Parametric tests

Introduction of Biostatistics & Parametric tests

1. Dr. Yash N. Panchal Resident Doctor Pharmacology Department AMC MET Medical College Date: 24/12/2021 PARAMETRIC TESTS

2. PRESENTATION LAYOUT Introduction of Biostatistics Types of Data Measures of Central tendency Parametric tests Z test t test

3. WHAT IS BIOSTATISTICS ? It is the term used when tools of statistics (means measured or counted fact) are applied to the data that is derived from biological science such as medicine Statistics = Datum = measured or Counted fact

4. Use of Biostatistics in Pharmacology After administration of any drug to human or animals in research, to find whether effect is due to drug or by chance ? To compare actions of 2 different drugs To find relative potency of new drug with respect to old standard drug

5. COMMON STATISTICAL TERMS

6. Types of data

7. Primary & Secondary Data Primary data – Individual researcher or research agency collect data by themselves. E.g – Experiment, Survey Secondary data – Individual researcher or research agency uses data that is already available E.g – Past records

8. Data Compilation & Presentation Raw data need to be compiled to make it more understandable one. This is done by Master chart Parameters entered in Column heading and Finding in raw After compilation, it need to be presented by various methods like 1- Tabulation 2- Graphs - For quantitative data – Histogram, Frequency Polygon, Scatter diagram, Line chart - For qualitative data – Bar diagram, Pie diagram, Pictogram

9. Measures of Central tendency In statistics, a central tendency is a central value that represents entire data set, and around it all other values gather It is called as an average or the center of the distribution Most common measures of central tendency are : 1- Arithmetic Mean 2- Median 3- Mode

10. Cont.… Importance of Central tendency: 1 - To find representative value 2 – To make more concise data 3 – To make comparisons 4 – Helpful in further statistical analysis

11. Mean The mean of set of values is the sum of the all measurements divided by the number of measurements Is most popular and widely used central tendency Overall most reliable central tendency is Mean , as it takes all the observations into consideration In Skewed data , the central tendency used is Median

12. Contd..

13. Mean for Grouped data

14. Median Is middle value of the sample when data is arranged in the ascending or descending order Median= [(n + 1) / 2] th  value where, n = number of odd observations

15. Median Contd.. For even number of distribution : Median is used as central tendency value for : 1 - Skewed data 2 - Ordinal qualitative data

16. Mode Is the value, which occurs most frequently in a set of measurements Is commonly used central tendency for Nominal qualitative data

17. Normal Distribution and Curve The commonest and most useful continuous distribution It is distribution where most results are located in the middle and few are spread on both sides It has the shape of bell Can entirely be described by its mean and standard deviation

18. Normal Distribution and Curve

19. Normal Distribution Characteristics Represents features of distribution of observations around the mean value Also known as Gaussian distribution/ Standard distribution As most values are clustered around central value, hence termed as normal distribution

20. Contd.. Has shape of bell , it is bilaterally symmetrical , if we draw perpendicular line from apex, curve is divided into 2 symmetrical halves Point of Coincide is where Mean = Median = Mode AUC is 100 % Mean ± 1 SD Cover 68.26% values Mean ± 2 SD Cover 95.4% values Mean ± 3 SD Cover 99.7% values

21. Statistical Tests Statistical tests are intended to decide whether a hypothesis about distribution of one or more populations or samples should be rejected or accepted

22. Hypothesis Hypo = Hypothetical ; sis = statement = just assuming the thing = statement yet to be verified. Is described in the terms of specific cause , specific outcome , time , place and person Example of complete hypothesis – Smoking of 30-40 cigarette daily for 20 years can cause lung cancer in 10% population Given by – Observational study Tested by – Analytical study Confirmed by – Experimental study

23. Ha & H0 Null Hypothesis - It states that there is no association between exposure and outcome Represented by H0 Alternative Hypothesis – A statement that directly contradicts the null hypothesis Represented by Ha

24. Parametric tests This are statistical test that make assumptions about the parameters of the population distribution(s) from which one’s data is drown It is based on the Parameters ( Mean, Median, Standard deviation, Standard error)

25. Parametric tests Characteristics Always applied in normally distributed data (Bell shaped curve) Scale – when data is in interval or ratio (Non-parametric – Nominal or Ordinal ) Used for Quantitative and qualitative data Measure of central tendency – Mean Information about population - Known

26. Tests of Statistical Significance Is a formal procedure for comparing observed data with a claim (Hypothesis) Helps researcher to confirm the Hypothesis Before initiation of any research study : Framing of research question Hypothesis is generated

27. Contd.. Results are obtained and compared with base to check significance E.g – If researcher want to compare heights of boys and girls H0 = Heights of boy and Ha = The heights of boys is higher girls are similar and Than girls, and so observed any difference difference in heights is real observed is by chance

