APPLICATION
OF
BIOSTATISTICS
IN
ORTHODONTICS
www.indiandentalacademy.com
INDIAN DENTAL ACADEMY
Leader in continuing dental education
www.indiandentalacademy.com

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STATISTICS
STATISTICS AS A SINGULAR NOUN IS “A
SCIENCE OF FIGURES”
WHERE AS PLURAL NOUN IT MEANS
“FIGURES” OR NUMERICAL DA...
BIOSTATISTICS
BIOSTATISTICS CAN BE DEFINED AS ART
AND SCIENCE OF COLLECTION,
COMPILATION, PRESENTATION, ANALYSIS
AND LOGIC...
STATISTICS
THE WORD STATISTIK IS DERIVED FROM
AN ITALIAN WORD STATISTA MEANING
STATESMAN.
GOTTFRED CHENWALL, A PROFESSOR A...
HISTORY OF
STATISTICS
DURING THE OUTBREAK OF PLAGUE IN
ENGLAND, IN 1532 THEY STARTED
PUBLISHING THE WEEKLY DEATH
STATISTIC...
HISTORY OF
STATISTICS..
IN 1662, CAPT.JOHN GRAUNT USED 30
YEARS OF THESE BILLS TO MAKE
PREDICTIONS ABOUT THE NUMBER
OF PEO...
KNOWLEDGE OF STATISTICAL
METHODS

1. ENABLES US TO MAKE INTELLIGENT USE OF
THE CURRENT LITERATURE.
2. OPENS UP NEW PATHS O...
LIMITATIONS
STATISTIC LAWS ARE NOT EXACT LAWS LIKE
MATHEMATICAL OR CHEMICAL LAWS BUT
ARE ONLY TRUE IN MAJORITY OF CASES.
E...
SUBDIVISIONS OF
STATISTICS
THEY CAN BE SEPERATED INTO TWO
BROAD CATEGORIES:
1. DESCRIPTIVE STATISTICS
2. INFERENTIAL STATI...
DESCRIPTIVE
STATISTICS
Norm

Sample
size

Mean

10

95% C I for Mean
Std.
Deviation

Std. Error

9.659

0.615891

10

7.59...
DAT
A
WHENEVER AN OBSERVATION IS MADE, IT
WILL BE RECORDED AND A COLLECTIVE
RECORDING OF THESE OBSERVATIONS,
EITHER NUMERI...
VARIABLE
IN EACH OF CASES A CERTAIN
OBSERVATION IS MADE FOR A
CHARACTERISTIC AND THIS
CHARACTERISTICS VARIES FROM ONE
OBSE...
TYPES OF DATA
I. QUALITATIVE / QUANTITATIVE
II. DISCRETE / CONTINUOUS
III. GROUPED / UNGROUPED
IV.PRIMARY / SECONDARY
V. N...
TYPES OF CLINICAL DATA THAT
CAN BE SUPPORTED BY
STATISTICS
STATISTICS CAN BE USED TO HELP THE
READER MAKE A CRITICAL EVALU...
NEED FOR ORGANISING THE
DATA
DATA ARE NOT NECESSARILY
INFORMATION, AND HAVING MORE DATA
DOES NOT NECESSARILY PRODUCE
BETTE...
METHODS OF PRESENTATION OF
DATA
•TABULATION
•CHARTS AND DIAGRAMS

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GUIDELINES PRESENTATION OF
TABLES
1. TABLE MUST BE NUMBERED
2. TITLE-BRIEF AND SELF EXPLANATORY –
SHOULD BE GIVEN
3. THE H...
GUIDELINES PRESENTATION OF
TABLES..
4. THE DATA MUST BE PRESENTED ACCORDING
TO SIZE OF IMPORTANCE CHRONOLOGICALLY, ALPHABE...
GUIDELINES PRESENTATION OF
TABLES..
6. TABLE SHOULD NOT BE TOO LARGE.
8. FIGURES NEEDING COMPARISON SHOULD
BE PLACED AS CL...
GUIDELINES PRESENTATION OF
TABLES..
Table-11Descriptive Statistics of Shear bond strength
Norm

