Lec 1: What is statistical inference?

BIOS 600 - Spring 2026

As you walk in…

Today, we’ll “collect” some data from the class and record on the whiteboard!

How many hours of sleep did you get last night? If you feel comfortable sharing, please draw a dot above the number corresponding to the number of hours of sleep you got. (Round to the nearest hour)

Draw each dot about 1 inch above the previous dot. Make dots about the same size. We’ll come back to this later in class.

Reading

No reading for today.

Announcements

• Lab 1 held today at 3:30pm in MHRC 0003.

• Fill out the Getting to Know You Survey (Canvas assignments) by Friday at 11:59pm.

• TA office hours will be Fridays 3:00-4:00pm in 6110 Mary Ellen Jones Building, or on Zoom.

• My office hours will be Tuesdays 9:45am-10:45am. This week and next week, in my office, 3104A. Afterwards, in McG 3106E (Hoteling Room 2)

• Reach out to the TA if you need help installing R/RStudio!

What is statistical inference (in a biostatistics context)?

A process that converts data into useful information, whereby practitioners

1. form a question of interest
2. collect and summarize data
3. and interpret the results

Identifying the population and question of interest

The population is the group we’d like to learn something about:

• What is the prevalence of diabetes among U.S. adults, and has it changed over time?

• Is there a relationship between tumor type and five-year mortality in breast cancer patients?

• Does the average amount of caffeine vary by vendor in 12 oz cups of coffee at UNC coffee shops?

If we had data from every unit in the population, we could just calculate what we wanted and be done!

Sampling from the population

Unfortunately, we (usually) have to settle with a sample from the population.

• Ideally, the sample is representative, allowing us to use probability and statistical inference to make conclusions that are generalizable to the broader population of interest.

Our Sleep Data

Based on our collective histogram, get in groups of 4 and discuss the following:

• What is our population?

• What is our sample?

• What does our sample show? Do we think it’s representative of our population? Why or why not?

• What limitations might we have? (How could we improve?)

Sampling methods

Probability sampling (e.g., simple random sampling, stratified, cluster, or multi-stage sampling)

• All units have a known chance of being selected

• More likely to be generalizable

• Can be more expensive and time-consuming

Non-probability sampling (e.g. quota, convenience, or snowball sampling)

• Some units unable to be selected, with no way of knowing size or effect of sampling errors

• Less generalizable to population of interest

• More convenient and less costly

Study design

Experimental studies (e.g. randomized control trials (RCTs))

• Researchers directly control exposures or treatment groups.

• Ability to make causal statements

• Less real-world applicability and generalizability

Observational studies (e.g. surveys)

• Researchers do not assign exposures or treatments

• Real-world setting with lower burden on participants

• Inability to prove causality

Example

• Study: The effect of a new diet on weight loss in adults

• Objective: To determine whether a new low-carbohydrate diet leads to significant weight loss compared to a standard diet in adults.

• Study Design:

  • Participants: 100 adults aged 25-45 with a BMI between 25 and 30
  • Randomization: Participants are randomly assigned to one of two groups:
    • Group A: 50 participants following the new low-carb diet
    • Group B: 50 participants following a standard diet.
  • Intervention: Group A follows the new diet for 12 weeks, while Group B follows their usual diet (standard diet)
  • Outcome measurement: Weight of participants is measured before the study begins and after 12 weeks.

Example

In small groups, discuss the following:

• Is this study an observational or experimental study? Why?

What can go wrong?

• Depending on the study design and sampling methods, different types of bias occur (again, we don’t have the full population, only a sample).

• Examples include:

  • Selection bias: sample does not accurately reflect target population
  • Reporting bias: tendency to under-report all information available
  • Many more: non-response bias, attrition bias, confounding, detection bias, lack of blinding, straight-up falsified data (this happens), …

and more!

A few years ago…

link to article

• seroprevalence = level of pathogen in a population

• From Conclusion: “The estimated prevalence of SARS-CoV-2 antibodies in Santa Clara County implies that COVID-19 was likely more widespread than indicated by the number of cases in late March, 2020”.

However…

What do some other people have to say about this study…?

