scope and need of biostatics

This powerpoint presentation gives a brief explanation about the biostatic data .this is quite helpful to individuals to understand the basic research methodology terminologys

1. SCOPE & NEED OF STATISTICAL APPLICATION TO BIOLOGICAL DATA DR. JYOTI SHARMA MDS I Dept of prosthodontics

2. GUIDED BY: DR. RAJLAKSHMI BANERJEE DR. Usha.M.RADKE DR .NEELAM.A.PANDE Reader A nd Guide Professor & HOD Professor& Guide DR. SAEE.P. DESHMUKH DR. TUSHAR MOWADE DR. ANUJ CHANDAK Reader & guide Reader & Guide Reader By : Dr . JYOTI SHARMA M.D.S.-I 03/05/2020

3. CONTENTS Definition Use Of Biostatics Basis Of Biostatics Measures Of Statistical Averages Or Central Tendency Measures Of Dispersion Normal Distribution/Normal Curve / Gaussian Distribution Standard Normal Deviation Test Of Significance Classification Of Tests Of Significance

4. 10.Standard Error Of Proportion 11.Standard Error Of Difference Between Two Means 12.Standard Error Of Difference Between Proportions 13.The Chi Square Test For Qualitative Data (X² Test ) 14.z -t e s t 15.Analysis Of Variance ( Anova ) Test 16.Correlation And Regression 17.R eg r essi o n 18.Conclusion

5. STATISTICS- is a science of compiling, classifying, and tabulating numerical data and expressing the results in a mathematical and graphical form. BIOSTATISTICS- is that branch of statistics concerned with the mathematical facts and data related to biological events. DEFINATION

6. USES OF BIOSTATISTICS To test whether the difference between two populations is real or by chance occurrence. To study the correlation between attributes in the same population. To evaluate the efficacy of vaccines. To measure mortality and morbidity. To evaluate the achievements of public health programs To fix priorities in public health programs To help promote health legislation and create administrative standards for oral health.

7. Basis Of Statistical Analysis Based On Three Primary Entities : The Population (U) The Set Of Characteristic Variables (V) The Probability Distribution (P)

8. Measures of statistical averages or central tendency C entral value around which all the other observations are distributed. Main objective is to condense the entire mass of dat a and to facilitate the comparison. T he most common measures of central tendency that are used in d ental sciences: Arithmetic mean M edian M ode

9. Refers to arithmetic mean . It is obtained by adding the individual observations divided by the total number of observations . Advantages – I t is easy to calculate. M ost useful of all the averages. Disadvantages – I nfluenced by abnormal values. Mean

10. When all the observation are arranged either in ascending order or descending order, the middle observation is known as median. In case of even number the average of the two middle values is taken. Median is better indicator of central value as it is not affected by the extreme values. Median

11. Most frequently occurring observation in a data is called mode . Not often used in medical statistics. EXAMPLE Number of decayed teeth in 10 children 2,2,4,1,3,0,10,2,3,8 Mean = 34 / 10 = 3.4 Median = (0,1,2,2, 2,3 ,3,4,8,10) = 2+3 /2 = 2.5 Mode = 3 Median – 2 Mode Mode

12. MEASURES OF DISPERSION Dispersion is the degree of spread or variation of the variable about a central value. Helps to know how widely the observations are spread on either side of the average. Most common measures of dispersion are: RANGE MEAN DEVIATION STANDARD DEVIATION

13. RANGE MEAN DEVIATION STANDARD D E V I A T I ON Defined as the difference between the value of the largest item and the smallest item. Gives no information about the values that lie between the extreme values. It is the average of the deviation from the arithematic mean. M.D= Ʃ(X-Xi) n Ʃ-sum of X- arithematic mean Xi- value of each observation in the data n- number of observation in the data Most important and widely used measure of studying dispersion. Greater the S.D , greater will be the magnitude of dispersion from the mean. Smaller S.D means a higher degree of uniformity of the observations. S.D= Ʃ( X - Xi ) ² n

14. When the data is collected from a very large number of people and a frequency distribution is made with narrow class intervals, the resulting curve is smooth and symmetrical- NARROW CURVE. These limits on either side of measurement are called confidence limits . Normal distribution/normal curve/ Gaussian distribution

15. STANDARD NORMAL DEVIATION There may be many normal curves but only one standard normal curve. Characteristics Bell shaped Perfectly symmetrical Frequency increases from one side reaches its highest and decreases exactly the way it had increased . Total area of the curve is one, its mean is zero and standard deviation is one . The highest point denotes mean, median and mode which coincide.

16. DISTRIBUTION CENTRAL TENDENCY NORMAL/GAUSSIAN MEAN = MEDIAN = MODE RIGHT/POSITIVE SKEWED MEAN > MEDIAN >MODE LEFT/ NEGATIVE SKEWED MEAN < MEDIAN < MODE

17. Test of significance •. Why it is done? -To assist administrations and clinicians in making decision. • The difference is real ? • Has it happen by chance ?

18. Classification of tests of significance The test which is done for testing the research hypothesis against the null hypothesis For Qualitative data:- 1. Standard error of difference between 2 proportions (SEp1-p2) 2. Chi-square test or X2 For Quantitative data:- 1. Unpaired (student) ‘t’ test 2. Paired ‘t’ test 3. ANOVA 4. z test

19. When different samples are drawn from the same population, the estimates might differ - sampling variability. It deals with technique to know how far the difference between the estimates of different samples is due to sampling variation. Standard error of mean Standard error of proportion Standard error of difference between two means Standard error of difference between two proportion . Tests of significance

20. 1. Standard error of mean: Gives the standard deviation of the means of several samples from the same population. Example : Let us suppose, we obtained a random sample of 25 males, age 20-24 years whose mean temperature was 98.14 deg. F with a standard deviation of 0.6. What can we say of the true mean of the universe from which the sample was drawn?