Sample
size

95% C I for
M...
PRESENTATION THROUGH
CHART / DIAGRAM /
GRAPH

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LINE CHART

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BAR
DIAGRAM
40
35
30
25
20
15
10
5
0

1st Qt r

2nd Qt r

3rd Qt r

4t h Qt r

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BAR DIAGRAM…
MULTIPLE BAR
COMPONENT
BAR

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HISTOGRAM

FREQUENCY POLYGON

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PIE
DIAGRAM

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SCATTER
DIAGRAMS

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BOX PLOT

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VENN
DIAGRAM

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PICTORGRAM

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SHADED MAPS / SPOT MAPS / DOT
MAPS

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STEPS IN STATISTICAL
METHODS

1. COLLECTION OF DATA
2. CLASSIFICATION
3. TABULATION

4. PRESENTATION BY GRAPHS
5. DESCRIPT...
TYPES OF
STUDIES
DESCRIPTIVE
•CORRELATIONAL
•CASE STUDIES
-CASE REPORTS
-CASE SERIES
•CROSS SECTIONAL
SURVEYS

ANALYTICAL
...
RESEARCH
DESIGNS
EXPLORATIVE
DESCRIPTIVE
DIAGNOSTIC
EXPERIMENTAL
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DESIGN OF THE
INVESTIGATION

1. RETROSPECTIVE SURVEYS
2. PROSPECTIVE SURVEYS
3. FOLLOW UP STUDIES
4. CROSS SECTIONAL
SURVE...
COHORT
STUDY
SUBJECTS ARE DIVIDED INTO GROUPS
DEPENDING ON PRESENCE OR ABSENCE OF
A RISK FACTOR AND THEN FOLLOWED UP
FOR A...
TROHOC STUDY
THE STUDY IS DESIGNED TO INVESTIGATE
THE ASSOCIATION BETWEEN A FACTOR AND
A DISEASE.THESE STUDIES ARE KNOWN A...
INTERVENTIONAL
STUDIES

THESE ARE ALSO KNOWN AS EXPERIMENTAL
STUDIES OR CLINICAL TRIALS. IN THESE
STUDIES THE INVESTIGATOR...
INTERVENTIONAL STUDIES
•RANDOMIZED CONTROLLED TRIALS/CLINICAL
TRIALS-WITH PATIENTS AS UNIT OF STUDY
•FIELD TRIALS/COMMUNIT...
STUDY DESIGNS
1. CASE REPORT
2. CASE SERIES REPORT
3. INCIDENCE PREVALENCE STUDIES
4. TROHOC STUDY
5. COHORT STUDY
6. RAND...
SAMPLING
SAMPLING IS THE SELECTION OF THE PART
OF AN AGGREGATE TO REPRESENT THE
WHOLE
SAMPLE A FINITE SUBSET OF STATISTICA...
SAMPLE SELECTION-GUIDELINES
1.WELL CHOSEN
2.SUFFICIENTLY LARGE

(TO MINIMIZE SAMPLING ERROR)

3.ADEQUATE COVERAGE

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

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PROBABILITY
SAMPLING
1. SIMPLE RANDOM SAMPLING- WITH OR WITHOUT
REPLACEMENT

2. SYSTEMATIC SAMPLING
3. STRATIFIED SAMPLING...
FACTORS INFLUENCING SAMPLE
SIZE
1. DIFFERENCE EXPECTED
2. POSITIVE CHARACTER
3. DEGREE OF VARIATION AMONG
SUBJECTS
4. LEVE...
DETERMINATION OF SAMPLE
SIZE
QUANTITATIVE DATA

