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# Biostatistics /certified fixed orthodontic courses by Indian dental academy

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The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.

Indian dental academy provides dental crown & Bridge,rotary endodontics,fixed orthodontics,
Dental implants courses.for details pls visit www.indiandentalacademy.com ,or call
0091-9248678078

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### Biostatistics /certified fixed orthodontic courses by Indian dental academy

2. 2.  Statistic or datum means a measured or counted fact or piece of information stated as a figure such as height of one person , birth of a baby ,etc. www.indiandentalacademy.com
3. 3.  Biostatistics:- It can be defined as an art and science of collection , compilation, presentation, analysis and logical interpretation of biological data affected by multiplicity of factors. It is the term used when the tools of statistics are applied to data that is derived from biological sciences such as medicine or dentistry. www.indiandentalacademy.com
4. 4.  Biostatistics can also be called as :-  Quantitative medicine  Science of variations  For such studies we need mathematical techniques called as statistical methods. www.indiandentalacademy.com
5. 5.  Depending upon the field of application there can be :-  Health statistics  Medical statistics  Vital statistics  These terms are overlapping and not exclusive of each other. www.indiandentalacademy.com
6. 6. Applications..  Physiology and anatomy  Pharmacology  Medicine  Community medicine  Community dentistry  Public health  Research field www.indiandentalacademy.com
7. 7. Common statistical terms..  Variable:- a characteristic that takes on different values in different persons ,place or things . It is denoted by X and notation for orderly series as X1, X2,X3…..Xn  Constant:- a character that do not vary.e.g mean , standard deviation etc www.indiandentalacademy.com
8. 8.  Observation:- An event and its measurement. e.g. blood pressure .  Observational unit:- the source that gives observations such as object, person , etc.  Data :- a set of values recorded on one or more observational units. www.indiandentalacademy.com
9. 9.  Population:- It is an entire group of people or study elements – person ,things or measurements for which we have an interest at a particular time .it may be finite or infinite.  Sample :- It is defined as a part of the population  Sampling unit:- each member of the population www.indiandentalacademy.com
10. 10.  Parameter:- it is the summary value or constant of the variable that describes the population such as mean variance , correlation coefficient ,proportion ,etc. e.g. mean height ,birth rate www.indiandentalacademy.com
11. 11.  Parametric test:- one in which population constants are used such as mean , variance etc and data tend to follow one assumed or established distribution such as normal, binomial ,Poisson, etc  Non- parametric tests:- no constants are used ,data do not follow any specific distribution and no assumptions are made . E.g. to classify good, better and best you allocate arbitrary no. to each category. www.indiandentalacademy.com
12. 12. Types of data.. A. Qualitative / Enumeration data Quantitative / measurement data B. Discrete Data Continuous Data C. Grouped Data Ungrouped Data www.indiandentalacademy.com
13. 13. D. Primary data Secondary data E. Nominal data Ordinal data www.indiandentalacademy.com
14. 14. Sources of data…  Census  Registration of vital events  Sample Registration System (SRS)  Notification of diseases  Hospital records  Epidemiological Surveillance  Surveys  Research Findings www.indiandentalacademy.com
15. 15. Methods of presentation of data... www.indiandentalacademy.com
16. 16. Principles of data presentation:- The data should be :-  arranged in such a way that it will arouse interest in reader.  Made sufficiently concise without loosing important details. www.indiandentalacademy.com
17. 17.  Presented in simple form to enable the reader to form quick impression and to draw some conclusions directly or indirectly.  Facilitate further statistical analysis.  Able to define a problem and suggest its solution. www.indiandentalacademy.com
