Expt 15_biostatistics, expermiental colo edited.pptx

lab work

1. Bios tatistical Methods in Experimental Pharmacology

2. Aim: Biostatistical Methods in Experimental Pharmacology Statistics may be defined as the method concerned with handling of numerical data derived from group of individuals. Biostatistics is a branch of statistics employed to biological or medical sciences. Biostatistics methods are crucial for designing studies, analyzing data, and drawing valid conclusions about drug efficacy and safety, ensuring rigorous research and preventing fraudulent practices. 

3. Importance of Biostatistics in Experimental Pharmacology: Ensuring Rigor and Validity: Biostatistics helps ensure that studies are designed and analyzed properly, leading to more reliable and valid conclusions.  Preventing Fraud: Rigorous statistical analysis can help detect and prevent fraudulent practices in research.  Informing Clinical Decisions: The findings of well-designed and analyzed studies can inform clinical decisions about the use of new drugs and treatments

4. In statistics, data refers to the collected values of variables for a set of individuals, objects, or events. Simply put: A variable is what you're measuring. Data is what you get when you actually measure it. Example: If your variable is "height" (in cm), then the data might be: 160 cm, 172 cm, 168 cm, 155 cm If your variable is "blood type" , then the data might be: A, O, B, AB, O Types of Data: Quantitative Data – Numbers representing counts or measurements. Example: Age = 22, 25, 30 Qualitative Data – Labels or categories. Example: Gender = Male, Female So in summary: Variable = the characteristic you're studying Data = the actual recorded values for that variable

5. Types of DATA

6. Nominal Data It  is a type of data that consists of categories or names that cannot be ordered or ranked. Nominal data is often used to categorize observations into groups, and the groups are not comparable. In other words, nominal data has no inherent order or ranking. Examples of nominal data include: Gender (Male or female), Race (White, Black, Asian), Religion (Hinuduism, Christianity, Islam, Judaism), Blood type (A, B, AB, O), etc. Qualitative Data It tells the features of the data in the statistics.

7. Ordinal Data It  is a type of data that consists of categories that can be ordered or ranked. However, the distance between categories is not necessarily equal. Ordinal data is often used to measure subjective attributes or opinions, where there is a natural order to the responses. Examples of ordinal data include: Education level (Elementary, Middle, High School, College), Job position (Manager, Supervisor, Employee), etc.

8. Quantitative Data (Numerical Data) It is the type of data that represents the numerical value of the data. Discrete Data Discrete data type is a type of data in statistics that only uses Discrete Values or Single Values. These data types have values that can be easily counted as whole numbers. Examples of the discrete data types are, Height of Students in a class Marks of the students in a class test Weight of different members of a family, etc.

9. Continuous Data Continuous data is the type of quantitative data that represents the data in a continuous range. The variable in the data set can have any value within the range of the data set. Examples of the continuous data types are, Temperature Range Salary range of Workers in a Factory, etc.

10. A variable is a symbol and placeholder for (historically) a quantity that may change, or (nowadays) any mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

11. In statistics, a variable is any characteristic, number, or quantity that can be measured or counted and can vary from one individual or observation to another. Types of Variables: Quantitative (Numerical) Variables Represent numerical values . Examples: Age, height, weight, blood pressure. Subtypes: Discrete : Countable values (e.g., number of students). Continuous : Measurable on a scale (e.g., temperature, income). Qualitative (Categorical) Variables Represent categories or labels . Examples: Gender, blood type, eye color. Subtypes: Nominal : No natural order (e.g., marital status). Ordinal : Ordered categories (e.g., education level: high school < college < postgraduate). Summary: A variable is something you're collecting data on that can change between different observations. It's the basic building block of any statistical analysis.