N=

4 SD2

L2

SD= STANDARD
DEVIATION
L = ALLOWABLE ERROR

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DETERMINATION OF SAMPLE
SIZE
QUALITATIVE DATA

P = POSITIVE
N=

4 pq

L2

CHARACTER

L = ALLOWABLE ERROR
Q = 1- p
www.indi...
DETERMINATION OF SAMPLE
SIZE
THE SAMPLE SIZE WAS DETERMINED FROM THE
PARAMETER OF ARCH LENGTH WITH THE LIKELY
CHANGE IN AR...
PRECISION
INDIVIDUAL BIOLOGICAL VARIATION,
SAMPLING ERRORS AND MEASUREMENT
ERRORS LEAD TO RANDOM ERRORS LEAD TO
LACK OF PR...
PRECISION
PRECISION=

square root of sample size
standarad deviation

STANDARD DEVIATION REMAINING THE
SAME, INCREASING TH...
STRATEGIES TO ELIMINATE
ERRORS
1. CONTROLS
2. RANDOMIZATION OR RANDOM
ALLOCATION
3. CROSS OVER DESIGN
4. PLACEBO
5. BLINDI...
EXPERIMENTAL VARIABILITY
ERROR/ DIFFERENCE /
VARIATION
THERE ARE THREE TYPES
1. OBSERVER-subjective / objective
2. INSTRUM...
BIAS IN THE SAMPLE
THIS IS ALSO CALLED AS SYSTEMATIC
ERROR. THIS OCCURS WHEN THERE IS A
TENDENCY TO PRODUCE RESULTS THAT
D...
BIAS IN THE
SAMPLE..
ACCURACY IS NOT AFFECTED BY THE
SAMPLE SIZE. THERE ARE AS MANY AS 45
TYPES OF BIASES, HOWEVER THE
IMP...
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ERRORS IN SAMPLING
SAMPLING ERRORS
Faulty sampling design

Small size of the sample

NON SAMPLING ERRORS
Coverage error

-...
DAHLBERG’S
FORMULA
DAHLBERG IN 1940 USED THIS FORMULA TO
CALCULATE THE METHOD ERROR
Method error=√Σd2
2n
WHERE d=DIFFERENC...
DISTRIBUTION
S
WHEN YOU HAVE A COLLECTION OF
POINTS YOU BEGIN THE INITIAL ANALYSIS
BY PLOTTING THEM ON A GRAPH TO SEE
HOW ...
DISTRIBUTIONTYPES

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

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NORMAL OR GAUSSIAN DISTRIBUTION

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CHARACTERISTICS OF NORMAL
DISTRIBUTION
1. THE CURVE HAS A SINGLE PEAK, THUS IT
IS UNI MODAL
2. IT HAS A BELL SHAPE
3. MEAN...
CONFIDENCE
LIMITS
POPULATION MEAN+1 SE LIMITS INCLUDE
68.27% OF THE SAMPLE MEAN VALUES
POPULATION MEAN+1.96 SE LIMITS
INCL...
CONFIDENCE
LIMITS
POPULATION MEAN+3.29 SE LIMITS
INCLUDE
99.9% OF THE SAMPLE MEAN VALUES
THESES LIMITS ARE CALLED CONFIDEN...
NORMAL DISTRIBUTIONS WITH
SAME MEAN AND VARIED STANDARD
DEVIATION

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BINOMIAL DISTRIBUTION
THE BINOMIAL DISTRIBUTION IS USED FOR
DESCRIBING DISCRETE NOT THE
CONTINUOUS DATA. THESE VALUES ARE ...
THE POISSON
DISTRIBUTION

IF IN A BINOMIAL DISTRIBUTION THE VALUE OF
PROBABILITY OF SUCCESS AND FAILURE OF
AN EVENT BECOME...
DISPERSION
?
DATA
SET

OBSERVATIONS

TOTAL

.MEAN

I

00

10

20

25

70

125

25

II

23

24

25

26

27

125

25

IT IS ...
DIFFERENT MEASURES OF
DISPERSION
1. RANGE
2. QUARTILE DEVIATION
3. COEFFICIENT OF QUARTILE DEVIATION
4. MEAN DEVIATION
5. ...
STANDARD DEVIATION
1. STANDARD DEVIATION INDICATES HOW
CLOSE THE INDIVIDUAL READINGS TO THE
MEAN.
2. THE SMALLER THE STAND...
COEFFICIENT OF
VARIATION