18. 18. Tables.. Sample of putty No. of impressions made Sample A 30 Sample B 40 Sample C 25 Sample D 25 www.indiandentalacademy.com
19. 19. Charts and diagrams for Qualitative data.. www.indiandentalacademy.com
21. 21. Pie or sector diagram.. Patients reported to department in 1 yr Complete dentures FPD RPD others www.indiandentalacademy.com
22. 22. Venn diagram.. Implants FPD RPD www.indiandentalacademy.com
23. 23. Pictogram.. Number of dentures delivered 2004 2005 2006 www.indiandentalacademy.com
24. 24. Shaded Maps,Spot Maps or Dot Maps • Represents the places where implant research centers can be established www.indiandentalacademy.com
25. 25. Charts and diagrams for Quantitative data.. www.indiandentalacademy.com
31. 31. Cumulative frequency diagram/ Ogive www.indiandentalacademy.com
32. 32. Scatter or Dot diagram www.indiandentalacademy.com
35. 35.  It should be rigidly defined  Its computation should be based on all observations  It should lend itself for algebraic treatment  It should be least affected by the extreme observations. www.indiandentalacademy.com
36. 36. 1) Arithmetic mean 2) Median 3) Mode 4) Quartiles 5) Geometric Mean 6) Harmonic mean 7) Weighted mean www.indiandentalacademy.com
37. 37. Average (arithmetic mean)  A.M = sum of observations number of observations Sample of putty No. of impressions made Sample A 30 Sample B 40 Sample C 25 Sample D 25 AM = 30+40+25+25 = 30 4 Thus on an average 30 impressions can be made out of a box of putty www.indiandentalacademy.com
38. 38.  Merits:-  Easy to calculate and understand  Based on all observations  Familiar to common man and rigidly defined  Capable of further mathematical calculations  Least affected by sampling fluctuations. More stable www.indiandentalacademy.com
39. 39.  Demerits:-  Only for quantitative data  Unduly affected by extreme values  Cannot be calculated when frequecy distribution is with open end classed  Sometimes AM is not among the observation  Cannot be determined graphically www.indiandentalacademy.com
40. 40. Median..  When all observations are arranged in ascending or descending order, the middle observation is known as median. 1. Ungrouped data Median = value of [ (n+1)/2] , if n is odd [ (n+1)/2] + [n/2] , if n is even 2 year No. of cases treated by P.Gs 2003 289 2001 350 2004 400 2005 410 2002 450 2000 500 2006 650 Year No. of cases treated by P.Gs 2000 500 2001 350 2002 450 2003 289 2004 400 2005 410 2006 650 www.indiandentalacademy.com
41. 41. ii. Grouped data:- median = I + N/2 – c.f. x h f where, N = total frequency f = frequency h = class width c.f = less than cumulative frequency of the class previous to the median class I = lower boundary of the median class www.indiandentalacademy.com
42. 42. Weight of infants in kg No. of infants 2.0 – 2.4 37 2.5-2.9 117 3.0-3.4 207 3.5-3.9 155 4.0- 4.4 48 4.5 and above 26 Weight of infants in kg No. of infants Cumulative frequency 1.95– 2.45 37 37 2.45-2.95 117 154 2.95-3.45 207 361 3.45-3.95 155 516 3.95- 4.45 48 564 4.45 and above 26 590 Median = 2.95 + 295- 154 x 3.29 = 3.29 207 3.29 kg is the median weight www.indiandentalacademy.com
43. 43.  Merits:-  Easy to calculate and understand  Can be computed for distribution with open end classes  Not affected by extreme observations  Applicable for both quantitative and qualitative data  Can be determined graphically www.indiandentalacademy.com
44. 44.  Demerits:-  Not based on all observations  Not rigidly defined  Not capable of further mathematical treatment www.indiandentalacademy.com
45. 45. Mode..  The observation that occurs most frequently in a series is known as mode i. Ungrouped data:- Diastolic blood pressure of 9 individual 86 90 92 70 86 98 86 80 86 Therefore the mode is 86 www.indiandentalacademy.com
46. 46. ii. grouped data:- mode = I + fm –f 1 x h 2 fm – f1 –f2 Where , I = lower boundary of the modal class fm = frequency of modal class f1 = frequency of pre modal class f2 = frequency of post modal class h = width of the class www.indiandentalacademy.com
47. 47.  Merits:-  Can be computed for distribution with open end classes  Not affected by extreme observations  Applicable for both quantitative and qualitative data  Can be determined graphically www.indiandentalacademy.com
