How to Report Odds Ratios and Relative Risk in APA 7

You open your logistic regression output and there is a column called Exp(B) with 2.67 in it, two interval columns and a p value with three zeros. You write “OR = 2.67, p < .001” in the table because that is what the papers on your desk do, and the reviewer sends back three things: the interval is missing, the Discussion says “2.67 times more likely” when that describes a relative risk, and the OR of 0.62 for the other predictor has been read as if it were a percentage of risk. All three are the same problem underneath: an odds ratio is a ratio of odds, not of probabilities, and almost everything written badly about it comes from forgetting that sentence. If what you need is to choose the right measure before reporting it, start with odds ratios and relative risk in clinical research; this article is about the format and the reading.

What an odds ratio needs

Three pieces: the OR, its 95% confidence interval in square brackets and, if your journal asks for it, the p value. The full template is OR = 2.67, 95% CI [1.70, 4.17], p < .001. None of them stands on its own: an OR with no interval is a point with no precision, an interval with no point makes the reader eyeball the center, and a p with no interval repeats information the interval already carries better. APA 7 asks for a confidence interval on every effect size estimate wherever one can be computed, and for an odds ratio one always can.

The formatting has two rules that get broken constantly. The first is the leading zero: an odds ratio can exceed 1 quite routinely, so it keeps it. You write OR = 0.62, 95% CI [0.44, 0.86], never “OR = .62”. That is what separates it from p, from r and from alpha, none of which can pass 1 and all of which drop the zero. The second is that the OR and both limits carry the same number of decimals, normally two. “OR = 2.7, 95% CI [1.70, 4.174]” is a table nobody has proofread.

The rest of the line follows the usual italics: p is italicized, CI is not, the limits sit in square brackets separated by a comma. On whether OR itself is italicized, the manual lists it among the statistical abbreviations and journals typeset it both ways, so pick one, check the instructions for authors and do not alternate within a manuscript. What is not negotiable is that CI stays upright and the p beside it does not.

There is a fourth piece that is not a number: the reference category. A 2.67 means nothing until the reader knows 2.67 relative to what. “Participants with clinical insomnia at baseline had higher odds of a depressive episode at one year than participants without insomnia (OR = 2.67, 95% CI [1.70, 4.17], p < .001)” reads in one pass. A table row saying “Insomnia: 2.67” with no note does not.

The interval decides, not the p value

If the 95% CI contains 1, the effect is not significant at α = .05; if it does not, it is. That is not an alternative rule or a happy coincidence: the Wald interval and the Wald p come out of the same standard error, so they agree by construction. On this scale 1 plays the part 0 plays in a mean difference, because a ratio of odds equal to 1 means the odds are identical in both groups. What the interval adds is the part the p never carries: how much information you have.

Compare two results a fast reader would file in the same drawer. The first is OR = 2.67, 95% CI [1.70, 4.17], p < .001. The second, from a study of 60 participants, is OR = 2.71, 95% CI [1.04, 7.06], p = .041. Both “come out”. The first says the effect is somewhere between moderate and large and cannot be nil. The second says your data are compatible with an effect of 1.04, which is essentially nothing, and with one of 7.06, which would be enormous; the point estimate of 2.71 is close to decorative. Reporting the p alone erases that difference, and that is precisely why APA 7 insists on the interval.

Notice that the interval is not centered on the OR: from 2.67 down to 1.70 is 0.97, and from 2.67 up to 4.17 is 1.50. That is not rounding. The interval is built on the log scale, where it is symmetric (ln 2.67 = 0.98 with a standard error of 0.23, so 0.98 ± 0.45), and both limits are then exponentiated back to the odds ratio scale. If you see a symmetric interval around an OR, somebody has computed OR ± 1.96 × SE on the wrong scale. When the sample is small or cells are nearly empty, the real coverage of the Wald interval drifts away from 95% and it is worth asking for a profile likelihood interval or a bootstrap one, saying in the text which you used.

There is one case where the problem lies neither in the p nor in the interval but in the test both come from: when the effect is huge and the cases are few, the standard error blows up and the Wald test loses power exactly where the effect is largest. The p and the interval still agree with each other (they share the standard error), but both contradict the likelihood ratio test, which does pick the effect up. This is the Hauck-Donner effect (Hauck and Donner, 1977), and you can spot it by eye. OR = 14.20, 95% CI [1.02, 198.40] is not a spectacular finding, it is a warning that one of your cells holds three people. That output is fixed with penalized likelihood (Firth, 1993) or with more data, not with an adjective in the Discussion.

An odds ratio is not a relative risk

Picture a cohort of 400 people followed for a year: 200 with clinical insomnia at baseline and 200 without. By the end of the year, 80 of the 200 with insomnia have had a depressive episode, and so have 40 of the 200 without. Risk is a proportion of the whole group: .40 against .20, so the relative risk is RR = 2.00, twice as high. Odds are a different sum, cases divided by non-cases: 80/120 = 0.67 against 40/160 = 0.25, and the ratio gives OR = 2.67. Same data, two numbers, and both sums are correct.