12. Descriptive statistics  uses data that provides a description of the population either through numerical calculated graphs or tables. It provides a graphical summary of data. It is simply used for summarizing objects, etc. There are two categories in this as follows. Measure of Central Tendency Measure of Variability

13. Measure of central tendency   is also known as summary statistics   that are used to represent the center point or a particular value of a data set or sample set. In statistics, there are three common measures of central tendency that are: Mean Median Mode

14. Median: The middle value of a data set when it is arranged in ascending or descending order. If there’s an odd number of observations, it’s the value at the center position. If there’s an even number, it’s the average of the two middle values. Example: Data set {3, 6, 9, 12, 15}.  Mode: The value that occurs most frequently in a data set. There can be one mode  (unimodal),  multiple modes  (multimodal),  or no mode if all values occur with the same frequency. Example: Data set {2, 3, 4, 4, 5, 6, 6, 6, 7}. Mode = 6 Median = 9 Example: Consider the data set {2, 4, 6, 8, 10}. (2+4+6+8+10/ 5) = (30/5) Mean = 6 Mean: The arithmetic average of a set of values. It’s calculated by adding up all the values in the data set and dividing by the number of values.

15. Measure of Variability The measure of Variability is also known as the  measure of dispersion  and is used to describe variability in a sample or population.  Range of Data It is a given measure of how to spread apart values in a sample set or data set. Range = Maximum value – Minimum value Variance In probability theory and statistics, variance measures a data set’s spread or dispersion. It is calculated by averaging the squared deviations from the mean.

16. Standard Deviation Standard Deviation is a measure of how widely distributed a set of values are from the mean. It compares every data point to the average of all the data points. A low  Standard Deviation  means values are close to the average, while a high standard deviation means values spread out over a wider range. Standard deviation is like the distance between points but is applied differently.

17. Inferential Statistics Inferential Statistics makes inferences and predictions about the population based on a sample of data taken from the population. It generalizes a large dataset and applies probabilities to draw a conclusion. It is simply used for explaining the meaning of descriptive stats. It is simply used to analyze, interpret results, and draw conclusions. Inferential Statistics is mainly related to and associated with hypothesis testing whose main target is to reject the null hypothesis.

18. Hypothesis testing  is a type of inferential procedure that uses sample data to evaluate and assess the credibility of a hypothesis about a population. Inferential statistics are generally used to determine how strong a relationship is within the sample. However, obtaining a population list and drawing a random sample is very difficult. 

19. Correlation Coefficient A correlation coefficient is a numerical estimate of the statistical connection that exists between two variables. The variables could be two columns from a data set or two elements of a multivariate random variable. The Pearson  correlation  coefficient (r) measures linear correlation, ranging from -1 to 1. It shows the strength and direction of the relationship between two variables. A coefficient of 0 means no linear relationship, while -1 or +1 indicates a perfect linear relationship. Coefficient of Variation The  Coefficient of Variation  (CV) is a statistical measure of the relative variability of data. It represents the ratio of the standard deviation to the mean and is often expressed as a percentage.

20. Models of Statistics Various models of Statistics are used to measure different forms of data. Some of the models of the statistics are added below: Skewness in Statistics ANOVA Statistics Degree of Freedom Regression Analysis Mean Deviation for Ungrouped Data Mean Deviation for Discrete Grouped data Exploratory Data Analysis Causal Analysis Associational Statistical Analysis

21. ANOVA Statistics ANOVA statistics is another name for the Analysis of Variance in statistics. In the ANOVA model, we use the difference of the mean of the data set from the individual data set to measure the dispersion of the data set. Analysis of Variance (ANOVA) is a set of statistical tools created by Ronald Fisher to compare means. It helps analyze differences among group averages.  ANOVA  looks at two kinds of variation: the differences between group averages and the differences within each group. The test tells us if there are disparities among the levels of the independent variable, though it doesn’t pinpoint which differences matter the most.

22. Associational Statistical Analysis Associational statistical analysis is a method that researchers use to identify correlations between many variables. It can also be used to examine whether researchers can draw conclusions and make predictions about one data set based on the features of another. Associational analysis examines how two or more features are related while considering other possibly influencing factors.

