINE OF BEST FIT IS THEN MADE TO CONNECT
THE MAJORITY OF THE PLOTTED VALUES.
ONE HAS TO LOOK AT A SCATTER PLOT OF
THE DATA BEFORE PLACING ANY IMPORTANCE
ON THE MAGNITUDE OF CORRELATION.
CORRELATION COEFFICIENT (r)
…

Height in cms Weight in Kg
1 182.1 79.5
2 172.5 61.5
3 175.7 68.2
4 172.8 66.4
5 160.3 52.6
6 165 .5 54.3
7 172.8 61.1
8 162.4 52.8
…

POSITIVE CORRELATION NEGATIVE CORRELATION
…

PARTIAL
POSITIVE CORRELATION
PARTIAL
NEGATIVE
CORRELATION
ABSOLUTELY
NO CORRELATION
…

LINEAR REGRESSION
ANALYSIS
LINEAR REGRESSION IS RELATED TO
CORRELATION ANALYSIS.
THIS SEEKS TO QUANTIFY THE LINEAR
RELATIONSHIP THAT MAY EXIST BETWEEN AN
INDEPENDENT VARIABLE “x” AND A DEPENDENT
VARIABLE “y”
Y=a+bx

LINEAR REGRESSION
ANALYSIS

use parametric Non parametric
To compare two paired
samples for equality of means
Paired ‘t” test Wilcoxan signed rank
test
To compare two independent
Unpaired ‘t” test Mann Whitney test
To compare more than two
ANOVA Kruskal-Wallis
Chi square test
COMPARABLE PARAMETRIC
and
NON PARAMETRIC TESTS

ARI Value Shear Bond strength
Group I Group
II A1
Group
II A2
Group
III
B1
Group
III B2
0
No adhesive left on the tooth
surface
2 3 1 0 2
1
Less than half of the adhesive left
on the tooth surface
3 1 4 2 1
2
More than half of the adhesive left
on the tooth surface
1 1 2 1 3
3
Entire adhesive left on the tooth
surface
4 5 3 7 4
ADHESIVE REMNANT
INDEX

WILCOXAN RANK TEST
(SIGNED RANK AND RANK
SUM)
THESE TESTS ARE NON-PARAMETRIC
EQUIVALENT OF STUDENT “t” TESTS.
WILCOXAN SIGNED RANK IS USED FOR
PAIRED DATA AND WILCOXAN RANK SUM IS
USED IN CASE OF UNPAIRED DATA.

KRUSKAL-WALLIS AND
FRIEDMAN
THESE ARE SIMILAR TO PARAMETRIC
ANOVA TESTS. KRUSKAL-WALLIS IS USED
FOR ONE WAY ANALYSIS OF VARIANCE
AND FRIEDMAN IS FOR TWO WAY
ANALYSIS OF VARIANCE.

SPEARMAN’S RANK
CORRELATION
SPEARMAN’S RANK CORRELATION AND
KENDALL’S RANK CORRELATION ARE THE
NON-PARAMETRIC EQUIVALENTS OF
CORRELATION COEFFICIENT TEST.

CHI SQUARE TEST (χ2
TEST)
THIS TEST IS A “ GOODNESS OF FIT” TEST,
USED TO FIND OUT THE ASSOCIATION
BETWEEN VARIABLES.THIS TEST IS USEFUL IN
VARIOUS SITUATIONS WHERE PROPORTIONS
OR PERCENTAGES OF TWO GROUPS ARE
COMPARED e.g. PROPORTIONS OF DIED AND
SURVIVED IN TREATED AND UNTREATED
CHILDREN WITH DIARRHOEA CAN BE

DISCRIMINANT FUNCTION
ANALYSIS
IT IS USED TO CLASSIFY CASES INTO THE
VALUES OF A CATEGORICAL DEPENDENT,
USUALLY A DICHOTOMY.IF DISCRIMINANT
FUNCTION ANALYSIS IS EFFECTIVE FOR A
SET OF DATA, THE CLASSIFICATION TABLE
OF CORRECT AND INCORRECT ESTIMATES
WILL YIELD A HIGH PERCENTAGE
CORRECT. www.indiandentalacademy.com

META
ANALYSIS
GENE GLASS(1976) COINED THE TERM ‘META
ANALYSIS’.
THE TECHNIQUE OF META ANALYSIS INVOLVES
REVIEWING AND COMBINING THE RESULTS OF
VARIOUS PREVIOUS STUDIES. PROVIDEDTHE
STUDIES INVOLVED SIMILAR TREATMENTS,
SIMILAR SAMPLES, AND MEASURED SIMILAR
OUTCOMES, THIS CAN BE A USEFUL APPROACH.

CONTROLLED/UNCONTROLLED
TRIALS
CLINICAL RESEARCH CAN INDEED HAVE
CONTROLS. PROVIDED THAT STUDIES ARE
CONDUCTED ON A PROSPECTIVE BASIS,
CONTROLLED CLINICAL STUDIES CAN BE QUITE
POWERFUL.
UNCONTROLLED CLINICAL STUDIES ARE OF
QUESTIONABLE VALIDITY, WHETHER OR NOTwww.indiandentalacademy.com

The sensitivity of a test is the probability that the
test is positive for those subjects who actually have
the disease. A perfect test will have a sensitivity of
100%. The sensitivity is also called the true positive
rate.
The specificity of a test is the probability that the
test is negative for those in whom the disease is
absent. A perfect test will have a specificity of I
100%. The specificity is also called the true negitive
rate.
SENSITIVITY, SPECIFICITY AND
ROC

TEST
RESULT
TRUE DISEASE STATUS OR
CHARACTERISTIC
DISEASE
PRESENT
DISEASE
ABSENT
TOTAL
POSITIVE
(+)
a ( 8) b (10) a +b=(18)
NEGATIVE
(-)
c (20) d ( 62) c+d = (82)
TOTAL a +c = (28) b +d (72) N =100
ROC…

ROC…

1.BE SKEPTICAL
2.LOOK FOR THE DATA
3.IDENTIFY THE TYPE OF STUDY
4.IDENTIFY THE POPULATION SAMPLED
5.DIFFERENTIATE BETWEEN DESCRIPTIVE
AND INFERENTIAL STATISTICS
JCO May 1997,307-
314
YANCEY’S 10 RULES
-Evaluating Scientific literature

6.QUESTION THE VALIDITY OF DESCRIPTIVE
STATISTICS
7.QUESTION THE VALIDITY OF INFERENTIAL
STATISTICS
8.BE WEARY OF CORRELATION AND REGRESSION
ANALYSES
9.LOOK FOR THE INDICES OF PROBABLE
MAGNITUDE OF TREATMENT EFFECTS
10.DRAW YOUR OWN CONCLUSIONS.
YANCEY’S 10 RULES
-Evaluating Scientific literature
JCO May 1997,307-www.indiandentalacademy.com

SOFTWARES-STATISTICAL
PACKAGES
SPSS
MINITAB
EPIINFO
MICROSOFT EXCEL

THANKYOU

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