21. Standard Error of Proportion Standard error of proportion may be defined as a unit that measures variation which occurs by chance in the proportions of a character from sample to sample or from sample to population or vice versa in a qualitative data .

22. Standard Error of Difference Between two Means The standard error of difference between the two means is 7 .5. The actual difference between the two means is (370 - 318) 52, which is more than twice the standard error of difference between the two means, and therefore "significant".

23. Standard Error of Difference Between Proportions The standard error of difference is 6 whereas the observed difference (24.4 - 16.2) was 8.2. In other words the observed difference between the two groups is less than twice the S.E. of difference, i.e., 2 x 6. There was no strong evidence of any difference between the efficacy of the two vaccines . Therefore, the observed difference might be easily due to chance.

24. Developed by Karl Pearson. Chi-square (x²) Test offers an alternate method of testing the significance of difference between two proportions . It has the advantage that it can also be used when more than two groups are to be compared . It is most commonly used when data are in frequencies such as in the number of responses in two or more categories . Prerequisites for Chi square (X2) test to be applied: – The sample must be a random sample – None of the observed values must be zero. – Adequate cell size The CHI SQUARE TEST FOR QUALITATIVE DATA (X² TEST)

25. STEPS Test the null hypothesis . Then the x 2 . Applying x 2 test . Finding the degree of freedom ( d.f ) Finding probability .

26. Steps in Calculating (X 2 ) value Make a contingency table mentioning the frequencies in all cells . 2. Determine the expected value (E) in each cell. 3. Calculate the difference between observed and expected values in each cell (O-E ). 4. Calculate X 2 value for each cell 5. Sum up X 2 value of each cell to get X 2 value of the table.

27. Z -T E S T Used to test the significance of difference in means for large samples. Criteria: Sample must be randomly selected. Data must be quantitative. The variable is assumed to follow a normal distribution in the population. Samples should be larger than 30.

28. ‘t’ test Very common test used in biomedical research. Applied to test the significance of difference between two means . It has the advantage that it can be used for small samples. Types of ‘t’ tests — Unpaired ‘t’ test — Paired ‘t’ test. In case of small samples, t-test is applied instead of Z-test . It was designed by W.S.Gossett whose pen name was Student. Hence, this test is also called Student’s t-test. t’ Test

29. Criteria for applying t-test 1 . Random samples 2. Quantitative data 3. Variable normally distributed 4. Sample size less than 30.

30. This test is applied to unpaired data of independent observations made on individuals of two different or separate groups or samples drawn from two populations , to test if the difference between the two means is real or it can be attributed to sampling variability . EXAMPLE: between means of the control and experimental groups. Unpaired t test Where S is Standard error of difference between two means

31. It is applied to paired data of dependent observation from one sample only when each individual given a pair of observations. The individual gives a pair of observation i.e. observation before and after taking a drug . Paired t test

32. Analysis of Variance (ANOVA) Test Not confined to comparing two sample means , but more than two samples drawn from corresponding normal populations. Eg. In experimental situations where several different treatments (various therapeutic approaches to a specific problem or various drug levels of a particular drug) are under comparison. It is the best way to test the equality of three or more means of more than two groups .

33. Requirements Data for each group are assumed to be independent and normally distributed Sampling should be at random One way ANOVA Where only one factor will effect the result between 2 groups Two way ANOVA Where we have 2 factors that affect the result or outcome Multi way ANOVA Three or more factors affect the result or outcomes between groups .

34. CORRELATION AND REGRESSION Correlation : When dealing with measurement on 2 sets of variable in a same person, one variable may be related to the other in same way. (i.e change in one variable may result in change in the value of other variable .) Correlation is the relationship between two sets of variable . Correlation coefficient is the magnitude or degree of relationship between 2 variables. ( varies from -1 to +1 ).

35. Obtained by plotting scatter diagram ( i.e one variable on x-axis and other on y-axis). Perfect Positive Correlation In this, the two variables denoted by letter X and Y are directly proportional and fully correlated with each other. The correlation coefficent ( r) = + 1, i.e. both variables rise or fall in the same proportion. Perfect Negative Correlation Values are inversely proportional to each other, i.e. when one rises, the other falls in the same proportion, i.e. the correlation coefficient ( r) = –1.

36. TYPES OF CORRELATION

37. R eg r essi o n To know in an individual case the value of one variable, knowing the value of the other, we calculate what is known as the regression coefficient of one measurement to the other. It is customary to denote the independent variate by x and the dependent variate by y. The value of b is called the regression coefficient of y upon x. Similarly, we can obtain the regression of x upon y.

38. 1. Categorical Vs Categorical Unrelated Related Chi square test McNemar test Fishers Exact test X=2 group, Y=2group X>2, Y>2 group Unrelated - Chi square test Fishers Exact test X :Group variable Y :Outcome variable

39. 2. Categorical Vs Quantitative X=2 & Y: Normal Unrelated Related Student’s t test Paired ‘t’ test X=2 group & Y: Non Normal Unrelated Related Wilcoxon ranksum Wilcoxon signrank X>2 group & Y: Non-Normal X> 2group & Y: Normal Unrelated Related One way Repeated ANOVA measures ANOVA Unrelated Related Kruskal Wallis Freidmans test Parametric Non-Parametric

40. Conclusion 1.For generation of evidence , we do studies taking sample from population. 2.We apply different statistical tests on selected sample to detect whether there is actual difference is there or not between new and old method. 3.Based on result of sample we apply findings of study on population for betterment. 4.So for drawing correct conclusion and extra polting findings of study on population we must understand which statistical test to use on which type of data.