WHEN YOU WANT TO COMPARE TWO OR
MORE SERIES OF DATA WITH EITHER
DIFFERENT UNITS OF MEASUREMENTS
...
STANDARD ERROR OF THE
Mean OF THE MEAN= STANDARD DEVIATION
STANDARD ERROR

A LARGE STANDARD ERROR IMPLIES THAT WE
SQUARE R...
“P” VALUESIGNIFICANCE

IT REPRESENTS THE PROBABILITY.
TO DETERMINE IF THE TREATMENT GROUP
IS DIFFERENT FROM CONTROL GROUP
...
CRITICAL RATIO, Z SCORE
It indicates how much an observation is bigger or
smaller than mean in units of SD
Z ratio =

Obse...
VARIANCE RATIO OR FISCHER “F”
TEST
FOR COMPARISON OF VARIANCE (SD2 )
BETWEEN THE GROUPS (OR SAMPLES SD12
AND SD22 ) VARIAN...
VARIANCE RATIO OR FISCHER “F”
TEST
IF THE CALCULATED F VALUES ARE
GREATER THAN THE VALUE TABULATED F
VALUE AT 0.05% OR AT ...
VARIANCE RATIO OR FISCHER “F”
TEST
LEVENE’S TEST FOR EQUALITY
F

Significance

10.35895

0.004764

SB with LED 40sec
SB wi...
NULL HYPOTHESIS
IT IS A HYPOTHESIS WHICH ASSUMES THAT
THERE IS NO DIFFERENCE BETWEEN TWO
VALUES SUCH AS POPULATION MEANS O...
NULL HYPOTHESIS…..
1. ALTERNATE HYPOTHESIS
2. TEST STATISTIC
3. DEGREES OF FREEDOM
4. SAMPLING ERRORS
5. LEVEL OF SIGNIFIC...
PROCEDURE FOR
TESTING THE
HYPOTHESIS

STEP-1 SET UP THE NULL HYPOTHESIS
STEP-2 SET UP THE ALTERNATE HYPOTHESIS
STEP-3 CHOO...
PROCEDURE FOR
TESTING THE
HYPOTHESIS…
STEP-5 OBTAIN THE TABLE VALUE AT THE
GIVEN LEVEL OF
SIGNIFICANCE
STEP-6 COMPARE THE ...
NULL HYPOTHESIS…..

POPULATION

CONCLUSION BASED ON
SAMPLE
NULL

NULL HYPOTHESIS

HYPOTHESIS

REJECTED

ACCEPTED

NULL HYP...
AREA OF ACCEPTANCE,
REJECTION

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TESTS OF
SIGNIFICANCE
Parametric

Non Parametric

1 Student paired T test

1 Wilcoxan signed rank test

2 Student unpaired...
STUDENT’S ‘t’ TEST
THIS TEST IS A PARAMETRIC TEST
DESCRIBED BY W.S.GOSSETT WHOSE PEN
NAME WAS “STUDENT”. IT IS USED FOR
SM...
STUDENT’S ‘t’ TEST
PAIRED ‘T’ TEST IS USED FOR A GROUP
WHICH IS ITS OWN CONTROL
Ex Effect of bionator on mandibular length...
ANALYSIS OF VARIANCE (ANOVA)
THIS TEST IS USED TO COMPARE THE
MEANS OF THREE OR MORE GROUPS
TOGETHER. THIS IS USED WHEN•SU...
ANALYSIS OF VARIANCE (ANOVA)
…

THE SHEAR BOND STRENGTH OF ADHESIVE
CURED USING FOUR DIFFERENT LIGHT
CURING UNITS ARE TO ...
ANOVA and POST HOC TESTMULTIPLE TEST OF
BONFERRONI

Source of
variation
Between groups
Within groups

Sum of
Squares
132.6...
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
THE...
TWO WAY ANALYSIS OF
VARIANCE
TWO WAY ANALYSIS CAN BE USED IN THE
ABOVE SITUATION IF THE INFLUENCE OF TIME
APART FROM THE C...
VARIABLE