48. 48.  Demerits:-  Not based on all observations  Not rigidly defined  Not capable of further mathematical treatment  It is indeterminate when the maximum frequency is at one end of the distrbution. www.indiandentalacademy.com
49. 49. Quartiles..  The values which divide the given data in four equal parts when the observations are arranged in order of magnitude are known as quartiles.  There will be three quartiles Q1 , Q2 and Q3 www.indiandentalacademy.com
50. 50. Geometric mean..  When values are given in geometric progression the G.M is taken GM = antilog [ sum ( f. log x) ] N N= sum (f) www.indiandentalacademy.com
51. 51. Harmonic means..  It is reciprocal of arithmetic mean of reciprocal observations.  For ungrouped data HM = n [ 1/x]  For frequency distribution HM = N Σ (f/x) www.indiandentalacademy.com
52. 52. Weighted mean..  While computing sometimes we need to prefer or give more importance to certain values than others… and thus weighted mean is calculated. WM = sum ( w. x) sum (w) www.indiandentalacademy.com
54. 54.  The variations or dispersion gives the information as to how individual observations are scattered or dispersed from the mean of a large series.  Deviation = observation - mean www.indiandentalacademy.com
55. 55. Measure of dispersion.. www.indiandentalacademy.com
56. 56.  Gives information on how individual observations are scattered or dispersed from the mean of a large series.  Different measures of dispersion are:- 1) Range 2) Quartile deviation 3) Coefficient of Quartile deviation 4) Mean deviation 5) Standard deviation 6) Variance 7) Coefficient of variance www.indiandentalacademy.com
57. 57. Mean deviation..  Based on all observations  Mean deviation = Sum I x – x I n www.indiandentalacademy.com
58. 58. Standard deviation  σ = √ Sum (x – x )2 n -1  The problem of negative variable is solved here and we can estimate the scatter in the population www.indiandentalacademy.com
59. 59. Variance  Nothing else but square of standard deviation and denoted by σ2 www.indiandentalacademy.com
60. 60. Day of reporting with complaint No. of patient reported 1 10 2 25 3 35 4 05 5 10 6 10 7 15 Mean = 110/7 = 15.7 SD = √ 668.34 = 10.5 6 Day of reporting with complaint No. of patient reported Ix- x I2 1 10 32.49 2 25 86.49 3 35 372.49 4 05 110.49 5 10 32.49 6 10 32.49 7 15 1.4 Total 668.34 www.indiandentalacademy.com
61. 61. Uses of Standard deviation:- a) Summarizes the deviation of a large distribution from mean in one figure used as a unit of variation b) Indicates weather the variation is real or due to special reason c) Helps in comparing two samples d) Helps in finding the suitable sample size for valid conclusion www.indiandentalacademy.com
62. 62. Merits of SD:-  Rigidly defined  Based on all observations  Doesn’t ignore the algebraic sign of deviation  Capable of further mathematical treatment  Not much effected by sample fluctuation www.indiandentalacademy.com
63. 63. Demerits of SD:-  Difficult to understand and calculate  Cannot be calculated for qualitative data and distribution with open end classes  Unduly affected by extreme deviations www.indiandentalacademy.com
65. 65.  Sampling method is a scientific and objective procedure of selecting units from a population and provides a sample that is expected to be representative of the population as a whole.  Results are generalized for the entire population which might not be completely correct ,thus sampling errors are there. www.indiandentalacademy.com
66. 66.  Thus :- Sample should be well chosen Sample must be sufficiently large There must be adequate coverage of the sample. www.indiandentalacademy.com
67. 67. Method of sampling.. www.indiandentalacademy.com
68. 68. A. Non-random sampling:- sample is chosen without conscious bias and may not represent the population.  Not useful and gives only the feel of the population  Also called as “Chunks” , “Accidental”, “incidental" or “samples of convenience” www.indiandentalacademy.com
69. 69.  For example we pick a group of 30 people out of a population without seeing there age , sex, social status etc for presence of a fixed prosthesis in their mouth. www.indiandentalacademy.com
