Biostatistics

Definition: Biostatistics is a branch of statistics that applies statistical methods to biological sciences.

Importance: It is essential for designing biological experiments, clinical trials, and epidemiological studies. It ensures data collected is relevant and sufficient to answer research questions.

• Designing Experiments: Planning experiments (e.g., determining sample size) to detect significant effects.
• Analyzing Data: Applying techniques to uncover trends, correlations, and patterns (e.g., effect of light/water on plant growth).
• Interpreting Results: Making sense of data (e.g., disease prevalence surveys) to guide decisions.
• Predicting Outcomes: Creating models to forecast future events (e.g., spread of infectious diseases) for planning resources.
• Public Health: Providing evidence-based insights for policy making (e.g., vaccination campaigns).

• Epidemiology: Studying distribution and determinants of health/disease (e.g., COVID-19 infection rates).
• Genetics: Analyzing inheritance of traits and links between genetic variations and diseases (e.g., diabetes markers).
• Agriculture: Analyzing crop yields, fertilizer effectiveness, and pest resistance.
• Clinical Trials: Designing and analyzing trials to test new treatments/drugs (e.g., drug vs. placebo).

Definition: The mean (or average) is the sum of all values in a data set divided by the number of values. It represents the central value.

Formula: $$Mean = \frac{\text{Sum of all Data Points}}{\text{Number of Data Points}}$$

Example:
Data (Heights in cm): 150, 160, 165, 155, 170
Sum = 150 + 160 + 165 + 155 + 170 = 800
Number of values ($n$) = 5
Mean = 800 / 5 = 160 cm.

Definition: The middle value of a data set when arranged in ascending or descending order.

Calculation Rules:

• Odd Number of Values ($n$): Median is the value at position $\frac{n+1}{2}$.
  Example: Data: 150, 160, 165, 155, 170. Sorted: 150, 155, 160, 165, 170. Median = 160.
• Even Number of Values ($n$): Median is the average of the two middle values.
  Example: Data: 150, 160, 165, 155. Sorted: 150, 155, 160, 165. Median = $\frac{155+160}{2}$ = 157.5.

Definition: The value that appears most frequently in a data set. A set can have one mode, multiple modes, or no mode.

Examples:

• Unimodal: 150, 160, 165, 155, 160 -> Mode: 160 (occurs twice).
• Bimodal: 150, 160, 160, 155, 155 -> Modes: 160 and 155.
• No Mode: 150, 160, 165, 155, 170 -> All occur once.

Definition: A graphical representation using bars of different heights/lengths to compare quantities of different categories.

Steps to Create:

1. Gather and organize data into categories.
2. Draw X-axis (Categories) and Y-axis (Values).
3. Determine scale for Y-axis (based on max value).
4. Draw bars of equal width corresponding to values.
5. Label axes and bars.

Example:
Species A: 40, B: 60, C: 30, D: 75, E: 20.
Bar for D would be tallest (75), E shortest (20).