Real-world examples of p-values in inferential statistics

Why start with real examples of p-values?

People don’t argue about the formula for a p-value. They argue about what it means in practice. That’s why the best examples of p-values in inferential statistics are not toy coin flips, but situations where a decision matters: approving a drug, launching a product, or changing a school curriculum.

A quick reminder in plain language: a p-value is the probability of seeing data at least as extreme as what you observed if the null hypothesis were actually true. Small p-values suggest your data are hard to reconcile with the null; large p-values suggest they’re very compatible with it.

Now let’s get into real examples of examples of p-values in inferential statistics across different fields.

Medical trial example of p-values: new blood pressure drug

Imagine a randomized controlled trial comparing a new blood pressure medication to a standard treatment. The null hypothesis says there is no difference in average systolic blood pressure reduction between the two groups.

Researchers collect data from 800 adults with hypertension. After 12 weeks:

• Standard treatment group: mean reduction = 8 mmHg
• New drug group: mean reduction = 11 mmHg

They run a two-sample t-test and get:

• Test statistic: t = 2.65
• p-value = 0.008 (two-sided)

How is this used in inferential statistics? At a significance level of 0.05, a p-value of 0.008 is interpreted as strong evidence against the null hypothesis of no difference. In other words, if the new drug were truly no better than standard care, seeing a difference this large or larger would happen less than 1% of the time just by chance.

Notice what this p-value does not say. It does not say there is a 0.8% chance the null is true. It quantifies how surprising the observed data are assuming the null is true. This is one of the best examples of p-values in inferential statistics because medical trials are where misinterpretation can have direct consequences.

For context on how clinical trials report p-values and related measures, see the FDA’s guidance on statistical principles in clinical trials at fda.gov.

Public health examples of p-values: vaccine effectiveness

Public health agencies constantly run inferential statistics on surveillance data. A timely example of examples of p-values in inferential statistics comes from vaccine effectiveness studies.

Suppose the Centers for Disease Control and Prevention (CDC) evaluates whether an updated influenza vaccine reduces hospitalizations among adults over 65. The null hypothesis: hospitalization rates are the same for vaccinated and unvaccinated people, after adjusting for age and comorbidities.

Analysts fit a logistic regression model and obtain an odds ratio of 0.75 for hospitalization in the vaccinated group, with:

• 95% confidence interval: 0.63 to 0.90
• p-value = 0.002

The p-value of 0.002 indicates that, if vaccination truly had no effect on hospitalization risk, data this extreme (or more extreme) would be very rare. In inferential statistics, this supports rejecting the null and reporting that the vaccine is associated with lower odds of hospitalization.

Modern public health reports, including many at cdc.gov, now emphasize confidence intervals and effect sizes alongside p-values. That trend has accelerated through 2024–2025 as journals and agencies push back against overreliance on a single threshold like 0.05.

Education research example of p-values: new math curriculum

Education researchers often test whether a new teaching method improves test scores. Consider a district piloting a new middle school math curriculum in 20 schools, compared to 20 control schools using the old curriculum.

After one year, average standardized math scores are:

• Control schools: mean = 72
• New curriculum schools: mean = 75

A multi-level model (students nested in schools) yields a p-value of 0.04 for the curriculum effect.

At the classic 0.05 cutoff, this is statistically significant. But here is where understanding examples of p-values in inferential statistics really matters:

• The effect size might be small (say, 0.15 standard deviations).
• The district might ask whether that gain justifies the cost of training, new materials, and teacher time.

So the p-value tells us the result is unlikely under the null of no effect, but decision makers still need to weigh effect size, cost, and equity. This is a good example of why statisticians keep saying: statistical significance is not the same as practical importance.

For more on interpreting educational research statistics, the What Works Clearinghouse at ies.ed.gov offers detailed technical documentation.

Business A/B testing: examples include click-through and conversion rates

Tech companies live on A/B tests. These are inferential statistics experiments disguised as product decisions.

Imagine an e-commerce site testing two versions of a checkout button:

• Version A: blue button (current version)
• Version B: green button (new design)

Over a week, each version is shown to 100,000 visitors.

• Version A conversion rate: 4.2%
• Version B conversion rate: 4.5%

A two-proportion z-test yields a p-value of 0.03.

Here, the null hypothesis states that the conversion rates are the same. The p-value of 0.03 suggests that, if there really were no difference, seeing a 0.3 percentage point gap (or larger) would only happen about 3% of the time due to random variation.

In practice:

• Product managers may decide to ship Version B.
• Data teams increasingly adjust p-values for multiple comparisons, because companies often run many A/B tests at once.

This is a modern example of examples of p-values in inferential statistics where p-values are paired with Bayesian methods or sequential testing rules to avoid false positives from constant experimentation.

Environmental science example of p-values: air pollution and asthma

Environmental epidemiologists regularly estimate associations between pollution levels and health outcomes. Consider a study of daily PM2.5 (fine particulate matter) and asthma emergency room visits in a large city.

The null hypothesis: there is no association between daily PM2.5 concentration and asthma ER visit counts.

A Poisson regression model finds that a 10 µg/m³ increase in PM2.5 is associated with a 5% increase in asthma ER visits, with:

• Rate ratio: 1.05
• 95% CI: 1.02 to 1.08
• p-value = 0.001

This p-value supports the conclusion that the association is statistically significant. But again, the effect size and public health context matter. A 5% increase can translate into a large number of extra visits in a city of millions.