MANOV
A

End of active
expansion

Immediately after
removal of appliance

36.325± 3.169

42.754± 3.030

42.302± ...
DETERMINATION OF “r”
VALUE
WHEN THE DEGREE OF LINEAR (STRAIGHT LINE)
ASSOCIATION BETWEEN TWO VARIABLES IS
REQUIRED, CORREL...
CORRELATION COEFFICIENT (r)
…
A LINE OF BEST FIT IS THEN MADE TO CONNECT
THE MAJORITY OF THE PLOTTED VALUES.
ONE HAS TO LO...
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
...
CORRELATION COEFFICIENT (r)
…
POSITIVE CORRELATION

NEGATIVE CORRELATION

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CORRELATION COEFFICIENT (r)
…

PARTIAL
POSITIVE CORRELATION

PARTIAL
NEGATIVE
CORRELATION
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ABS...
LINEAR REGRESSION
ANALYSIS
LINEAR REGRESSION IS RELATED TO
CORRELATION ANALYSIS.
THIS SEEKS TO QUANTIFY THE LINEAR
RELATIO...
LINEAR REGRESSION
ANALYSIS

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COMPARABLE PARAMETRIC
and
NON PARAMETRIC TESTS
use

parametric

Non parametric

To compare two paired
samples for equality...
ADHESIVE REMNANT
INDEX
ARI Value

Shear Bond strength
Group I

Group
II A1

Group
II A2

Group
III
B1

Group
III B2

0
No ...
WILCOXAN RANK TEST
(SIGNED RANK AND RANK
SUM)
THESE TESTS ARE NON-PARAMETRIC
EQUIVALENT OF STUDENT “t” TESTS.
WILCOXAN SIG...
KRUSKAL-WALLIS AND
FRIEDMAN
THESE ARE SIMILAR TO PARAMETRIC
ANOVA TESTS. KRUSKAL-WALLIS IS USED
FOR ONE WAY ANALYSIS OF VA...
SPEARMAN’S RANK
CORRELATION
SPEARMAN’S RANK CORRELATION AND
KENDALL’S RANK CORRELATION ARE THE
NON-PARAMETRIC EQUIVALENTS ...
CHI SQUARE TEST (χ2
TEST)
THIS TEST IS A “ GOODNESS OF FIT” TEST,
USED TO FIND OUT THE ASSOCIATION
BETWEEN VARIABLES.THIS ...
DISCRIMINANT FUNCTION
ANALYSIS
IT IS USED TO CLASSIFY CASES INTO THE
VALUES OF A CATEGORICAL DEPENDENT,
USUALLY A DICHOTOM...
META
ANALYSIS
GENE GLASS(1976) COINED THE TERM ‘META
ANALYSIS’.
THE TECHNIQUE OF META ANALYSIS INVOLVES
REVIEWING AND COMB...
CONTROLLED/UNCONTROLLED
TRIALS
CLINICAL RESEARCH CAN INDEED HAVE
CONTROLS. PROVIDED THAT STUDIES ARE
CONDUCTED ON A PROSPE...
SENSITIVITY, SPECIFICITY AND
ROC
The sensitivity of a test is the probability that the
test is positive for those subjects...
SENSITIVITY, SPECIFICITY AND
ROC…
TEST
RESULT

POSITIVE
(+)
NEGATIVE
(-)
TOTAL

TRUE DISEASE STATUS OR
CHARACTERISTIC
DISE...
SENSITIVITY, SPECIFICITY AND
ROC…

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YANCEY’S 10 RULES
-Evaluating Scientific literature
1. BE SKEPTICAL
2. LOOK FOR THE DATA
3. IDENTIFY THE TYPE OF STUDY
4. ...
YANCEY’S 10 RULES
-Evaluating Scientific literature
6. QUESTION THE VALIDITY OF DESCRIPTIVE
STATISTICS
7. QUESTION THE VAL...
SOFTWARES-STATISTICAL
PACKAGES
SPSS
MINITAB
EPIINFO
MICROSOFT EXCEL

www.indiandentalacademy.com
THANKYOU
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Transcript of " statistics in orthodontics /certified fixed orthodontic courses by Indian dental academy "

