Introduction to Biostatistics

High-yield biostatistics summary — MED101

Based on your lecture PDF: :codex-file-citation{path=“sandbox:/workspace/scratch/b22979b85533/upload/INTRODUCTION_TO_BIOSTATISTICS_MED101_26_27.pdf” purpose=“source”}

1. What is biostatistics?

The application of statistics to biological and medical data. It helps us summarize data, understand variation, quantify uncertainty, and make evidence-based decisions.

Patients respond differently to diseases and treatments; biostatistics helps us interpret these differences.

2. Essential definitions

Term

Meaning

Example

Population

Entire group we want to study

All adults with hypertension

Sample

Subset we actually measure

Hypertensive patients at one hospital

Variable

Characteristic measured in each individual

Age, blood pressure, smoking status

Parameter

Numerical characteristic of a population

True population mean BP: μ

Statistic

Numerical value calculated from a sample

Sample mean BP: x̄

Remember: a statistic estimates a parameter.

We sample because studying the whole population is often impractical. The sample should represent the population.

3. Types of data — especially testable

Type

Key feature

Examples

Qualitative/categorical

Describes categories

Blood group, smoking status

Nominal

Categories have no order

Blood group, diabetes type, smoker/non-smoker

Ordinal

Categories have an order, but differences between levels are not necessarily equal

Cancer stage, triage level, pain categories

Quantitative/numerical

Describes numerical amounts

Height, weight, number of visits

Discrete

Countable values, usually whole numbers

Number of patients or hospital visits

Continuous

Can take any value within a range

Height, weight, temperature, troponin

Exam traps:

  • A numerical label does not automatically make a variable quantitative: cancer stages 1–4 are ordinal.

  • Yes/no variables are binary nominal variables.

  • Counts → discrete; measurements → continuous.

  • Age is conceptually continuous, even when recorded in whole years.

4. Measurement scales

Scale

Ordered?

Equal intervals?

True zero?

Example

Nominal

No

—

—

Blood group

Ordinal

Yes

Not guaranteed

—

Cancer stage

Interval

Yes

Yes

No

Temperature in °C

Ratio

Yes

Yes

Yes

Weight, height, age

True zero means absence of the measured quantity.

  • 20°C is not twice as hot as 10°C because Celsius has no true zero.

  • 80 kg is twice 40 kg because weight uses a ratio scale.

The data type and measurement scale determine which summaries and statistical tests are appropriate.

5. Independent versus dependent variables

  • Independent variable = predictor/exposure: what may influence the result.

  • Dependent variable = outcome: the result measured.

Example: studying whether smoking predicts lung cancer:

Smoking = independent variable; lung cancer = dependent variable.

6. Descriptive versus inferential statistics

Descriptive

Inferential

Summarizes the data collected

Uses a sample to draw conclusions about a population

Means, proportions, tables, graphs

Confidence intervals and hypothesis tests

  • Mean: average value.

  • Standard deviation (SD): spread of values around the mean.

  • Proportion: number with a characteristic ÷ total number.

Example: 60 smokers among 200 patients → 60/200 = 0.30 = 30%.

7. Normal distribution and the empirical rule

A normal distribution is a symmetrical bell-shaped curve. Most observations cluster around the mean; extreme values are uncommon.

Range

Approximately included

Mean ± 1 SD

68%

Mean ± 2 SD

95%

Mean ± 3 SD

99.7%

Example: mean height = 170 cm, SD = 10 cm:

  • 160–180 cm: 68%

  • 150–190 cm: 95%

  • 140–200 cm: 99.7%

These percentages apply to normally distributed data.

8. Probability and medical testing

Probability ranges from 0 to 1: impossible to certain.

  • OR → addition: for mutually exclusive events.
    Rolling 5 or 6: 1/6 + 1/6 = 1/3.

  • AND → multiplication: for independent events.
    Rolling two consecutive sixes: 1/6 × 1/6 = 1/36.

Increased risk does not mean certainty: smoking increases lung-cancer risk, but not every smoker develops lung cancer.

Bayes’ theorem: disease prevalence affects the meaning of a positive test.

Using the lecture’s example, assuming 90% sensitivity and 90% specificity, with disease prevalence of 1%:

Among 1,000 people

Test positive

10 have the disease

9 true positives

990 do not have it

99 false positives

Thus, the probability of disease after a positive result is 9/108 ≈ 8.3%, despite the test’s 90% sensitivity and specificity.

Rare disease → positive results may include many false positives.

9. Confidence intervals and hypothesis testing

Confidence interval (CI): expresses uncertainty around an estimate.

Example: mean cholesterol 200 mg/dL; 95% CI 190–210.

  • Narrower CI → greater precision.

  • Larger samples generally produce narrower CIs.

  • Strictly, a 95% CI method captures the true parameter in 95% of repeated samples.

Hypothesis testing:

  • H₀, null hypothesis: no difference or association.

  • H₁, alternative hypothesis: a difference or association exists.

  • p-value: assuming H₀ is true, the probability of results at least as extreme as those observed.

  • At α = 0.05, p < 0.05 → reject H₀.

  • p ≥ 0.05 → fail to reject H₀; this does not prove equality.

Statistical significance does not automatically mean clinical importance.

10. Life tables, representation, and ethics

  • Life tables: describe survival across ages and help estimate mortality and remaining life expectancy.

  • Unrepresentative samples → limited generalizability.

  • Underrepresenting women, children, or minority groups may lead to misleading conclusions and harmful decisions.

Must memorize: population versus sample; parameter versus statistic; nominal versus ordinal; discrete versus continuous; interval versus ratio; predictor versus outcome; descriptive versus inferential; 68–95–99.7; CI precision; and the meaning of p < 0.05.