Agencies like the U.S. Environmental Protection Agency and the National Institutes of Health (NIH) often fund these studies; see nih.gov for examples of large-scale environmental health research where p-values are one part of the inferential toolkit.

Sports analytics: example of p-values in player performance

Sports analysts use inferential statistics to avoid being fooled by streaks and small samples. Suppose an NBA team wants to know whether a player’s improved three-point shooting this season is likely to persist.

Last season: 33% from three over 400 attempts.
This season (so far): 38% over 150 attempts.

The null hypothesis: the player’s true three-point percentage has not changed; the observed jump is random.

A test for difference in proportions yields a p-value of 0.07.

This is a borderline case. Under the usual 0.05 standard, the team would not reject the null. But a p-value of 0.07 still means the data are somewhat surprising under the null. In practice:

• Scouts might treat this as suggestive but not conclusive.
• Analysts might wait for more attempts before updating contracts or playing strategy.

Sports provide some of the most intuitive examples of p-values in inferential statistics because fans already think in terms of streaks, regression to the mean, and small-sample noise—even if they don’t call it that.

Social science survey: examples of p-values in opinion polling

Pollsters often compare attitudes between groups. Imagine a national survey asking whether respondents support a new climate policy.

Support among:

• Adults under 35: 68%
• Adults 35 and older: 60%

The null hypothesis: support is the same in both age groups.

A test for the difference in proportions produces a p-value of 0.015.

This suggests that, if there were truly no difference in support between age groups, seeing an 8-point gap (or larger) would only happen about 1.5% of the time by chance.

Here, examples of examples of p-values in inferential statistics help clarify how pollsters talk about “statistically significant differences” between demographic groups. The p-value backs up the claim that younger adults are more supportive, beyond what we’d expect from sampling error alone.

Modern practice: how p-values are used (and abused) in 2024–2025

Over the past decade—and continuing into 2024–2025—there has been a noticeable shift in how journals and professional societies talk about p-values.

A few key trends:

• Less worship of 0.05
  The American Statistical Association (ASA) has repeatedly warned against treating p < 0.05 as a magic stamp of truth. Many journals now encourage reporting exact p-values, confidence intervals, and effect sizes instead of binary “significant / not significant” labels.

• More transparency and pre-registration
  In clinical trials, psychology, and economics, pre-registering hypotheses and analysis plans helps prevent “p-hacking” (trying many analyses until something yields a small p-value). This makes examples of p-values in inferential statistics more trustworthy because the test wasn’t chosen after seeing the data.

• Greater use of alternative approaches
  Bayesian methods, false discovery rate controls, and estimation-focused reporting are increasingly common, especially in high-throughput fields like genomics and A/B testing.

None of this makes p-values obsolete. It just means they’re treated as one piece of the inferential puzzle. When you look at real examples of examples of p-values in inferential statistics today, you’ll almost always see them reported alongside effect sizes and uncertainty intervals.

For a thoughtful discussion, the ASA’s statements and follow-up commentaries are available through the American Statistical Association at amstat.org.

Common mistakes when interpreting examples of p-values

Looking across all the examples above, the same misunderstandings keep showing up. A few to watch for:

• Confusing p-value with the probability the null is true
  The p-value is P(data | null), not P(null | data).

• Ignoring study design and sample size
  With a huge sample, trivial effects can produce tiny p-values. With a tiny sample, even large effects can yield large p-values.

• Treating 0.049 and 0.051 as night-and-day
  In reality, those two p-values provide almost the same level of evidence. Sharp cutoffs create an illusion of certainty.

• Using p-values without context
  A good example of p-values in inferential statistics always mentions the effect size, confidence interval, and the real-world implications, not just “p < 0.05.”

When you read research in medicine, economics, or social science, ask yourself: if the p-value were hidden, would the rest of the reporting still let you judge the size and importance of the effect? If the answer is no, the study is leaning too hard on a single number.

FAQ: short answers built from real examples

Q: Can you give a simple example of a p-value in everyday life?
Think of flipping a coin that’s supposed to be fair. You flip it 20 times and get 17 heads. If you test the null hypothesis that the coin is fair, the p-value is the probability of getting 17 or more heads out of 20 flips if the coin is truly fair. That probability is very small, so the p-value is small, and you’d suspect the coin is biased.

Q: In the best examples of p-values, what else should be reported besides the p-value itself?
Good practice includes the effect size (how big the difference or association is), a confidence interval, the sample size, and details of the study design. For instance, a medical trial should report the absolute risk reduction, not just that p = 0.01.

Q: Are there examples of statistically significant results that don’t matter in practice?
Yes. With huge datasets, a tiny difference—say, a 0.1°F change in average body temperature—can easily have p < 0.001. Statistically, that’s significant. Practically, it might be irrelevant. This is why examples of p-values in inferential statistics always need context.

Q: Do scientists still rely on p-values in 2024–2025?
They do, but with more caution. Many journals require authors to avoid phrases like “trend toward significance” and to discuss the limitations of p-values. You’ll see more emphasis on estimation, replication, and pre-registered analyses in current research.

Q: How many examples of p-values do I need to really understand them?
Honestly, more than one. Seeing p-values in medical trials, A/B tests, surveys, and lab experiments helps you see the pattern: a p-value always connects a null hypothesis, a test statistic, and the probability of data at least as extreme as what you observed under that null.

If you focus on concrete, real examples of examples of p-values in inferential statistics—rather than memorizing a formula—you’ll be much better prepared to read research critically, design your own studies, and avoid the most common misinterpretations that still show up in papers and headlines.