  1. 1. APPLICATION OF BIOSTATISTICS IN ORTHODONTICS www.indiandentalacademy.com
  2. 2. INDIAN DENTAL ACADEMY Leader in continuing dental education www.indiandentalacademy.com www.indiandentalacademy.com
  3. 3. www.indiandentalacademy.com
  4. 4. STATISTICS STATISTICS AS A SINGULAR NOUN IS “A SCIENCE OF FIGURES” WHERE AS PLURAL NOUN IT MEANS “FIGURES” OR NUMERICAL DATA OR INFORMATION. www.indiandentalacademy.com
  5. 5. 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 www.indiandentalacademy.com
  6. 6. 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. www.indiandentalacademy.com
  7. 7. 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 www.indiandentalacademy.com
  8. 8. 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. www.indiandentalacademy.com
  9. 9. 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
  10. 10. 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.
  11. 11. SUBDIVISIONS OF STATISTICS THEY CAN BE SEPERATED INTO TWO BROAD CATEGORIES: 1. DESCRIPTIVE STATISTICS 2. INFERENTIAL STATISTICS www.indiandentalacademy.com
  12. 12. 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 www.indiandentalacademy.com
  13. 13. 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 www.indiandentalacademy.com
  14. 14. 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
  15. 15. TYPES OF DATA I. QUALITATIVE / QUANTITATIVE II. DISCRETE / CONTINUOUS III. GROUPED / UNGROUPED IV.PRIMARY / SECONDARY V. NOMINAL / ORDINAL www.indiandentalacademy.com
  16. 16. 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. www.indiandentalacademy.com
  17. 17. 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 www.indiandentalacademy.com
  18. 18. METHODS OF PRESENTATION OF DATA •TABULATION •CHARTS AND DIAGRAMS www.indiandentalacademy.com
  19. 19. 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 www.indiandentalacademy.com
  20. 20. GUIDELINES PRESENTATION OF 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 www.indiandentalacademy.com
  21. 21. GUIDELINES PRESENTATION 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. www.indiandentalacademy.com
  22. 22. GUIDELINES PRESENTATION OF 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 www.indiandentalacademy.com Upper bound 10.09 8.34 10.7
  23. 23. PRESENTATION THROUGH CHART / DIAGRAM / GRAPH www.indiandentalacademy.com
  24. 24. LINE CHART www.indiandentalacademy.com
  25. 25. BAR DIAGRAM 40 35 30 25 20 15 10 5 0 1st Qt r 2nd Qt r 3rd Qt r 4t h Qt r www.indiandentalacademy.com
  26. 26. BAR DIAGRAM… MULTIPLE BAR COMPONENT BAR www.indiandentalacademy.com
  27. 27. HISTOGRAM FREQUENCY POLYGON www.indiandentalacademy.com
  28. 28. PIE DIAGRAM www.indiandentalacademy.com
  29. 29. SCATTER DIAGRAMS www.indiandentalacademy.com
  30. 30. BOX PLOT www.indiandentalacademy.com
  31. 31. VENN DIAGRAM www.indiandentalacademy.com
  32. 32. PICTORGRAM www.indiandentalacademy.com
  33. 33. SHADED MAPS / SPOT MAPS / DOT MAPS www.indiandentalacademy.com
  34. 34. 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 www.indiandentalacademy.com
  35. 35. TYPES OF STUDIES DESCRIPTIVE •CORRELATIONAL •CASE STUDIES -CASE REPORTS -CASE SERIES •CROSS SECTIONAL SURVEYS ANALYTICAL •OBSERVATIONAL - CASE CONTROL - COHORT •INTERVENTIONAL -CLINICAL TRIALS -ANIMAL EXPERIMENTS www.indiandentalacademy.com
  36. 36. RESEARCH DESIGNS EXPLORATIVE DESCRIPTIVE DIAGNOSTIC EXPERIMENTAL www.indiandentalacademy.com
  37. 37. DESIGN OF THE INVESTIGATION 1. RETROSPECTIVE SURVEYS 2. PROSPECTIVE SURVEYS 3. FOLLOW UP STUDIES 4. CROSS SECTIONAL SURVEYS 5. PROPHYLACTIC TRIALS www.indiandentalacademy.com 6. THERAPEUTIC TRIALS
  38. 38. 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. www.indiandentalacademy.com
  39. 39. 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. www.indiandentalacademy.com
  40. 40. 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.
  41. 41. 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 www.indiandentalacademy.com
  42. 42. 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 www.indiandentalacademy.com
