ANOVA AND F1,F2 SIMILARITY AND DISSIMILARITY FACTORS

The PowerPoint presentation titled "ANOVA, F1, and F2 Factors: Understanding Statistical Analysis in Research" delves into the fundamentals of ANOVA and its application in experimental design. It begins with an introduction to ANOVA, explaining its role in comparing means across multiple groups and distinguishing between variance within and between groups. The presentation elucidates the concept of factors in ANOVA, particularly focusing on F1 and F2 factors, which represent categorical variables influencing the outcome variable. Detailed explanations are provided on how these factors are defined, structured, and analyzed within the ANOVA framework, highlighting their significance in experimental control and interpretation of results. Practical examples and case studies illustrate how ANOVA is applied in various research settings, including clinical trials, social sciences, and industrial studies. The presentation also covers essential statistical assumptions, such as homogeneity of variances and normality, ensuring robustness in ANOVA outcomes. Lastly, the presentation discusses advanced topics like factorial ANOVA and interactions between F1 and F2 factors, offering insights into how these interactions affect experimental outcomes and the interpretation of statistical significance.

1. ANOVA AND SIMILARITY AND DISSIMILARITY FACTORS Presented By- Hatasha Vaddadi M.Pharm 1 st sem SoP , Parul University Guided By- Bhargavi Mistry Ass. Professor, Pharmaceutics SoP , Parul University

2. Contents Introduction to Anova Types of Anova Principle of Anova One way Anova Two way Anova Applications of anova Similarity and dissimilarty factors Summary References 27-12-2023 2

3. Introduction ANOVA stands for Analysis of varience . It is statistical tool used to observe the variability found inside a data set into 2 parts- one parametric variable and one or more independent variable . Discovered by Ronald fisher. 3 27-12-2023

4. How ANOVA work ? Like other types of statistical tests. ANOVA compares the means of different groups and shows you if there are any statistical differences between the means. ANOVA is classified as an omnibus test statistic. This means that it can't tell you which specific groups were statistically significantly different from each other, only that at least two of the groups were. 27-12-2023 4

5. It's important to remember that the main ANOVA research question is whether the sample means are from different populations. There are two assumptions upon which ANOVA rests: First: Whether the technique of data collection, the observations within each sampled population are normally distributed. Second: the sampled population has a common variance (s2). 27-12-2023 5

6. Principle Of ANOVA The basic principle of Analysis of Variance is to compare the variance within each group to the variance between groups. If the between-group variance is greater than the within-group variance, then there is a statistically significant difference between the means of the groups. 6 27-12-2023

7. 27-12-2023 7 Techniques of Anova One way anova Two way anova Eg Mean output of three workers Eg. Mean Based on working hours and working conditions

8. One Way ANOVA 27-12-2023 8 Simplest type of anova involving single source of variation or factor Techniques involves as follows- 1. Obtaining mean of each sample i.e. X 1 , X 2 ,X 3 ……… X k 2. Finding the mean of sample means X 1 + X 2 +X 3+ ………+ Xk No. of samples (k) X=

9. 27-12-2023 9 3. Calculate the sum of squares for varience between the samples, 5. Calculate the sum of squares for variance within the samples( or within): 4. Calculate mean square (MS) between : MS Between=SS between/(K-1)

10. 27-12-2023 10 6. Calculate mean square (MS) within: MS within=SS within/(n-k) 7. Calculate SS for total variance: SS for total variance= SS between+ SS within. The degrees of freedom for between and within must add up to the degrees of freedom for total variance i . e, (n-1)= (k-1)+(n-k)

11. 27-12-2023 11 8. Finally, f ratio may be worked out as under F ratio=MS between/ MS within This ratio is used to judge weather the difference among several sample means is significant or is just a matter of sampling flucatuations .

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13. Two Way ANOVA 27-12-2023 13 Two way ANOVA technique is used when the data are classified on the basis of two factors. A statistical test used to determine the effect of two nominal predictor variables on a continuous outcome variable. Two way ANOVA test analyzes the effect of the independent variables on the expected outcome along with their relationship to the outcome itself.

