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 DATA OR INFORMATION.
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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” www.indiandentalacademy.com
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
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
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
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 A MEANINGFUL MANNER www.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 www.indiandentalacademy.com
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
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DATA 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
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 VARIABLE www.indiandentalacademy.com
TYPES OF DATA I. QUALITATIVE / QUANTITATIVE II. DISCRETE / CONTINUOUS III.GROUPED / UNGROUPED IV.PRIMARY / SECONDARY V. NOMINAL / ORDINAL www.indiandentalacademy.com
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
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 PROMPT AND EFFECTIVE DECISIONS. www.indiandentalacademy.com
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 HEADINGS OF COLUMNS AND ROWS MUST BE CLEAR, SUFFICIENT, CONCISE AND FULLY DEFINED www.indiandentalacademy.com
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 OBSERVATIONS FROM WHICH THEY ARE DERIVED. www.indiandentalacademy.com
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
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
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Upper bound
10.09
8.34
10.7
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 Qtr
2nd Qtr
3rd Qtr
4th Qtr
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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. DESCRIPTIVE STATISTICS 6. ESTABLISHMENT OF RELATIONSHIP 7. INTERPRETATION
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TYPES OF STUDIES ANALYTICAL
DESCRIPTIVE
•OBSERVATIONAL
•CORRELATIONAL
- CASE CONTROL
•CASE STUDIES
- COHORT
-CASE REPORTS
•INTERVENTIONAL
-CASE SERIES
-CLINICAL TRIALS
•CROSS SECTIONAL SURVEYS
-ANIMAL EXPERIMENTS
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RESEARCH DESIGNS EXPLORATIVE DESCRIPTIVE DIAGNOSTIC EXPERIMENTAL www.indiandentalacademy.com
DESIGN OF THE INVESTIGATION 1. RETROSPECTIVE SURVEYS 2. PROSPECTIVE SURVEYS 3. FOLLOW UP STUDIES 4. CROSS SECTIONAL SURVEYS 5. PROPHYLACTIC TRIALS 6. THERAPEUTIC TRIALS www.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. www.indiandentalacademy.com
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
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 www.indiandentalacademy.com
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
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 A STUDY www.indiandentalacademy.com
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 4. CLUSTER SAMPLING 5. SUB SAMPLING/ MULTISTAGE SAMPLING 6. MULTIFACE SAMPLING www.indiandentalacademy.com
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 6. DROP OUT RATE
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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 CHARACTER N=
4 pq
L2
L = ALLOWABLE ERROR Q = 1- p
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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
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
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
STRATEGIES TO ELIMINATE ERRORS 1. CONTROLS 2. RANDOMIZATION OR RANDOM ALLOCATION 3. CROSS OVER DESIGN 4. PLACEBO 5. BLINDING TECHNIQUE
-SINGLE/ DOUBLE BLINDING
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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
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
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
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ERRORS IN SAMPLING SAMPLING ERRORS
NON SAMPLING ERRORS
Faulty sampling design
Coverage error
Small size of the sample
Observational error
-due to non response or non cooperation of the informant -due to interviewers bias,imperfect exptl. design,or interaction Processing error
-due to errors in statistical analysis
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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
DISTRIBUTIONS WHEN YOU HAVE A COLLECTION OF POINTS YOU BEGIN THE INITIAL ANALYSIS BY PLOTTING THEM ON A GRAPH TO SEE HOW THEY ARE DISTRIBUTED
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DISTRIBUTION-TYPES 1. NORMAL-GAUSSIAN 2. BINOMIAL 3. POISSON 4. RECTANGULAR OR UNIFORM 5. SKEWED 6. LOG NORMAL 7. GEOMETRIC www.indiandentalacademy.com
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, 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)
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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 THE SAMPLE MEAN VALUES www.indiandentalacademy.com
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
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 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 IS DEFINED BYTHE BINOMIAL DISTRIBUTION. www.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 OFwww.indiandentalacademy.com LARGE SERIES.
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
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 VARY WIDELY. 4. THE SD TENDS TO GET SMALLER AS THE www.indiandentalacademy.com SAMPLE SIZE INCREASES.
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
STANDARD ERROR OF THE Mean STANDARD ERROR OF THE MEAN= STANDARD DEVIATION
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. www.indiandentalacademy.com
“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
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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
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 N1-1 AND N2-1 www.indiandentalacademy.com
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
VARIANCE RATIO OR FISCHER “F” TEST
LEVENE’S TEST FOR EQUALITY F
Significance
10.35895
0.004764
SB with LED 40sec SB with Halogen40sec
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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
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 8. ONE TAILED / TWO TAILED TEST www.indiandentalacademy.com
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
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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
NULL 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
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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 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
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
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
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
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 THEM. www.indiandentalacademy.com
ANOVA and POST HOC TESTMULTIPLE TEST OF BONFERRONI Source of variation
Sum of Squares
df
Mean Square
F
Sig.
Between groups
132.6448
4
33.1612
17.2515
<0.00000012
86.4999
45
1.92222
Within groups
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
RESULTS OF ANOVA 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) www.indiandentalacademy.com
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
MANOVA VARIABLE
Before appliance insertion
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
4.046± 1.115
Not measured
Molar cusp width Molar gingival width Canine cusp width Canine gingival width Diastema width Maxillary perimeter Screw separation Anterior suture expansion Comparison of skeletal and dental changes between 2 point and 4 point rapid palatal 1.000 expanders AJO:2003 Not 123;321-328 Not measured 1.837± measured Posterior suture expansion
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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
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
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
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CORRELATION COEFFICIENT (r)… POSITIVE CORRELATION
NEGATIVE CORRELATION
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CORRELATION COEFFICIENT (r)…
PARTIAL POSITIVE CORRELATION
PARTIAL NEGATIVE CORRELATION ABSOLUTELY www.indiandentalacademy.com
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 www.indiandentalacademy.com
LINEAR REGRESSION ANALYSIS
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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
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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
3 Entire adhesive left on the tooth 4 5 3 surface www.indiandentalacademy.com
7
4
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
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
SPEARMAN’S RANK CORRELATION SPEARMAN’S RANK CORRELATION AND KENDALL’S RANK CORRELATION ARE THE NON-PARAMETRIC EQUIVALENTS OF CORRELATION COEFFICIENT TEST.
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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 COMPARED. www.indiandentalacademy.com
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. www.indiandentalacademy.com
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 THEY ARE SUBJECTED TO STATISTICAL ANALYSIS. www.indiandentalacademy.com
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
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
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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. IDENTIFY THE POPULATION SAMPLED 5. DIFFERENTIATE BETWEEN DESCRIPTIVE AND INFERENTIAL STATISTICS
JCO May 1997,307-314
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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
1997,307-314
SOFTWARES-STATISTICAL PACKAGES SPSS MINITAB EPIINFO MICROSOFT EXCEL
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