Is the Association Real, or Just Chance?
How do we know an association is real and not just chance?
💡 An , a p-value, and a together decide whether an association is real, and the interval shows both the size and the certainty of the effect.
Prerequisite check
- A SNP is a single-letter spot where people commonly differ; a genome-wide association study (GWAS) tests hundreds of thousands to millions of SNPs at once without guessing a gene first.
- The (TDT) uses case-parent trios; a heterozygous parent should pass a 50 percent of the time by chance, so over- flags an associated .
What you will learn
Goal: Students will interpret an , a p-value, and a , and decide whether an association is statistically significant.
- An association means two things tend to occur together; an (or ) measures effect size, where 1.0 means no difference.
- A p-value is the probability of a result at least this extreme if there were truly no effect; by convention p < 0.05 is called statistically significant.
- For a ratio measure, if the includes 1.0 the result is not significant; if it excludes 1.0 it is.
- TOPS reported a of 0.59 (95 percent CI 0.36 to 0.99, P = 0.04), so its result is significant but not by a wide margin; a CI that straddles 1.0 is a .
Model: A ratio that excludes 1.0, and one that crosses it
In the TOPS trial, 558 infants with were repaired at either 6 months or 12 months, and the outcome was (a speech problem) at age 5. The earlier-surgery group did better: 8.9% had the problem versus 15.0% in the later group. The reported effect was a of 0.59, with a of 0.36 to 0.99, and P = 0.04 [PMID:37646677]. Read it like this: a ratio of 0.59 means earlier surgery cut the risk to about 59 percent of the later-surgery risk; the interval 0.36 to 0.99 is the plausible range for the true effect, and it stops just below 1.0.
In a five-country of clefts during COVID-19, some exposures produced odds ratios whose 95 percent confidence intervals crossed 1.0 (an interval running from below 1 to above 1). The authors treated those as not statistically significant, and described a tangled picture where maternal fear and stress raised risk while a separate measure pointed the other way, a pattern they read as a stress-and-reporting artifact, not biology [PMID:37118740].
Explore (work the model before reading on)
- In Model 1, what is the (here a ), and what is its ?
- In Model 2, what does it mean that a crosses 1.0?
- For a ratio measure, 1.0 means no difference. The TOPS interval is 0.36 to 0.99. Does that interval include 1.0, and what does that tell you about significance?
- The TOPS p-value was 0.04. A p-value is the probability of seeing a result this extreme if there were truly no difference. Why does a small p-value make it was just chance a weaker explanation?
- Suppose a new study reports an of 1.8 but a of 0.7 to 4.6. The point estimate looks alarming. What would you, the biostatistician, conclude, and why?
- In one sentence, what pattern did your team find about when an association counts as real?
Guided notes
Three numbers
- An association means two things tend to occur together; the (or ) measures effect size, and a value of ____ means no difference, above 1.0 raised risk, below 1.0 lowered risk.
- The p-value is the probability of a result at least this extreme if there were truly ____ (no) effect; by convention p < ____ (0.05) is called statistically significant.
Reading the interval
- The is the plausible range for the true effect; for a ratio, if the CI ____ (includes) 1.0 the result is not significant, and if it excludes 1.0 it is.
- The TOPS interval (0.36 to 0.99) just excludes 1.0, so the result is significant but not by a wide margin; a CI that straddles 1.0 is a .
Why pros prefer the interval
- The shows two things a bare p-value hides: the size of the effect and how precise it is.
- A small p-value makes pure chance an unconvincing explanation, but a wide interval that crosses 1.0 warns that the effect may be nothing at all.
Reading the Research
- Skim the title and abstract first to get the gist.
- Circle the one sentence that states the main claim.
- Box the evidence the authors give for that claim.
- Mark one sentence that confuses you, and move on.
Vetted readings for this lesson
- Gamble C, et al. 2023. Timing of Primary Surgery for Cleft Palate (TOPS trial). N Engl J Med. [PMID:37646677]
- Sabbagh HJ, et al. 2023. COVID-19 risk factors and orofacial clefts, five Arab countries: case-control study. BMC Oral Health. [PMID:37118740]
- Park JW, et al. 2007. Association between IRF6 and nonsyndromic cleft lip/palate in four populations. Genet Med. [PMID:17438386]
Track your progress today
Check these off as you work through the lesson, then submit. This tells Mr. Mendoza how you're doing so he can help the class. It does not replace turning in your producible.
Use the code Mr. Mendoza gave you, not your name. Saved on this device.
- Read the Model and answered the Explore questions.
- Filled in the guided notes in my own words.
- Defined the new vocabulary with an example.
- Built the producible: Sort three practice findings into significant or not significant with one sentence each (Variant A: OR 2.1, 95 percent CI 1.3 to 3.4, p = 0.002; Variant B: OR 1.4, 95 percent CI 0.9 to 2.2, p = 0.11; Technique C: risk ratio 0.62, 95 percent CI 0.40 to 0.96, p = 0.03), then state whether the largest effect size is automatically the most trustworthy.
- Wrote my Claim, Evidence, and Reasoning exit ticket.
Exit ticket (Claim, Evidence, Reasoning)
- Claim: The association reported in TOPS between earlier surgery and better speech is statistically significant.
- Evidence: The numbers were a of ____ with a 95 percent CI of ____ to ____ and P = ____.
- Reasoning: This counts as significant because the ____ (excludes 1.0) and the p-value ____ (is below 0.05).
| Criterion | Proficient | Developing | Beginning |
|---|---|---|---|
| Complete | Every required part of the artifact is present and filled in. | Most parts are present, but one is missing or left blank. | Several parts are missing. |
| Accurate | The science and data are correct and match the evidence. | Mostly correct, with a small factual slip. | Key science or data is wrong. |
| Scientific reasoning (CER) | States a claim, backs it with specific evidence, and explains the reasoning. | Has a claim and evidence, but the reasoning is thin or missing. | Gives an answer with no evidence or reasoning. |
| Professional communication | Clear, organized, and labeled the way a clinician or scientist would write it. | Readable but disorganized or missing labels. | Hard to follow. |
| Submitted | Turned in the right way (Schoology for routine work) and confirmed. | Turned in, but in the wrong place or unconfirmed. | Not turned in. |
- CompleteProficient: Nothing is left blank: the model fills every part of "Sort three practice findings into significant or not significant with one sentence each (Variant A: OR 2.1, 95 percent CI 1.3 to 3.4, p = 0.002; Variant B: OR 1.4, 95 percent CI 0.9 to 2.2, p = 0.11; Technique C: risk ratio 0.62, 95 percent CI 0.40 to 0.96, p = 0.03), then state whether the largest effect size is automatically the most trustworthy.".
- AccurateProficient: Every number and claim matches the case evidence.
- Scientific reasoning (CER)Proficient: It names a claim, cites the specific evidence, and explains the reasoning, not just the answer.
- Professional communicationProficient: It is organized and labeled like a real chart note.
- SubmittedProficient: It would be turned in on Schoology and confirmed.
Where this leads: careers
What's next: One p-value below 0.05 feels convincing, but a GWAS runs about a million tests at once. If 0.05 lets through a 1-in-20 fluke, how many flukes slip through a million tests, and why do gene studies demand a far tinier p-value?