14. 27-12-2023 14 Two way ANOVA test analyzes the effect of the independent variables on the expected outcome along with their relationship to the outcome itself Two way ANOVA design may have repeated measurements of each factor or may not have repeated values.

15. Types Of Two Way ANOVA 27-12-2023 15 ANOVA technique in context of two way design when repeated values are not there - It includes calculation of residual or error variation by subtraction, once we have calculated the sun of squares for total variance between varieties of the other treatment. ANOVA technique in context of two way design when repeated values are there . – we can obtain a separate independent measure of inherent or smallest variations. -interaction variation: Interaction is the measure of inter relationship among the two different classifications .

16. 27-12-2023 16 Graphical method for studying interaction in two-way design. – For graphs we shall select one of the factors to be used as the x-axis. Then we plot the averages for all the samples on the graph and connect the averages for each variety of other factor by a distinct line. If the connecting lines do not cross over each other, then the graph indicates that there is no interaction. But if the lines do cross, they indicate definite interaction or inter-relation between the two factors.

17. 27-12-2023 17 This graph indicates that there is a significant interaction because the different connecting lines for groups of people do cross over each other. We find that A and B are affected very similarly,but C is affected differently.

18. Applications Of ANOVA Pharmaceutical Research 27-12-2023 18 Pharmacodynamics data analysing Evaluation of pharmacokinetic data In bio equivalence studies the similarities between the samples can be analysed Clinical trials Dissolution profiles study

19. Similarity And Dissimilarity Factors 27-12-2023 19 These equations described by Moore and Flanner Both equations are endorsed by the FDA as acceptable method for dissolution profile comparison. f1 Value - difference factor f2 Value - similarity factor They are used to studying the comparison of dissolution profiles of the two dosage forms. It can be calculated using Excel or various readymade software ( E.g - PhEq _ bootstrap)

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21. Difference Factor f1 27-12-2023 21 It calculated the percentage difference between two curves at each time point and measured relative error between two curves. f1 equation is the sum of absolute values of vertical distance between reference (Rt) and test (Tt) mean % release values i.e. (Rt-Tt) at each dissolution point. Where R1= reference dissolution value N= No. of dissolution time point Tt= test dissolution value

22. Similarity Factor f2. 27-12-2023 22 I ndicates the average percentage of similarity between two dissolution profiles. f2 equation is logarithmic transformation of average squared vertical distance between reference and test mean dissolution values at each time point, multiplied by an approximate weighing i.e Wt (Rt-Tt) . Where, R1- Reference dissolution value- No. of dissolution time point Tt- Test dissolution value Wt - Optimal weighting factor

23. Summary 27-12-2023 23 Analysis of variance, or ANOVA, is a statistical method that separates observed variance data into different components to use for additional tests. Dissolution studies can be done by both anova and f1 and f2 factor methods.

24. References 27-12-2023 24 Pictures - https://microbenotes.com/anova/ https://inspiredwebdev.com/create-dynamic-sticky-table-of-contents/ https://www.istockphoto.com/photos/table-of-contents-book https://reviewediting.wordpress.com/2012/07/12/table-of-contents-front-matter-vs-back-matter/ https://www.wallstreetprep.com/knowledge/conservatism-principle/ https://jhpolice.gov.in/road-safety/mandatory-road-signs https://www.computerhope.com/jargon/s/search.htm

25. Text content- St L, Wold S. Analysis of variance (ANOVA). Chemometrics and intelligent laboratory systems. 1989 Nov 1;6(4):25972. https://www.sciencedirect.com/science/article/abs/pii/0169743989800954 Tabachnick BG, Fidell LS. Experimental designs using ANOVA. Belmont, CA: Thomson/Brooks/Cole; 2007 Dec 6. https://www.researchgate.net/profile/Barbara-Tabachnick/publication/259465542_Experimental_Designs_Using_ANOVA/links/5e6bb05f92851c6ba70085db/Experimental-Designs-Using-ANOVA.pdf https://brill.com/display/book/9789463510868/BP000006.xml Ross A, Willson VL. One-way anova . InBasic and advanced statistical tests 2017 Jan 1 (pp. 21-24). Brill. 24-12-2023 25

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