23. Methods of statistical analysis: The methods of statistical analysis will depend on the purpose of the study, the design of the experiment, and the nature of the resulting data. Parametric statistical analysis Non- parametric tests Test of significance: Parametric tests : Student’s t-test, Chi square test, Analysis of variance. 2. Non parametric test : Kruskal – wallis H-test, ii) Wilcoxon’s signed rank test

24. Parametric Test A parametric test makes assumptions about the parameters (like mean and standard deviation) and the distribution of the data—usually that it follows a normal distribution . ✅ Assumptions: Data is normally distributed Sample size is sufficiently large Data is measured on an interval or ratio scale Homogeneity of variances (equal variances between groups 📌 Examples: t-test (e.g., comparing means of two groups) ANOVA (Analysis of Variance) Pearson correlation Linear regression ✅ Use when: Your data is numerical and normally distributed You want more powerful and precise results (if assumptions are met) 🔹 Non-Parametric Test A non-parametric test does not assume a specific distribution for the data. It’s used when parametric test assumptions aren’t met . ✅ Features: No need for normal distribution Can be used with ordinal data or non-normal numerical data Often based on ranks rather than actual values 📌 Examples: Mann–Whitney U test (instead of t-test) Kruskal–Wallis test (instead of ANOVA) Wilcoxon signed-rank test Spearman’s rank correlation Chi-square test ✅ Use when: Data is skewed , ordinal , or sample size is small You’re unsure whether the data meets parametric assumptions

25. The Chi-square test of independence , also known as the Chi-square test of association, is a statistical method used to determine whether there is a relationship between two categorical variables. It does not measure the strength of the association but rather assesses whether the relationship is statistically significant. This test works by comparing the observed data (what we actually see) with the expected data (what we would expect if there were no relationship between the variables). If the difference between these values is large enough, it suggests that the variables are related. For example, we can use a Chi-square test to examine whether gender influences the type of product a person buys. If the p-value from the test is greater than 0.02, it indicates that there is no statistically significant relationship between gender and product choice, meaning any observed differences are likely due to chance. If the p-value is less than 0.02, it indicates that there is a statistically significant relationship between the two categorical variables. In other words, the difference between the observed and expected data is unlikely to be due to random chance. For example, if we test whether gender influences the type of product purchased and get a p-value below 0.02, it suggests that gender and product choice are related in a meaningful way. This means that gender may play a role in determining what type of product a person is more likely to buy.

26. explanation: Typically, significance levels are set at 0.05 (5%) , 0.01 (1%) , or 0.10 (10%) , depending on the level of confidence desired. Here’s why 0.02 might be used: Stricter than 0.05 – A 0.02 threshold reduces the chances of a Type I error (false positive), meaning we are more cautious before concluding that the variables are related. Less strict than 0.01 – A 0.02 level still allows for some flexibility, unlike the 0.01 level , which is more conservative and often used in highly rigorous studies. Context-dependent – In some research areas, 0.02 might be chosen based on prior studies or industry standards. In short, if the p-value is less than 0.02 , we reject the null hypothesis (no relationship) and conclude that there is a statistically significant association. If it is greater than 0.02 , we fail to reject the null hypothesis, meaning there's not enough evidence to say the variables are related. The level of confidence refers to how sure we are that our statistical results are accurate and not due to random chance. It is expressed as a percentage and is directly related to the significance level (α) in hypothesis testing. How It Works: The confidence level and the significance level (α) are complementary: Confidence Level=1−α For example: If α = 0.05 (5%), the confidence level is 95% . If α = 0.02 (2%), the confidence level is 98% . A 95% confidence level means that if we repeated the experiment multiple times, we would expect the results to be correct 95 out of 100 times . The remaining 5% represents the risk of making a Type I error (rejecting a true null hypothesis).