28. Z test Z test is used for dealing with issues relating to large samples when the frequency is greater than or equal to 30 It is used when population standard deviation is known Assumptions : Population is normally distributed : The sample is drawn at random Conditions : Population standard deviation, Mean (Parameter) is known : Size of sample is large

29. Contd… Z test For Qualitative data For quantitative data 1 - Z test for single proportion 1- Z test for single mean 2 - Z test for difference 2- Z test for difference in mean in proportion

30. Z test For Single Proportion To find significant difference between sample proportion and population proportion and to check whether sample is representative or not

31. Contd… H0 = Population proportion P is equal to Sample proportion Po (P=Po) Ha : Two tailed : P ≠ Po : Left tailed : P < Po : Right tailed : P > P0

32. Example A survey claimed that 9 out of 10 doctors recommend Aspirin for their patients with headaches. To test this claim, a random sample of 100 doctors is obtained. Of these 100 doctors, 82 indicate that they recommend aspirin. Is this claim accurate ? Use alfa = 0.05

33. Z table

34. Contd.. If Zc > Zt, then H0 = null hypothesis is rejected = there is difference in proportion between population data and sample data If Zt > Zc, then Null hypothesis accepted There is no difference between sample proportion and population proportion at 5% level of α

35. Z test – Difference between two proportion

36. Z test – Difference between two proportion Suppose we want to know if there is difference in the proportion of residents who supports a certain law in country A compared to the proportion who support the law in country B. To test, perform a two proportion z test at significance level 0f 0.05

37. Z test – Difference between two proportion 1 – The collected data: Sample 1 – Sample size n1 = 50 Proportion in favor of law P1 = 0.67 Sample 2 – Sample size n2 = 50 Proportion in favor of law P2 = 0.57 2- Define the Hypothesis ; H0: P1 = P2 Ha: P1 ≠ P2

38. P value for Z score

39. Z test For Significance of Mean

40. Z test For Significance of Mean Are the IQ scores of students at one school of the Ahmedabad above the national average ? Scores of national IQ test are normed to have a mean of 100 and standard deviation of 15. in simple random sample of 25 students of one of the school of Ahmedabad the mean IQ was 110. Use default Confidence interval of 95

41. Z test For Difference between two mean

42. t test

43. Student’s t test Developed by the W.S Gosset in 1908 and he had to use a pen name “ STUDENT ’’ because of his employer’s policy in publishing research results at that time It compares the difference between means of different groups to determine whether the difference is statistically significant

44. One sample t test Assumption s : Population is normally distributed : Sample is drown from the population and it should be random : We should know the population mean Conditions : Size of the sample is small (< 30) : Population standard deviation is not known

45. Contd.. In one sample t-test, we know the population mean We draw a random sample from the population, measure the sample mean and compare sample mean with population mean and make a statistical decision as to whether or not the sample mean is different from the population

46. Contd..

47. Contd..

48. T table

49. Two sample t test Used when two independent random sample come from the normal population having unknown or same variance We test the null hypothesis that the two population means are same μ 1 = μ 2

50. Two sample t test

51. Paired t-test Used when measurements are taken from the same subject before and after some manipulation or treatment E.g- To determine the significance of difference in blood pressure before and after the administration of the experimental substance

52. Paired t-test Contd.. Assumptio ns : Population is normally distributed : Sample is drown from the population and it should be random Conditions : Sample are related with each other : Size of the sample are small and equal : Standard deviation in population are equal or not known

53. Paired t-test Contd..

54. Paired t-test Contd..

55. Paired t-test Contd..

56. ANOVA Is Analysis of variance It is collection of statistical models used to analyze the difference between GROUP means or variance Compares multiple groups at one time Was developed by R.A Fischer Also called ad F test

57. ANOVA Contd..

58. One Way ANOVA Compares two or more unmatched groups when data are categorized in one factor E.g – Comparing control group with three different doses of the aspirin - Comparing the productivity of three or more employee based on working hours in company

59. Two Way ANOVA Used to determine the effects of two nominal variables on a continuous outcome variable Analyzes the effect of independent variable on the expected outcome along with their relationship to the outcome itself E.g – Comparing the productivity of the employee based on the working hours and working conditions

60. REFERENCES Methods in Biostatistics: For Medical Students and Research Workers by B.K.Mahajan; Jaypee Brothers Medical Publishers Pvt. Limited, 01-Dec-2020. Fagerland, M.W., 2012. t-tests, non-parametric tests, and large studies—a paradox of statistical practice?.  BMC medical research methodology ,  12 (1), pp.1-7. Kitchen, C.M., 2009. Nonparametric vs parametric tests of location in biomedical research.  American journal of ophthalmology ,  147 (4), pp.571-572. Postgraduate Pharmacology 1 st Edition 2020 by Sougata Sarkar