70. 70. Another type in same is judgment type sample:-  Quota samples:- the investigator is interested in getting some predetermined no. of units for the sample. E.g. in terms of sex, education  Purposive sampling:- Selected because the investigator believes that they represent the population under study. e.g. literacy rate www.indiandentalacademy.com
71. 71. B. Probability sampling:- each individual in the population has a probability of getting selected  Gives a better picture of the population and results can be generalized www.indiandentalacademy.com
72. 72.  Types of sampling:- 1) Simple random sampling 2) Systematic sampling 3) Stratified sampling 4) Cluster sampling  If probability sampling is done in more than one stage then there can be two stage or multistage sampling www.indiandentalacademy.com
73. 73. Simple random sampling..  Selection solely based on chance  Done for a small homogenous population  E.g. choosing samples from a dental unit for efficacy of soft liners  Can be of two types:-  Without replacement ( when population is infinite)  With replacement ( when population is finite) Hence prepare a sample frame , decide the sample size and then randomly pick the sample size that is needed.www.indiandentalacademy.com
74. 74. Systemic sampling..  Only first unit is selected randomly and rest are chosen in a pre-determined pattern automatically as complete list of population is available  Due to simplicity and low cost this is a preferred method and helps establishing control over the field of work.  E.g. choosing a sample from the population in Dhankawadi for presence of a dental prosthesis. www.indiandentalacademy.com
75. 75. Stratified sampling..  Population is divided into groups or strata and then the desired sample size is picked from these homogenous groups  Lesser the differences with in the strata more is the difference in between the strata, which means greater gain.  Proportional Allocation www.indiandentalacademy.com
76. 76.  It is more precise  Nature and size of the strata can be known, hence better application of the results for the population.  E.g. oral health status of population living in Katraj.We can divide this population into strata www.indiandentalacademy.com
77. 77. Cluster sampling..  The population is divided into smallest possible groups or clusters and then these clusters are chosen by simple random sampling method  Useful when the list of elements in sample is not available.  Necessary prerequisite is that every cluster should correspond to only one cluster so that there are no repetitions or omissions. www.indiandentalacademy.com
78. 78.  Large number of small clusters are preferred over small number of large clusters.  Disadvantage is that the clusters might contain same type of elements.  E.G. we divide the population of Pune in clusters according to the area and then do a study for prosthetic needs of the population www.indiandentalacademy.com
79. 79.  Sub Sampling  Random Digit Dial  Sampling by computers www.indiandentalacademy.com
81. 81. Non-Sampling Errors..  Discrepancy between the survey value and the true value is called as observational or response error.  Present right from the planning of the survey to the analysis of the data. www.indiandentalacademy.com
82. 82.  Faults at planning level. E.g. incomplete coverage , faulty method of selection or estimation  Faults in carrying out the instructions by the enumerator  Faults by the respondents  There can also be Non-Response Errors where data could not be collected due to any reason. E.g. subject unavailable. www.indiandentalacademy.com
83. 83.  It is better to omit a lost sample or element than to substitute with another one  Omission creates small biased samples while substitution creates large biased samples. www.indiandentalacademy.com
84. 84. Sampling Errors..  These errors are by chance and concern incorrect rejection or acceptance of the Null Hypothesis  Can be of two types :-  Type I  Type II www.indiandentalacademy.com
85. 85. Type I:-  Also called as Alpha error or error of first kind  if null hypothesis is false then noType I error  Some studies take an alpha error of 5% as cut off limit for rejecting null hypothesis.  Repeated testing or multiple comparisons increases the likelihood of type I error www.indiandentalacademy.com
