Biostatistics for Public Health Students

Many public health students arrive worried about statistics. They need not be. Biostatistics is a toolkit for answering questions like "Did this program work?" and "Is this exposure linked to this illness?" Once you see it as a way to think clearly under uncertainty, it becomes less intimidating.

This guide covers the main ideas you will meet in a first course, in plain language. Your instructor and textbook set the exact content, so use this as a companion.

Why it matters

Public health decisions affect many people. Whether a vaccine is effective, whether a screening program saves lives and whether a neighborhood has unusually high rates of an illness all depend on data. Biostatistics helps you tell real patterns from chance, and weak evidence from strong. It also helps you read research critically, which every practitioner needs to do.

Types of data

Knowing the type of variable determines which methods fit.

1. Categorical, nominal. Groups without order, such as blood type or county.
2. Categorical, ordinal. Ordered groups, such as stage of disease or satisfaction rating.
3. Numerical, discrete. Counts, such as number of visits.
4. Numerical, continuous. Measurements, such as blood pressure or weight.

Before analyzing anything, identify each variable's type and how it was measured.

Describing data

Descriptive statistics summarize a dataset.

• Center: mean, median and mode. The median resists the effect of outliers.
• Spread: range, interquartile range, variance and standard deviation.
• Shape: symmetric, skewed or having several peaks.
• Graphs: histograms, box plots, bar charts and scatterplots.

Always look at a graph before computing tests. A picture often reveals outliers, errors or patterns that numbers hide.

Probability and distributions

Probability gives a language for uncertainty. A few ideas appear everywhere:

• Events, probabilities and conditional probabilities.
• The normal distribution, a bell-shaped curve that describes many measurements.
• The binomial distribution for counts of successes in a fixed number of trials.
• Sampling distributions, which show how a statistic varies from sample to sample.

The central limit theorem says that averages of large samples tend to follow a normal distribution, which is why many tests work.

Samples and populations

You rarely measure everyone. You study a sample and use it to infer something about a population. Good inference depends on how the sample was chosen. Random sampling helps avoid bias. Convenience samples can mislead. Sample size matters, because larger samples give more precise estimates.

Confidence intervals

A confidence interval gives a range of plausible values for a population quantity. For example, "The prevalence was 12 percent, with a 95 percent confidence interval from 10 to 14 percent." Narrower intervals mean more precision. Intervals tell you more than a single number because they show uncertainty, and they often convey more than a p-value alone.

Hypothesis tests and p-values

A hypothesis test asks whether the data are consistent with a null hypothesis, usually "no difference" or "no association." The p-value is the probability of seeing results at least as extreme as yours if the null hypothesis were true.

Remember:

• A small p-value suggests the data are unlikely under the null, but it does not prove the alternative.
• A p-value does not measure the size of an effect or its importance.
• Statistical significance is not the same as practical significance.
• A non-significant result does not prove there is no effect. The study might be too small.

Report effect sizes and intervals alongside p-values.

Common tests

Choose a test by thinking about your question, variable types and study design, and check its assumptions.

Regression

Regression models the relationship between an outcome and one or more predictors.

• Linear regression for numerical outcomes.
• Logistic regression for yes or no outcomes, giving odds ratios.
• Poisson or negative binomial regression for counts and rates.
• Cox regression for time-to-event outcomes.

Regression lets you adjust for other factors, which helps handle confounding. Interpret coefficients carefully and in context, and remember that association does not equal causation.

Bias, confounding and causation

Many results mislead because of bias, not chance. Selection bias, measurement error and confounding can distort findings. A confounder is a factor linked to both the exposure and the outcome. Study design, randomization and adjustment help, but they do not eliminate all problems. Epidemiology basics for students explores these ideas in more depth.

Software

Most programs teach one or more packages: R, SAS, Stata, SPSS or Python. Learn to import data, check it, run summaries, make graphs and fit basic models. Save your code or syntax so you can reproduce your work. Do not run tests blindly. Think about what the output means and whether the assumptions are reasonable. The statistics assignment help guide describes the kinds of problems common in coursework.

Study tips

1. Focus on concepts first. Ask what each method is for.
2. Work problems every week. Statistics is a skill.
3. Draw pictures. Sketch distributions and data.
4. Write interpretations in sentences. "The mean was higher in group A by 3 points (95 percent CI 1 to 5)."
5. Use office hours and study groups.
6. Keep a formula and decision sheet for choosing tests.
7. Start assignments early, since software issues take time.

Reporting honestly

Report what you did, including exclusions, missing data and multiple tests. Avoid cherry-picking analyses that give small p-values. Describe limitations. Present numbers in plain language so non-statisticians can understand. Ethical practice means telling the whole story, even when results are not exciting.

A worked example

Suppose a health department tests whether a text-message reminder program raises vaccination rates. In the group that received reminders, 620 of 1,000 people were vaccinated. In the comparison group, 540 of 1,000 were. The difference is 8 percentage points. A confidence interval for that difference might run from about 4 to 12 points, which does not include zero, and a chi-square test would give a small p-value.

A sensible write-up says: "Vaccination was 8 percentage points higher among people who received reminders (95 percent CI 4 to 12), suggesting the program helps." It also notes whether people were randomly assigned. If they were not, you should say that other differences between groups might explain part of the gap.

Sample size and power

A study with too few people can miss real effects. Power is the chance that a study will detect an effect of a given size if it exists. Planning sample size before collecting data helps you avoid wasted effort and misleading negative results. When reading studies, ask whether the sample was large enough for the question, and treat small studies with extra caution.

Missing data

Real datasets have gaps. People skip survey questions, drop out of studies or have incomplete records. Check how much is missing, whether missingness seems random and what the analysis did about it. Simply dropping incomplete cases can bias results. Report what you did and, where possible, check whether conclusions change under reasonable alternatives.

Making your own cheat sheet

Create a one-page guide for yourself. List each variable type, the graphs that fit it, the tests that fit each question and the assumptions to check. Add the plain-language interpretation of a confidence interval and a p-value. Update the sheet as you learn. By the end of the course you will have a personal reference that you can also use in later classes and on the job.

Common mistakes

• Reading p-values as proof.
• Ignoring assumptions.
• Confusing association with causation.
• Skipping the graph.
• Reporting results without interval estimates.
• Testing many things and highlighting the one that worked.

Final thoughts

Biostatistics is a core public health skill that you can learn with patience. Understand variable types, describe data carefully, learn the logic of intervals and tests, and always interpret results in context. The ability to read and present numbers honestly will serve you throughout your career.