statistics in orthodontics /certified fixed orthodontic courses by Indian dental academy

APPLICATION
OF
BIOSTATISTICS
IN
ORTHODONTICS
www.indiandentalacademy.com

INDIAN DENTAL ACADEMY
Leader in continuing dental education


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 statistics”
“An ounce of truth produces tons of

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.

HISTORY OF
STATISTICS
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.

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 www.indiandentalacademy.com A
SOFTWARES IN

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 GROUPwww.indiandentalacademy.com
OF INDIVIDUALS.

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

DESCRIPTIVE
STATISTICS
Norm

Sample
size

Mean

10

95% C I for Mean
Std.
Deviation

Std. Error

9.659

0.615891

10

7.596

10

Min

Max

Lower
bound

Upper
bound

0.19476168

9.218418476

10.099581

8.34

10.7

0.816921

0.25833312

7.011609886

8.1803901

6.36

8.95

7.568

1.741518

0.5507163

6.322193174

8.8138068

3.6

9.47

10

5.824

1.636773

0.51759315

4.653122953

6.9948770

4.37

8.93

10

10.374

1.688939

0.53408946

9.165805693

11.582194

8.21

12.97

LED 40 sec
LED 20 sec
Argon Laser 10 sec
Argon Laser 5 sec
Halogen Light 40 sec


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 PERSONS

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 www.indiandentalacademy.com
VARIABLE

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

TABLES..
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..
Table-11Descriptive Statistics of Shear bond strength
Norm

Sample
size

95% C I for
Mean

Mean
SD

Min

S.E.
Lower
bound

LED 40sec

10

9.659

0.6158

0.1947

Max

9.2184


Upper
bound

10.09

8.34

10.7

PRESENTATION THROUGH
CHART / DIAGRAM /
GRAPH


LINE CHART


BAR
DIAGRAM
40
35
30
25
20
15
10
5
0

1st Qt r

2nd Qt r

3rd Qt r

4t h Qt r


BAR DIAGRAM…
MULTIPLE BAR
COMPONENT
BAR


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 TRIALS

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.

TROHOC STUDY
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.

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 CASECONTROL.
EX-ANIMAL EXPERIMENTS,ISOLATED TISSUE
EXPERIMENTS,IN www.indiandentalacademy.com
VITRO EXPERIMENTS.

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 DESIRED

DETERMINATION OF SAMPLE
SIZE
QUANTITATIVE DATA

N=

4 SD2

L2

SD= STANDARD
DEVIATION
L = ALLOWABLE ERROR


SIZE
QUALITATIVE DATA

P = POSITIVE
N=

4 pq

L2

CHARACTER

L = ALLOWABLE ERROR
Q = 1- p

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 BLINDING

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
Faulty sampling design

Small size of the sample

NON SAMPLING ERRORS
Coverage error

-due to non response or non
cooperation of the informant
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


DISTRIBUTIONTYPES

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

DISTRIBUTION-TYPES..
UNIFORM OR
RECTANGULAR
BIMODAL


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 THEwww.indiandentalacademy.com VALUES
SAMPLE MEAN

CONFIDENCE
LIMITS
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


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 POPULATION

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.

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 LARGE

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 MEASUREMENTS

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

STANDARD ERROR OF THE
Mean OF THE MEAN= STANDARD DEVIATION
STANDARD ERROR

A LARGE STANDARD ERROR IMPLIES THAT WE
SQUARE ROOT OF NUMBER OF SUBJECTS
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.

Population means are best used as bases for comparison,not as treatment
goals.

“P” VALUESIGNIFICANCE

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 SD12
AND SD22 ) 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

TEST
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

10.35895

0.004764

SB with LED 40sec
SB with Halogen40sec


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.

NULL HYPOTHESIS…..
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


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


PROCEDURE FOR
TESTING THE
HYPOTHESIS…
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

NULL HYPOTHESIS…..

POPULATION

CONCLUSION BASED ON
SAMPLE
NULL

NULL HYPOTHESIS

HYPOTHESIS

REJECTED

ACCEPTED

NULL HYPOTHESIS
TRUE

TYPE I ERROR

CORRECT
DECISION

NULL HYPOTHESIS
FALSE

CORRECT
DECISION

TYPE II ERROR


AREA OF ACCEPTANCE,
REJECTION


TESTS OF
SIGNIFICANCE
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

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

STUDENT’S ‘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

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.

ANALYSIS OF VARIANCE (ANOVA)
…

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

ANOVA and POST HOC TESTMULTIPLE TEST OF
BONFERRONI

Source of
variation
Between groups
Within groups

Sum of
Squares
132.6448

df
4

Mean
Square
33.1612

86.4999

45

1.92222

F

Sig.

17.2515

<0.00000012

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

The mean difference is significant at the .05 levels

RESULTS OF
ANOVA
IF F 1 >F 0.05 >F 0.01
THEN THE PROBABILITY OF SIGNIFICANCE IS
P<0.05 P<0.01 RESPECTIVELY
F 1 <F 0.05
THEN THE PROBABILITY OF SIGNIFICANCE IS
P>0.05(not significant)

TWO WAY ANALYSIS OF
VARIANCE
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.


VARIABLE

MANOV
A

End of active
expansion

Immediately after
removal of appliance

36.325± 3.169

42.754± 3.030

42.302± 2.926

29.119± 2.446

Not measured

35.063± 2.230

29.725± 2.886

32.943± 2.913

32.759± 2.476

23.411± 3.247

26.637± 3.200

26.526± 2.914

0.719± 0.814

3.095± 1.447

Not measured

73.256± 4.133

77.137± 4.224

76.157± 4.759

Not measured

5.790± 1.141

Not measured

Not measured

Molar cusp width

Before appliance
insertion

4.046± 1.115

Not measured

Molar gingival width
Canine cusp width
Canine gingival width
Diastema width
Maxillary perimeter
Screw separation
Anterior suture expansion
Not measured
1.837± expanders
Comparison of skeletal and dental changes between 2 point and 4 point rapid palatal 1.000 AJO:2003 Not measured
123;321-328
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.

CORRELATION COEFFICIENT (r)
…
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.

…
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


COMPARABLE PARAMETRIC
and
NON PARAMETRIC TESTS
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


ADHESIVE REMNANT
INDEX
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

7

4

3
Entire adhesive left on the tooth
4
5
3
surface

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.


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 NOT

SENSITIVITY, SPECIFICITY AND
ROC
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.

ROC…
TEST
RESULT

POSITIVE
(+)
NEGATIVE
(-)
TOTAL

TRUE DISEASE STATUS OR
CHARACTERISTIC
DISEASE
DISEASE
TOTAL
PRESENT
ABSENT
a ( 8)

b (10)

a +b=(18)

c (20)

d ( 62)

c+d = (82)

a +c = (28)

b +d (72)

N =100


ROC…


YANCEY’S 10 RULES
-Evaluating Scientific literature
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 1997,307314

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.
JCO May

1997,307-

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


THANKYOU

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