27. The Student's t-test is a statistical test used to compare the means of two groups and determine whether the difference between them is statistically significant . 🎓 Why is it called "Student's" t-test? It was developed by William Sealy Gosset , who wrote under the pen name "Student" while working for Guinness Brewery 🍺. They used it to test beer quality with small sample sizes! 🧪 When do you use a t-test? When you're comparing two groups When the data is numerical and (ideally) normally distributed When sample sizes are relatively small (but can be used for large samples too)

28. Use of t-test In medical research , t-test is among the three or four most commonly use statistical tests. The purpose of a t-test is to compare the means of a continous variable in two research samples in orders to determine whether or not the difference betweenthe two observed means exceeds the difference that would be expected by chance from random samples. Some important terms used in t-test – Degree of freedom The t-distrbution The term degree of freedom refers to the number of observations that are free to vary. The degrees of freedom for any tests are considered to be the total sample size minus 1 degree of freedom for each mean that is calculated.

29. Application of biostatistics in pharmacology and medicine: To find the action of drug – when drug is given to the animal or human beings to see the changes produced due to drug or by chance. ii) Biostatics in pharmacology used to compare the action of two drugs or two consecutive dosages of the same drug. iii) It is used to find the potency of a new drug with a standard drug. iv) To compare the efficacy of a particular drug, operation, or line of treatment v) It is used to find a relationship between two characteristics such as cancer and smoking. vi) To identify signs and symptoms of a disease or syndrome. vii) It is use to trial on sera and vaccines in the field – ratio of assault or death between the vaccinated subjects is compared between the unvaccinated subjects to find out observed difference is statistically significant. viii) In epidemiological studies the role of causative elements is statistically tested.

30. ix) In clinical medicine biostatistics use for documentation of medical history of diseases. design and control clinical studies. Evaluating the quality of different procedures. x) In preventive medicine it is use to provide the dimensions of any health problem in the community. It is use to discover basic factors underlying the ill-health. To asses the health programs which was introduced in the community. To introduce and promote health legislation. xi) It is helpful in pharmaceutical industry to overcome matters related to the medicines, issues of designing experiments, to analysis of drug trials, issues related to the commercialization of medicines. xii) It is use to asses the activity of drug. To find out analysis and the interpretation of results. Recognize risk factors for diseases. Design, monitor, analyze, interpret and report the results of clinical studies. xiii) Identify and expand treatments for diseases and approximate their effects.

31. The marks obtained by 30 students in a math test are as follows: Marks: 45, 50, 50, 55, 55, 55, 55, 60, 60, 60, 62, 65, 65, 65, 68, 70, 70, 72, 75, 75, 75, 78, 80, 80, 85, 85, 85, 85, 85, 90 a) Find the Mode of the data. b) Calculate the Variance of the data. Question

32. The mode is the value that occurs most frequently in the dataset. 45 → 1 time 50 → 2 times 55 → 4 times 60 → 3 times 62 → 1 time 65 → 3 times 68 → 1 time 70 → 2 times 72 → 1 time 75 → 3 times 78 → 1 time 80 → 2 times 85 → 5 times 90 → 1 time 85 occurs most frequently (5 times), the Mode = 85

33. Marks (Class Interval) Frequency (f) 40 – 50 5 50 – 60 8 60 – 70 12 70 – 80 20 80 – 90 10 90 – 100 5 Calculate the Mode from the grouped data:

34. Identify the Modal Class The Modal Class is the class interval with the highest frequency. From the table, the highest frequency is 20 in the class interval 70 – 80 . So, the Modal Class = 70 – 80 .

35. Where: L = Lower boundary of the modal class = 70 f1​ = Frequency of the modal class = 20 f0​ = Frequency of the class before the modal class = 12 f2​ = Frequency of the class after the modal class = 10 h = Class width = 10 (difference between upper and lower boundaries)

36. Population Variance (σ²) It measures the spread of data for the entire population. Use Population Variance when you have data for the entire group you’re studying. Sample Variance (s²) It estimates the spread of data for a sample taken from a population. Use Sample Variance when you’re working with a subset of data and want to generalize the results to the whole population