86. 86. Type II:-  Error Of Second type or Beta error  Occurs when null hypothesis is accepted when actually it is false  If null hypothesis is true then there is no Type II error www.indiandentalacademy.com
87. 87. Sample size..  A sample size can be calculated by using the standard formulae should have :-  Required level of statistical significance of the expected result  Acceptable chance of missing a real effect  Magnitude of the effect under investigation  Prevalence of disease  Relative sizes of groups being concerned www.indiandentalacademy.com
88. 88.  Smaller the sample size….lesser is the precision precision = √n s where n = sample size s = SD for the sample www.indiandentalacademy.com
89. 89. Bias in sample..  Also called as systemic error a. Selection bias:- distortion in manner of selection b. Measurement bias:- distortion in the measurement www.indiandentalacademy.com
90. 90. c. Confounding bias:- associated with both exposure and outcome. Cause problem when unequally distributed between the sample and the control group. Can be controlled by randomization, restriction and matching at designing stage and stratification and statistical modeling at analysis stage. www.indiandentalacademy.com
91. 91. Probability..  Chance of an event occurring  Trial  Events:- various outcome of a trial  Exhaustive event:- total no. of possible outcomes  Favorable events:-no. of cases favorable to an event www.indiandentalacademy.com
92. 92.  Mutually exclusive events:- when happening of one event precludes the other.  Equally likely events  Independent events  Sample space:- totality of all possible outcomes www.indiandentalacademy.com
93. 93.  probability = favorable no. of events exhaustive no. of events p + q = 1 www.indiandentalacademy.com
94. 94.  Subjective probability:- probability based on personal evaluations or believes. E.g. when a dental surgeon feels that one companies' material is better than other though there be no scientific prove.  Conditional probability:- when there are conditions to be followed in a trial. E.g. when we compare the oral health care facilities provided by the dental hospitals, now difference lies in the area or condition they work www.indiandentalacademy.com
95. 95. Normal distribution..  Binominal distribution  Uniform distribution  Skewed distribution  Normal / Gaussian distribution  Log normal distribution  Poisson distribution  Geometric distribution  Others:- multinominal ,exponential etc distribution www.indiandentalacademy.com
96. 96. Normal distribution Y axis X axis www.indiandentalacademy.com
97. 97.  For comparison we also use standard normal curve in which the population mean is taken as zero and the Standard deviation as 1 www.indiandentalacademy.com
98. 98. Test of significance.. www.indiandentalacademy.com
99. 99.  Tests a hypothesis  Null hypothesis:- a hypothesis which assumes that there is no difference between the population means. Denoted by Ho  Alternative hypothesis:- a hypothesis that differs from the null hypothesis. Denoted by H1 www.indiandentalacademy.com
100. 100.  Degree of freedom:- the number of independent observations which are used in statistics.  Level of significance (α):- the probability of committingType I error  Power of the test:- the probability of committingType II error. Denoted by β and 1-β.this is the probability of taking a correct decision. www.indiandentalacademy.com
101. 101.  Critical regions:- Regions of acceptance and rejection a. one tailed test b. two tailed test  Confidence limit www.indiandentalacademy.com
102. 102. Procedure for testing a hypothesis.. 1. Set up a null hypothesis 2. Set up an alternate hypothesis.This gives an idea weather it is a one or two tailed test. 3. Choose the appropriate level of significance 4. Compute the value of test statistic ”z” www.indiandentalacademy.com
103. 103. Procedure for testing a hypothesis.. z = observed difference standard error 5. Obtain the table value at given level of significance 6. Compare the value of z with that of table value 7. Draw the conclusion www.indiandentalacademy.com
104. 104. Z test  Also called as Large Sample test or Normal test  Statistical value of particular importance is called as proportion and is obtained by dividing the individual events by total no. of events www.indiandentalacademy.com