The gap is not cosmetic. Writing “participants with insomnia were 2.67 times more likely to become depressed” reads the OR as if it were an RR, and in this example that inflates the effect by 33%: the probability doubled, it did not multiply by 2.67. The bias runs in a fixed direction and it is worth keeping that direction in mind, because it always flatters your hypothesis: when the outcome is common, the OR sits further from 1 than the RR, higher for a risk factor and lower for a protective one. An OR never lands between the RR and 1.

The OR hugs the RR when the outcome is rare. Move the same comparison to an incidence of 2% against 1% (20 cases in 1,000 and 10 in 1,000) and the RR is still 2.00 while the OR drops to 2.02: there, the confusion changes nothing. The most cited convention puts the boundary at roughly 10% incidence in the unexposed group, and it is a convention rather than a threshold with legal force. In psychiatric epidemiology that rules out a good many outcomes at a stroke, because the prevalence of depression, anxiety or problematic use in the samples we normally analyze usually sits above 10%.

Some designs have no relative risk to give. In a case-control study you decide how many cases and how many controls to recruit, so the outcome proportions were set by hand and computing a risk from them is meaningless; the OR is the only measure that survives that sampling, which is the historical reason it is everywhere. If you have a cohort or a trial and the outcome is common, you can convert with the formula of Zhang and Yu (1998), RR = OR / [(1 − P₀) + (P₀ × OR)], where P₀ is the risk in the unexposed group: with .20 and 2.67 it returns exactly 2.00. The point conversion is fine; its interval has been argued over for twenty years for running too narrow (Greenland, 2004), so if relative risk is your primary estimate, fit a log-binomial model or a Poisson regression with robust standard errors and report that instead.

How to read an odds ratio below 1

An OR under 1 means the characteristic goes with less of the outcome. Suppose that in the same study high social support goes with less treatment dropout: OR = 0.62, 95% CI [0.44, 0.86], p = .005. The literal reading is that the odds of dropping out are 38% lower in the high-support group than in the reference group, because (0.62 − 1) × 100 = −38. What that figure is not: “a 38% lower chance of dropping out”. That sentence describes a risk, and with an outcome as common as dropout the real risk reduction is a good deal smaller than 38%.

A protective odds ratio can be turned around, and sometimes it reads far better that way. The reciprocal of 0.62 is 1/0.62 = 1.61, so the same finding becomes “the odds of dropout were 1.61 times higher in the low social support group”. To flip the interval you invert both limits and swap their order: [0.44, 0.86] becomes [1.16, 2.27]. It is the same estimate with a different reference category, not a new analysis, and nothing needs declaring beyond which group is the comparison.

All of this works in reverse because the odds ratio scale is multiplicative, not additive. One is the center, and 0.50 and 2.00 are the same effect size in opposite directions, exactly as 0.62 and 1.61 are. That is also the explanation for the asymmetric interval above, and the reason a forest plot puts its axis on a log scale: on a linear axis the protective half of the range is squashed between 0 and 1 while the risk half stretches to infinity, and the intervals look like sizes they are not.

Neither an OR of 2.67 nor one of 0.62 says anything clinical on its own, because a ratio does not carry the starting level inside it. With a baseline risk of 20%, an OR of 2.67 moves you from 20% to 40%: twenty more people in every hundred. With a baseline risk of 0.1%, that same 2.67 moves you from 0.1% to 0.27%. Same number, two completely different findings, so always report the raw counts and the event rate in each group alongside it. A reviewer at a health journal will ask for them anyway.

Where the number comes from: a 2 × 2 table or a logistic regression

With two binary variables, the crude odds ratio is a cross-multiplication: ad/bc, that is (80 × 160)/(120 × 40) = 2.67 on the data above. The interval comes from the standard error of the logarithm, the square root of the sum of the reciprocals of the four cells, which here is 0.23. If any cell is zero, the OR runs to zero or to infinity and the output stops being interpretable; the classic fix is to add 0.5 to all four cells (Haldane, 1956), and it goes in the table note rather than happening quietly. If you would rather not do the arithmetic by hand, the odds ratio calculator returns the OR, the relative risk, the 95% CI and the formatted line.

The moment a covariate enters, the number comes from a logistic regression and the OR is exp(B). A coefficient of B = −0.48 with SE = 0.17 gives exactly the OR = 0.62 from the previous section, and the interval for the OR is the exponential of the interval for B. An adjusted odds ratio is labeled as such (aOR or “adjusted OR”) and the note says what it was adjusted for: “adjusted for age, gender and baseline depressive symptoms”. An adjusted OR presented without that list is a number the reader can neither reproduce nor compare with anyone else's.

When the predictor is continuous, the OR is per one unit of the variable, and you chose that unit when you built the dataset. An OR of 1.03 per point on a 63-point scale sounds like nothing and is not: rescaled to tens, the same effect is OR = 1.34 per 10 points, because 1.03 to the power of 10 is 1.34. Rescaling to something interpretable (ten points, one standard deviation, five years of age) is legitimate and worth doing, as long as you say what unit the OR is in. What is not allowed is rescaling after checking which version crosses .05.

