Lernzettel: Biostatistics for Biological Data Analysis

Biological Data & Statistical Principles Revision Sheet

1. 📌 Essentials

• Statistics: Science of analyzing numerical data to infer biological phenomena.
• Biostatistics: Application of statistical methods to biological and medical data.
• Population: Entire set of units; Sample: Subset used for inference.
• Variables: Qualitative (nominal, ordinal); Quantitative (discrete, continuous).
• Data Organization: Data matrices, classification, frequency distributions.
• Descriptive Stats: Mean, median, mode (central tendency); variance, SD, IQR (dispersion).
• Probability: Likelihood of an event; values between 0 and 1.
• Normal Distribution: Symmetric bell curve; 68-95-99.7 rule.
• Correlation (r): Measures linear association; ranges from -1 to +1.
• Regression: Predicts one variable from another; Y = a + bX.
• Hypothesis Testing: Null vs. alternative; p-value indicates significance.
• Outliers & Skewness: Outliers are points outside 1.5×IQR; skewness indicates asymmetry.
• Causality: Requires cause-effect relationship, not just correlation.

2. 🧩 Key Structures & Components

• Population — Entire set of units under study.
• Sample — Subset drawn for analysis.
• Variables — Characteristics measured:
  • Qualitative: Nominal (categories), Ordinal (ordered).
  • Quantitative: Discrete (counts), Continuous (measurements).
• Data matrix — Organized data in rows (units) and columns (variables).
• Frequency distribution — Counts or proportions of variable values.
• Probability — P(event) = number of favorable outcomes / total outcomes.
• Normal distribution — Bell-shaped, symmetric curve.
• Pearson’s r — Measures linear correlation.
• Regression line — Y = a + bX, models relationship.
• Hypothesis testing framework — Null hypothesis (H0), alternative (HA).

3. 🔬 Functions, Mechanisms & Relationships

• Data collection → Population or sample.
• Variables are measured and organized into data matrices.
• Descriptive statistics summarize central tendency and variability.
• Probability quantifies likelihood of events, guiding inference.
• Normal distribution models many biological variables; 68-95-99.7 rule describes data spread.
• Correlation (r) indicates strength/direction of linear association.
• Regression predicts dependent variable (Y) from independent variable (X).
• Hypothesis testing assesses if observed data significantly differ from null expectations.
• Outliers/skewness influence data interpretation; must be identified and considered.
• Causality involves establishing cause-effect, not just association.

4. 📊 Comparative Table

Item	Key Features	Notes / Differences
Population	Entire set of units; basis for data collection	Census vs. sample
Sample	Subset for inference; should be representative	Randomization improves validity
Qualitative Variables	Nominal: categories; Ordinal: ordered categories	No numeric meaning
Quantitative Variables	Discrete: countable; Continuous: measurable quantities	e.g., number of cells vs. weight
Distribution Shape	Symmetric (normal) vs. skewed (positive/negative skew)	Affects analysis and modeling

5. 🗂️ Hierarchical Diagram

Statistics
 ├─ Data Collection
 │   ├─ Population
 │   └─ Sample
 ├─ Variables
 │   ├─ Qualitative
 │   │    ├─ Nominal
 │   │    └─ Ordinal
 │   └─ Quantitative
 │        ├─ Discrete
 │        └─ Continuous
 ├─ Data Organization
 │   └─ Frequency tables
 ├─ Data Visualization
 │   ├─ Bar, Pie, Histogram, Scatter, Boxplot
 ├─ Descriptive Statistics
 │   ├─ Central: Mean, Median, Mode
 │   └─ Dispersion: Range, Variance, SD, IQR
 ├─ Probability
 │   ├─ Event, P(event)
 │   └─ Venn diagrams, independence
 ├─ Correlation
 │   └─ Pearson’s r
 ├─ Regression
 │   └─ Y = a + bX
 ├─ Hypothesis Testing
 │   ├─ Null (H0), Alternative (HA)
 │   └─ p-value, significance level
 └─ Distribution
     ├─ Normal (Gaussian)
     └─ Parameters: μ, σ, IQR

6. ⚠️ High-Yield Pitfalls & Confusions

• Confusing correlation with causation; correlation does not imply causality.
• Overlooking outliers, which can distort mean and SD.
• Misinterpreting skewness as data symmetry.
• Assuming normality without verification; many biological data are skewed.
• Using parametric tests on non-normal data.
• Ignoring confounders in causal inference.
• Misapplying p-value thresholds; significance does not imply practical importance.
• Over-reliance on mean in skewed distributions; median may be better.
• Neglecting to check for independence in statistical tests.

7. ✅ Final Exam Checklist

• Understand the difference between population and sample.
• Identify and classify variables (qualitative vs. quantitative).
• Organize data into frequency tables and visualizations.
• Calculate and interpret measures of central tendency and dispersion.
• Recognize the properties of the normal distribution.
• Compute and interpret Pearson’s correlation coefficient.
• Develop regression equations and interpret slope/intercept.
• Formulate null and alternative hypotheses.
• Calculate p-values and determine significance.
• Detect outliers and assess skewness.
• Understand the concepts of dependence, causality, and confounding.
• Know the parameters of distributions: μ, σ, IQR.
• Recognize the importance of data distribution shape in analysis.
• Avoid common pitfalls: mistaking correlation for causation, ignoring outliers, assuming normality without verification.

End of Revision Sheet