105. 105.  If IzI > 3 then Ho is always rejected or else may be accepted  if IzI> 1.96, Ho is rejected, 5% level of significance or else may be accepted  if IzI> 2.58, Ho is rejected, 1% level of significance or else may be accepted One tail test Two tail test www.indiandentalacademy.com
106. 106. Can be:-  Test for qualitative data  Test for quantitative data www.indiandentalacademy.com
107. 107.  E.g :- in Department of Prosthodontics , out of 120 cases treated 35 were of implant. Check whether the proportion of implant cases is 40%. www.indiandentalacademy.com
108. 108.  Let p be the sample proportion of implant cases done p = 35 = 0.29 120 P = 0.40 Ho : the proportion is 40 % H1 : the proportion is not 40% Z = p-P = 0.29-0.40 = -2.46 SE √ Reject the null hypothesis at 5% and since the value is greater than 1.96 Thus the proportion of implant cases is not 40% 0.40 x 0.60 120 www.indiandentalacademy.com
109. 109. Small sample test..  When the sample size is less than 30  T- test  Unpaired t- test  Paired t-test  Chi- Square test www.indiandentalacademy.com
110. 110. t-test  W.S Gosset,1908  Also called as student’s t test  Assumptions:- 1) Sample must be random 2) Population standard deviation is not known 3) The distribution of population from which the sample is drawn is normal www.indiandentalacademy.com
111. 111.  Test regarding single mean:  For testing the significance of difference between sample mean and population mean t = x – μ s/ √n where, S2 = sum ( x- x )2 n-1 Values are seen with the table for this test and then decide the significance www.indiandentalacademy.com
112. 112.  E.g Nine individuals are chosen from a population and their mouth openings were fond out to be ( in mm) as 40,45,30,35,50,52,47,39,40. discuss the mean mouth opening is 40mm Solution:- Ho : the mean mouth opening is 40 mm H1 : the mean mouth opening is not 40 mm www.indiandentalacademy.com
113. 113. X X-X (X-X)2 40 -2 4 45 3 9 30 -12 144 35 -7 49 50 8 64 52 10 100 47 5 25 39 -3 9 40 -2 4 Total 378 408 X= 378 = 42 9 S2= 408 = 51 8 t = 42-40 = 0.8 7.14/ 3 www.indiandentalacademy.com
114. 114. At degree of freedom of 8 the value of t is 3.355 at 1% l.o.s Conclusion:- therefore the mean mouth opening may be 40 mm.The difference occurred due to sample fluctuation www.indiandentalacademy.com
115. 115. Unpaired t test  Two equivalent independent samples are studied  The two samples should be random from normal population having unknown or same variance t = observed difference SE www.indiandentalacademy.com
116. 116. Paired t test  When the two samples are dependent and sample size is same  E.G. increase in flexural strength of acrylic denture before and after using glass fibers 1. Set up the null hypothesis 2. Set up the alternative hypothesis 3. Obtain the difference of paired observation, d = x- y 4. Compute the mean of difference d = sum (d)/n www.indiandentalacademy.com
117. 117. Paired t test 5. Find the SD of difference and calculate SE SD of d (S) = √ sum ( d – d)2 n-1 SE of difference = SD of difference √n www.indiandentalacademy.com
118. 118. 6. Work out the value of t t = d √n S 7. Find out the value from the t table 8. Reject or accept 9. Draw the conclusion www.indiandentalacademy.com
119. 119.  E.g: In the trial for the impact strength for 10 acrylic resin bars with and without reinforcement with glass fibers the readings were before ( in kg load) 10, 12, 7, 9, 13 ,17,8,12,10,15 after 16, 19,12,14,15,18,18,17,16,10 Test the efficacy of fiber reinforcement Ho: glass fiber reinforcement is not effective H1: glass fiber reinforcement is effective www.indiandentalacademy.com
120. 120. Sample no. Before After d = Ix1-x2I (d-d)2 1 10 16 -6 0.64 2 12 19 -7 3.24 3 7 12 -5 0.4 4 9 14 -5 0.4 5 13 15 -2 10.4 6 17 18 -1 17.6 7 8 18 -10 23.04 8 10 17 -7 3.24 9 12 16 -4 1.44 10 15 10 5 0.4 Total 52 60.80 Mean = 52/10=5.2 SD(d)= √60.8/9= 2.6 SE = 2.6 = 0.86 √9 t = 5.2/0.86= 6.04 www.indiandentalacademy.com
121. 121. the value of t at 1% l.o.s is 1.83 for a degree of freedom of 9 Conclusion:- Thus the glass reinforcement is highly effective www.indiandentalacademy.com
122. 122. Chi Square test  Plays an important role in the problem where information is obtained by counting or enumerating instead of measuring.  Use to test:- a) Independence of attributes b) Goodness of fit of the distribution www.indiandentalacademy.com