Three main issues brought up in blog

1. Sampling bias

• Study recruited participants through Facebook ads, may have attracted people more concerned about COVID-19 or those who thought they were already exposed \(\rightarrow\) overestimation of seroprevalence (level of pathogen in a population)

  • Symptomatic/exposed individuals may have signed up to get tested, especially when testing was limited.

  • Participants may have recruited others in their network

• Without a truly random sample, findings are less generalizable and reproducible

The issues, continued

2. Statistical adjustments: High false positive rate could drive results

• Study had high false positive rate (2 FP out of 401 known negative samples, about 0.5%), but with a wide confidence interval! (FP Rate could be above 1.2%)

• Study reported only 50 positives out of ~3300 participants, so such a high FP rate could account for a significant portion - if not all - of the positive results. (\(\frac{2}{401}\cdot 3300 = 17\)) Yikes!

• It could even be more! (re-calibrate the assay on a different set of 401 known negative samples, you may get 0/401 FP or even 6/401).

The issues, continued

3. Implausibility compared to previous pandemics

• Results would imply much faster spread than previous pandemics

• Not impossible, but a reason to be a bit more skeptical of results.

An additional issue…

4. Transparency

• Study does not make its raw data, code, and full methodology publicly available

• Without access to these, other researchers cannot replicate the study or verify its findings, undermining the reproducibility of the research

• Transparency essential for the scientific process (particularly in high-stakes studies!)

Reproducibility and replicability

• Reproducibility: being able to take original data and code to reproduce all numerical findings.

• Replicability: being able to independently repeat an entire study without use of the original data (generally with the same methods)

Best practices from the American Statistical Association:

• End-to-end scripting of research

• From the moment you “read in” your raw data, document the code you used for data cleaning, visualization, and analysis

• Use of version control and documentation (we will not use this in our class)

• Publication of code along with data

The current replication crisis

• misconduct, including image manipulation

• submitting falsified data to secure federal research grants

Fraudulent data can lead to unreliable research findings, waste resources, and erode trust in scientific integrity!

What is biostatistics good for?

• 📊 Turning Data Into Insight
  Biostatistics helps us move beyond raw numbers to identify meaningful patterns in health and disease.

• 🧪 Evaluating Interventions
  From vaccines to health policies, biostatistics allows us to rigorously test what really works.

• 🌍 Promoting Health Equity
  Careful analysis helps uncover disparities in health outcomes and guide solutions for underserved communities.

• 🔮 Forecasting & Prevention
  Models help us anticipate outbreaks, chronic disease trends, and the impact of prevention strategies.

• 🏥 Improving Patient Care
  Biostatistics drives evidence-based medicine by connecting research to better clinical decisions.

What is biostatistics good for?

• When we appropriately apply statistical inference methods, they can do a lot of good!

What is biostatistics good for?

What is biostatistics good for?

Activity: Biostatistics for public good!

Step 1: Explore Google Scholar

• Search for a research paper where biostatistics is used to improve public health (e.g., studies on vaccines, health disparities, chronic disease prevention, environmental exposures, health policy).

Step 2: Share & Discuss

• Form groups of 3. Each person shares the paper they found. As a group, discuss:

• What is the paper studying? How are biostatistics being applied? Why is this meaningful or impactful for public health?

Participation

Step 3: Reflect & Submit

• Take a screenshot of the abstract/front page of your chosen paper

• Write a short reflection (3–4 sentences):

  • What do you find interesting/important about the paper you chose?

  • How does it show the value of biostatistics?

Submit the screenshot + reflection on Canvas

Due this Friday at 11:59pm

In this course, we will…

• Apply descriptive techniques commonly used to summarize public health data.
• Learn methods to analyze real-world data to answer research questions in a biomedical setting.
• Use Quarto within RStudio (now Posit) to write reproducible reports.
  • Reading in data, cleaning data, visualization, analysis, interpretation
• Communicate results from statistical analyses to a general audience.

Recap

• What is (bio)statistical inference?

• Identifying the population of interest

• Sampling types and biases

• Reproducibility crisis: falsifying data

• Biostatistics for public good!

Next class

• Probability Basics