  43. 43. 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 www.indiandentalacademy.com
  44. 44. SAMPLE SELECTION-GUIDELINES 1.WELL CHOSEN 2.SUFFICIENTLY LARGE (TO MINIMIZE SAMPLING ERROR) 3.ADEQUATE COVERAGE www.indiandentalacademy.com
  45. 45. METHODS OF SAMPLING 1. NON RANDOM SAMPLING 2. PROBABILITY SAMPLING www.indiandentalacademy.com
  46. 46. 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 www.indiandentalacademy.com
  47. 47. FACTORS INFLUENCING SAMPLE SIZE 1. DIFFERENCE EXPECTED 2. POSITIVE CHARACTER 3. DEGREE OF VARIATION AMONG SUBJECTS 4. LEVEL OF SIGNIFICANCE DESIRED- p VALUE www.indiandentalacademy.com 5. POWER OF THE STUDY DESIRED
  48. 48. DETERMINATION OF SAMPLE SIZE QUANTITATIVE DATA N= 4 SD2 L2 SD= STANDARD DEVIATION L = ALLOWABLE ERROR www.indiandentalacademy.com
  49. 49. DETERMINATION OF SAMPLE SIZE QUALITATIVE DATA P = POSITIVE N= 4 pq L2 CHARACTER L = ALLOWABLE ERROR Q = 1- p www.indiandentalacademy.com
  50. 50. DETERMINATION OF SAMPLE 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 www.indiandentalacademy.com
  51. 51. 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 www.indiandentalacademy.com
  52. 52. PRECISION PRECISION= square root of sample size standarad deviation STANDARD DEVIATION REMAINING THE SAME, INCREASING THE SAMPLE SIZE INCREASES THE PRECISION OF THE STUDY. www.indiandentalacademy.com
  53. 53. STRATEGIES TO ELIMINATE ERRORS 1. CONTROLS 2. RANDOMIZATION OR RANDOM ALLOCATION 3. CROSS OVER DESIGN 4. PLACEBO 5. BLINDING TECHNIQUE -SINGLE/ DOUBLE BLINDING www.indiandentalacademy.com
  54. 54. EXPERIMENTAL VARIABILITY ERROR/ DIFFERENCE / VARIATION THERE ARE THREE TYPES 1. OBSERVER-subjective / objective 2. INSTRUMENTAL 3. SAMPLING DEFECTS OR ERROR OF BIAS www.indiandentalacademy.com
  55. 55. 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. www.indiandentalacademy.com
  56. 56. 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 www.indiandentalacademy.com
  57. 57. www.indiandentalacademy.com
  58. 58. 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 www.indiandentalacademy.com
  59. 59. 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 www.indiandentalacademy.com
  60. 60. 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 www.indiandentalacademy.com
  61. 61. DISTRIBUTIONTYPES 1. NORMAL-GAUSSIAN 2. BINOMIAL 3. POISSON 4. RECTANGULAR OR UNIFORM 5. SKEWED 6. LOG NORMAL 7. GEOMETRIC www.indiandentalacademy.com
  62. 62. DISTRIBUTION-TYPES.. UNIFORM OR RECTANGULAR BIMODAL www.indiandentalacademy.com
  63. 63. NORMAL OR GAUSSIAN DISTRIBUTION www.indiandentalacademy.com
  64. 64. 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) www.indiandentalacademy.com
  65. 65. 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 POPULATION MEAN+2.58 SE LIMITS INCLUDE 99% OF THEwww.indiandentalacademy.com VALUES SAMPLE MEAN
  66. 66. CONFIDENCE LIMITS POPULATION MEAN+3.29 SE 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 www.indiandentalacademy.com
  67. 67. NORMAL DISTRIBUTIONS WITH SAME MEAN AND VARIED STANDARD DEVIATION www.indiandentalacademy.com
  68. 68. 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 www.indiandentalacademy.com
  69. 69. 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
  70. 70. 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 www.indiandentalacademy.com
  71. 71. 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 www.indiandentalacademy.com
  72. 72. 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 www.indiandentalacademy.com
  73. 73. 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 www.indiandentalacademy.com
  74. 74. 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 www.indiandentalacademy.com goals.
  75. 75. “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
  76. 76. 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. www.indiandentalacademy.com
  77. 77. 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 www.indiandentalacademy.com
  78. 78. VARIANCE RATIO OR FISCHER “F” 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 www.indiandentalacademy.com
