JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD Pharm. D IV Year BIOSTATISTICS AND RESEARCH METHODOLOGY Previous Question Paper (June/July - 2022 - R08)

Determining the sample size for simple comparative experiments involving normally distributed variables is essential to ensure sufficient statistical power to detect a meaningful difference between two groups. The calculation depends on the desired significance level, the power of the test, the expected effect size, and the population variance.

For a comparison between two independent groups with equal sample sizes (n) and known or estimated common standard deviation (σ), the formula for a two-sided test is:

Where the variables are defined as follows:

• Z_α/2: The critical value from the standard normal distribution corresponding to the significance level (α). For a 5% significance level, Z_0.025 is 1.96.
• Z_β: The critical value corresponding to the desired power (1-β). For 80% power, Z_0.20 is 0.84.
• σ: The estimated population standard deviation, often derived from pilot studies or previous literature.
• δ (delta): The minimum clinically or scientifically significant difference between the two group means that the researcher wishes to detect.

The steps to determine the sample size are:

1. Define the null hypothesis (no difference) and the alternative hypothesis (a difference of magnitude δ exists).
2. Select the significance level (α), typically 0.05, to control Type I error.
3. Select the power (1-β), typically 0.80 or 0.90, to control Type II error.
4. Estimate the population variance (σ²) based on prior data.
5. Calculate the required sample size per group using the formula. If the result is not an integer, always round up to the nearest whole number to maintain the required power.

If the population variance is unknown, the t-distribution is used instead of the normal distribution, which requires an iterative process as the degrees of freedom depend on the sample size itself. In such cases, software or statistical tables are typically employed to solve for n.

A scientific research report is a formal document that communicates the findings of an investigation to the scientific community. It follows a structured format to ensure clarity, reproducibility, and logical flow.

The standard structure of a research report includes:

1. Title: A concise, descriptive statement of the research topic.
2. Abstract: A brief summary (usually 150-250 words) covering the objective, methods, key results, and conclusion.
3. Introduction: Background information, literature review, statement of the problem, and research objectives or hypotheses.
4. Materials and Methods: A detailed description of the study design, population, sampling techniques, data collection tools, and statistical methods used.
5. Results: Presentation of data findings using text, tables, and graphs without interpretation.
6. Discussion: Interpretation of the results, comparison with previous studies, implications, limitations, and suggestions for future research.
7. Conclusion: A summary of the main findings and their significance.
8. References: A list of all cited sources in a standardized format (e.g., Vancouver or APA).

Data presentation is the process of organizing data to make it understandable and meaningful. The primary methods include:

1. Textual Presentation: Using paragraphs to describe data, suitable for small datasets or to highlight specific trends.
2. Tabular Presentation: Organizing data into rows and columns. Tables allow for precise reference and comparison of multiple variables.
3. Graphical/Diagrammatic Presentation: Visual representation which is more effective for identifying patterns and trends. Common types include:
   • Bar Charts: For comparing categorical data.
   • Histograms: For displaying frequency distributions of continuous variables.
   • Pie Charts: To show the proportion of parts in a whole.
   • Line Graphs: To show changes over time or continuous trends.
   • Scatter Plots: To visualize the relationship between two numerical variables.