123. 123.  General procedure :- 1. Write down the null hypothesis 2. Obtain the expected frequencies 3. Compute the value of chi square test X2=Sum ( observed – expected )2 Expected 4. Find out the degree of freedom 5. Obtain the value from the table 6. Compare the value 7. Draw the conclusion www.indiandentalacademy.com
124. 124.  E.gSex O group A group B group Ab group total Male 105 50 45 15 215 Female 115 60 40 10 225 Total 220 110 85 25 440 Expected frequency= RT x CT GT Sex O group A group B group Ab group Male 107.5 53.57 46.42 12.22 Female 112.5 56.25 48.58 12.78 www.indiandentalacademy.com
125. 125.  Ho: blood group is independent of sex  H1: blood group is not independent of sex X2 = 3.42 Degree of freedom = (r-1) (c-1)= 3 Value of X2 for 3 degree of freedom is 7.81 at 5% l.o.s Conclusion:- Blood group is independent of the sex www.indiandentalacademy.com
126. 126. Correlation..  Joint relation of two variables  Positive Correlation  Negative Correlation  Easiest method of studying it is the graphical method  E.G: correlation between size of edentulous arch and retention of the denture www.indiandentalacademy.com
127. 127.  Correlation Coefficient  By Prof. Karl Pearson r = n (Sum xy)- n ( x y ) √ [Sum x2 – n x 2 ] √ [Sum y2 – Sum n y 2]  also known as product moment correlation coefficient  - 1 ≤ r ≤ 1  When no correlation then r=0 www.indiandentalacademy.com
128. 128. Linear regression..  Regression means to step back  To predict unknown value of a variable when value of one is known  Can be :-  Simple regression  Multiple regression E.g. lets suppose we have data about the attrition seen in complete dentures in 5 yr and we want to know the attrition that would have been seen in 3 yrs. www.indiandentalacademy.com
129. 129. Y = a+ b X b= ∆y / ∆x Y a = y intercept ∆x x+∆xx www.indiandentalacademy.com
130. 130. Analysis Of Variance  ANOVA is a collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables, usually called factors in Design of experiments www.indiandentalacademy.com
131. 131.  sometimes known as Fisher's ANOVA or Fisher's analysis of variance, due to the use of Fisher's F-distribution as part of the test of statistical significance. www.indiandentalacademy.com
132. 132.  There are three conceptual classes of such models:  Fixed-effects model assumes that the data come from normal populations which may differ only in their means.  Random-effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy  Mixed effects models describe situations where both fixed and random effects are present. www.indiandentalacademy.com
133. 133.  One-wayANOVA is used to test for differences among three or more independent groups.  Another-wayANOVA for repeated measures is used when the subjects are subjected to repeated measures; this means that the same subjects are used for each treatment. Note that this method can be subject to carryover effects. www.indiandentalacademy.com
134. 134.  FactorialANOVA is used when the experimenter wants to study the effects of two or more treatment variables.The most commonly used type of factorialANOVA is the 2x2 (read: two by two) design, where there are two independent variables and each variable has two levels or distinct values. www.indiandentalacademy.com
135. 135.  Multivariate analysis of variance (MANOVA) is used when there is more than one dependent variable.  Both main effects and interactions between the factors may be estimated www.indiandentalacademy.com
136. 136.  Variance ratio :- F = estimate of variance based on the variation between the groups estimate of variance based on the variation within the groups Degree of freedom = no. of observations - 1 www.indiandentalacademy.com
137. 137. Non parametric test  Distribution free method of analysis  Observations should be continuous but not necessarily defined as required in other tests  No assumptions are made for the population  Sample observations have to be independent  Easier to conduct and understand but less powerful than the parametric tests www.indiandentalacademy.com
138. 138. 1. The sign test 2. Wilcoxon signed rank test 3. Mann -Whitney U test 4. Wilcoxon Rank Sum test 5. Kruskal –Wallis test 6. Kolmogrov- Smirnov test www.indiandentalacademy.com