  79. 79. VARIANCE RATIO OR FISCHER “F” TEST LEVENE’S TEST FOR EQUALITY F Significance 10.35895 0.004764 SB with LED 40sec SB with Halogen40sec www.indiandentalacademy.com
  80. 80. 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 www.indiandentalacademy.com SHOULD BE CLEAR.
  81. 81. 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 www.indiandentalacademy.com
  82. 82. 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 www.indiandentalacademy.com
  83. 83. 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 www.indiandentalacademy.com
  84. 84. 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 www.indiandentalacademy.com
  85. 85. AREA OF ACCEPTANCE, REJECTION www.indiandentalacademy.com
  86. 86. 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 www.indiandentalacademy.com
  87. 87. 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 www.indiandentalacademy.com
  88. 88. 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 www.indiandentalacademy.com
  89. 89. 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
  90. 90. 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 www.indiandentalacademy.com
  91. 91. 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 www.indiandentalacademy.com
  92. 92. 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) www.indiandentalacademy.com
  93. 93. 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. www.indiandentalacademy.com
  94. 94. 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 www.indiandentalacademy.com expansion
  95. 95. 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. www.indiandentalacademy.com
  96. 96. 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. www.indiandentalacademy.com
  97. 97. 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 www.indiandentalacademy.com
  98. 98. CORRELATION COEFFICIENT (r) … POSITIVE CORRELATION NEGATIVE CORRELATION www.indiandentalacademy.com
  99. 99. CORRELATION COEFFICIENT (r) … PARTIAL POSITIVE CORRELATION PARTIAL NEGATIVE CORRELATION www.indiandentalacademy.com ABSOLUTELY NO CORRELATION
  100. 100. 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 www.indiandentalacademy.com
  101. 101. LINEAR REGRESSION ANALYSIS www.indiandentalacademy.com
  102. 102. 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 samples for equality of means Unpaired ‘t” test Mann Whitney test To compare more than two samples for equality of means ANOVA Kruskal-Wallis Chi square test www.indiandentalacademy.com
  103. 103. 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 www.indiandentalacademy.com
  104. 104. 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. www.indiandentalacademy.com
  105. 105. 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. www.indiandentalacademy.com
  106. 106. SPEARMAN’S RANK CORRELATION SPEARMAN’S RANK CORRELATION AND KENDALL’S RANK CORRELATION ARE THE NON-PARAMETRIC EQUIVALENTS OF CORRELATION COEFFICIENT TEST. www.indiandentalacademy.com
  107. 107. 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 www.indiandentalacademy.com
  108. 108. 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
  109. 109. 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. www.indiandentalacademy.com
  110. 110. 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 www.indiandentalacademy.com
  111. 111. 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. www.indiandentalacademy.com
  112. 112. SENSITIVITY, SPECIFICITY AND 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 www.indiandentalacademy.com
  113. 113. SENSITIVITY, SPECIFICITY AND ROC… www.indiandentalacademy.com
  114. 114. 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 www.indiandentalacademy.com
  115. 115. 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. www.indiandentalacademy.com JCO May 1997,307-
  116. 116. SOFTWARES-STATISTICAL PACKAGES SPSS MINITAB EPIINFO MICROSOFT EXCEL www.indiandentalacademy.com
  117. 117. THANKYOU www.indiandentalacademy.com

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