Matched designs take their own route. If you matched each case to a control on age and gender, or if you measure the same people before and after, the ordinary 2 × 2 table ignores the matching and underestimates the effect: the odds ratio comes from the discordant pairs, b/c, and the test is McNemar's or a conditional logistic regression. A matched analysis run as though it were independent shows up immediately in the Method section, and it is a common reason for major revisions.

What it looks like in the text and in the table

In the Results section, the full sentence carries the comparison, the counts, the estimate and its interval. For example: “Clinical insomnia at baseline was associated with a depressive episode at one year: 80 of 200 participants with insomnia (40.0%) compared with 40 of 200 without insomnia (20.0%), OR = 2.67, 95% CI [1.70, 4.17], p < .001. After adjusting for age, gender and baseline depressive symptoms, the association held, adjusted OR = 2.31, 95% CI [1.42, 3.76], p < .001.” In two lines the reader has the design, the magnitude, the precision and what the covariates did.

Past three or four predictors that stops being a paragraph and becomes a table. The columns a reviewer expects are predictor, B, SE, the test statistic, p, OR and the 95% CI, either as one bracketed column or as two columns holding the limits. A row looks like this: high social support, B = −0.48, SE = 0.17, z = −2.82, p = .005, OR = 0.62, 95% CI [0.44, 0.86]. The table note carries the reference category for every predictor, the N, the list of covariates in the adjustment and any correction you applied.

In the Discussion, write the sentence in the language of odds or convert it, but do not mix the two. “The odds of a depressive episode were 2.67 times higher” is correct; “the risk doubled (RR = 2.00, from 20.0% to 40.0%)” is also correct and reads better outside the guild. What you cannot do is take the 2.67 and drop it into a sentence about probability. If you are unsure which version you have written, read it aloud listening for “probability”, “risk” or “times more likely”: when those words sit next to an OR, the sentence needs rewriting.

Frequently asked questions

How do you report an odds ratio in APA 7?

With the OR, its 95% confidence interval in square brackets and, if the journal asks for it, the p value: OR = 2.67, 95% CI [1.70, 4.17], p < .001. All three numbers carry two decimals, the OR keeps its leading zero because it can exceed 1, p is italicized and drops its zero, and CI stays upright. Beside them you need the reference category and the raw counts for each group, because a ratio without a starting level cannot be interpreted.

Is an odds ratio significant if the confidence interval includes 1?

No. One is the null value on this scale, just as 0 is for a mean difference, so an interval containing it means the effect is not significant at α = .05. The Wald interval and the Wald p come from the same standard error and agree by construction, so the two can never contradict each other. What the interval adds is precision: OR = 2.71, 95% CI [1.04, 7.06] clears the threshold and is compatible with almost anything, whereas OR = 2.67, 95% CI [1.70, 4.17] genuinely pins the effect down.

What is the difference between an odds ratio and relative risk?

Relative risk compares proportions (cases out of the whole group) and the odds ratio compares odds (cases out of non-cases). With 80 cases in 200 against 40 in 200, the RR is .40/.20 = 2.00 and the OR is (80/120)/(40/160) = 2.67. When the outcome is common the OR always sits further from 1 than the RR, so confusing them inflates the effect — here by 33%. With rare outcomes the two nearly coincide (2% against 1% gives RR = 2.00 and OR = 2.02), and below about 10% incidence the difference rarely changes a conclusion.

What does an odds ratio below 1 mean?

That the characteristic goes with less of the outcome, which is to say it is protective. An OR of 0.62 means the odds of the outcome are 38% lower than in the reference group, not that the probability falls by 38%. If it reads better the other way round, invert it: 1/0.62 = 1.61, and the same finding becomes odds 1.61 times higher in the reference group, with the interval inverted and its limits swapped ([0.44, 0.86] becomes [1.16, 2.27]).

Can I convert an odds ratio into a relative risk?

If you know the risk in the unexposed group and the design lets you talk about risk at all (a cohort or a trial, never a case-control), yes: RR = OR / [(1 − P₀) + (P₀ × OR)], the formula of Zhang and Yu (1998). With P₀ = .20 and OR = 2.67 it returns RR = 2.00. The point estimate behaves well, but its interval has long been criticized for coming out too narrow (Greenland, 2004), so if relative risk is your main result it is better to fit a log-binomial model or a Poisson regression with robust standard errors.

Is OR italicized in APA 7?

The manual lists OR among the statistical abbreviations and journals typeset it both in italics and upright, so what you will be held to is consistency: check the instructions for authors, choose one form and keep it in the text and in the tables. The rest of the line has no second version: p, B, SE and N are always italicized, CI is always upright, and the interval always sits in square brackets with a comma between the limits.

With the OR, its 95% CI in square brackets, the reference category, the counts for each group and a Discussion written in the language of odds, your odds ratio is reported the way APA 7 asks. When the design gets harder — common outcomes where you genuinely need the relative risk, matched cases and controls, or models with separation that return impossible intervals — that is what my statistical consulting is for.