RES 4353 Module 4 Interpretation of Statistical Results Example

Twice the Odds Is Not Twice the Risk: Interpreting the Statistics in a Study of Teaspoon Units and Parents' Dosing Errors

Student Name

American College of Education

RES4353: Evidence-based Health Education and Literacy

Module 4 Assignment

Instructor Name

October 26, 2026

The Study and Its Headline

Earlier modules in this course examined the evidence behind a community health center pharmacy's plan to print liquid medicine doses in milliliters only. One of the key studies, by Yin et al. (2014), studied 287 parents, English or Spanish speaking, who left one of two emergency departments with a liquid medicine for their child, and asked whether the unit written on the instructions, milliliters or teaspoons and tablespoons, was associated with dosing errors. An error was defined as a measured dose more than 20% away from the intended or prescribed dose. The headline, repeated in later citations, is that teaspoon and tablespoon instructions came with twice the odds of an error.

A pharmacy manager reading that headline might conclude that switching units would halve errors. This paper works through the study's statistics in order, from simple percentages to adjusted odds ratios, confidence intervals, subgroup differences and mediation, to show what the numbers do and do not support.

Starting With the Percentages

The simplest numbers are often the most useful. Overall, 39.4% of parents measured the intended dose incorrectly, and 41.1% made an error against the prescribed dose. Among parents using teaspoon or tablespoon units, 42.5% made an error with the intended dose, compared with 27.6% of parents using milliliters only. The comparable figures for the prescribed dose were 45.1% and 31.4%.

Two things stand out before any modeling. First, errors were common in both groups; even with milliliters only, more than a quarter of parents measured incorrectly, so no change of units alone would eliminate the problem. Second, the absolute difference for the intended dose was about 15 percentage points. Put in terms a manager can use, if the unit difference were fully causal, switching roughly seven parents from teaspoons to milliliters would prevent one error, since one divided by 0.149 is about 6.7.

P-Values

The study reports P = .02 for the difference in intended-dose errors and P = .04 for prescribed-dose errors. The p-value speaks to one limited matter: if the two groups truly made errors at the same rate, how often would a gap this big or bigger turn up by chance alone? Values below the conventional .05 threshold are called statistically significant. They do not measure how large or important a difference is, and a value of .04 is only just below the line. The p-values say that chance alone is an unlikely explanation for the gaps; they say nothing about whether a gap of this size matters, which is the question the confidence interval and the percentages answer better.

Adjusted Odds Ratios

The headline figures are adjusted odds ratios from multiple logistic regression: 2.3 for the intended dose and 1.9 for the prescribed dose. Odds are the probability of an event divided by the probability of it not happening, so an error rate of 42.5% corresponds to odds of about 0.74. An odds ratio compares the odds in two groups. Adjustment means the model estimated the association while holding constant parent age, language, country of origin, race and ethnicity, socioeconomic status, education, health literacy, child age, chronic disease and study site. That matters because parents who use teaspoons might differ in other ways, such as education or language, that also affect errors.

The point most readers miss is that odds ratios exaggerate relative risk when the outcome is common. Zhang and Yu (1998) described a method for converting an odds ratio into an approximate relative risk using the outcome rate in the comparison group. Applying it with the 27.6% error rate among milliliter users, an adjusted odds ratio of 2.3 corresponds to a relative risk of about 1.7. For the prescribed dose, 1.9 becomes about 1.5. Twice the odds, in a study where errors are this common, means roughly 50% to 70% more errors, not twice as many.

Confidence Intervals

Each adjusted odds ratio comes with a 95% confidence interval: 1.2 to 4.4 for the intended dose and 1.03 to 3.5 for the prescribed dose. The interval gives the range of values compatible with the data, and because both exclude 1.0, the value meaning no association, both results are statistically significant, consistent with the p-values. But the intervals are wide. The true intended-dose odds ratio could be as small as 1.2, a modest association, or as large as 4.4. The prescribed-dose interval nearly touches 1.0. With 287 parents split across unit groups, the study was large enough to detect an association but not to pin down its size precisely. A practical way to use such an interval is to plan around its lower end. If the pharmacy's case for milliliter-only labels still holds when the association is as weak as an odds ratio of 1.2, the decision does not depend on the study's imprecision; if the case would collapse at that value, the manager should look for stronger evidence before investing. Here the change costs little, since the pharmacy only needs to alter a label template, so even the modest end of the interval is enough to justify it.

Subgroups and Mediation

The authors report that the associations were greater for parents with low health literacy and for those who did not speak English. When the effect of one factor differs across levels of another, it is called effect modification or interaction. For the pharmacy, it means the families most at risk are likely to benefit most from milliliter-only labels, which strengthens the case for the change in a clinic where many families speak Spanish.

The study also found that use of nonstandard instruments, such as kitchen spoons, partly mediated the association. Mediation means that part of the effect of teaspoon units on errors travels through a pathway: teaspoon units lead some parents to reach for a kitchen spoon, and kitchen spoons lead to errors. Because the mediation was partial, some of the association remains even among parents using proper tools. The practical lesson is that milliliter labels and a proper dosing tool work on the same pathway, and providing both is sensible.

Observational Estimates Versus Experimental Ones

Because the 2014 study was cross-sectional, its odds ratios describe association, not effect, even after adjustment, since unmeasured differences between prescribers or families could remain. A later randomized experiment by the same group offers a check. When parents were randomly assigned labels and tools, those given milliliter-and-teaspoon labels made more errors than those given milliliter-only labels, with an adjusted odds ratio of 1.3 and a confidence interval of 1.05 to 1.6 (Yin et al., 2017). The experimental estimate is smaller than the observational one, which is a common pattern when confounding inflates associations, and it concerns a measuring task rather than home dosing. Read together, the two studies suggest a real but moderate benefit from milliliter-only labeling, larger for the families with the fewest advantages, and best delivered alongside syringes and clear instructions. That is the conclusion the final evidence brief should carry to the pharmacy.

References

Yin, H. S., Dreyer, B. P., Ugboaja, D. C., Sanchez, D. C., Paul, I. M., Moreira, H. A., Rodriguez, L., & Mendelsohn, A. L. (2014). Unit of measurement used and parent medication dosing errors. Pediatrics, 134(2), e354-e361. https://doi.org/10.1542/peds.2014-0395

Yin, H. S., Parker, R. M., Sanders, L. M., Mendelsohn, A., Dreyer, B. P., Bailey, S. C., Patel, D. A., Jimenez, J. J., Kim, K.-Y. A., Jacobson, K., Smith, M. C. J., Hedlund, L., Meyers, N., McFadden, T., & Wolf, M. S. (2017). Pictograms, units and dosing tools, and parent medication errors: A randomized study. Pediatrics, 140(1), Article e20163237. https://doi.org/10.1542/peds.2016-3237

Zhang, J., & Yu, K. F. (1998). What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA, 280(19), 1690-1691. https://doi.org/10.1001/jama.280.19.1690