Elevated plus maze and open field statistics: many anxiety measures, locomotion and one primary outcome

Quick answer. The elevated plus maze (EPM) and open field each give several correlated measures of the same anxiety-like behaviour, plus measures of activity. Before testing, choose one primary outcome (for example the percentage of time in the open arms) or a composite score of a few percentage measures, test that, and treat the rest as secondary with a multiple-comparison correction. Check locomotion (closed-arm entries, distance): counts such as open-arm entries rise when a mouse simply moves more. In a simulation of 10 vs 10 mice with no real effect, reporting a difference if any of five anxiety measures (three from the EPM, two from the open field) reached p < 0.05 gave 14.1% false positives; the primary outcome gave 4.0% and the composite 4.9%. With a knockout that was only 30% more active, the count measures suggested “less anxiety” in 17.0% of studies.

Terms used below. Elevated plus maze (EPM): a raised plus-shaped maze with two open and two enclosed arms; more time or entries in the open arms is read as less anxiety. Open field: an open arena; more time in the centre is read as less anxiety only if locomotion is unchanged, and distance travelled measures activity. Primary outcome: the single measure chosen in advance to answer the main question and to set the sample size. Composite score: the average of several measures after putting each on a common scale. z-score: (value − reference mean) ÷ reference standard deviation (SD), here using the wild-type mice as reference. Familywise error rate: the chance of at least one false positive across a set of tests. Covariate: a measured value (here activity) added to a model to adjust the comparison; ANCOVA is an ANOVA with a covariate. Interaction: an effect of genotype that differs between sexes. Holm correction: a multiple-comparison correction that controls the chance of any false positive across a set of tests and is less strict than Bonferroni (which multiplies each p-value by the number of tests); it gives adjusted p-values. ANOVA: an extension of the t-test to more than two groups or to several factors, such as genotype and sex. SD units: a difference expressed as a multiple of the wild-type standard deviation. Rearing: standing on the hind legs, counted as an activity measure. Locomotion: how much an animal moves, regardless of where. Welch t-test: a two-group t-test that does not assume equal spread. 95% confidence interval (CI): the range of values compatible with the data. Power: the chance of detecting an effect that is really there. False positive: a “significant” result when there is no real effect.

Which analysis for your question

Question	Analysis	Report
Does the treatment change anxiety-like behaviour?	One primary outcome chosen in advance (for example % open-arm time), Welch t-test or ANOVA across animals; if many animals never enter the open arms, see the zero-entries row	Difference with 95% CI, n animals
Several anxiety measures should move together	Composite: mean z-score of a few percentage measures, defined in advance	Difference in SD units with 95% CI
Secondary measures	All other anxiety measures with a Holm correction, reported in full	Each difference with adjusted p
Is a change in anxiety measures explained by activity?	Name the activity measures in advance (total arm entries in the EPM, distance in the open field); report them with CIs; if activity differs, prefer percentage measures and add an analysis with activity as a covariate (ANCOVA) as a secondary check	Activity differences with 95% CI
Many animals with zero open-arm entries	Report how many; analyse entries as counts out of total entries, or the proportion of animals entering	Counts and proportions
Both sexes	ANOVA or regression with genotype, sex and their interaction; report each sex (the example data are one sex)	Effects by sex
Already tested every measure without a primary outcome	Report all measures, apply Holm across all of them, and call the result exploratory	All differences with adjusted p

Pellow and colleagues validated the EPM, reporting that clinically effective anxiolytics increased “the percentage of time spent on the open arms and the number of entries into the open arms” (Pellow et al. 1985). Walf and Frye summarise: “An increase in open arm activity (duration and/or entries) reflects anti-anxiety behavior” (entries counted as a number also rise with general activity, so use them as percentages of all entries), and list timing of testing, prior handling, sex and age among the factors that change the result (Walf and Frye 2007). In the open field, more time in the centre is read as less anxiety only if activity is similar, because differences in locomotor ability can distort time-in-zone measures (Seibenhener and Wooten 2015). ARRIVE 2.0 asks authors, “For hypothesis-testing studies, specify the primary outcome measure, i.e. the outcome measure that was used to determine the sample size” (Percie du Sert et al. 2020).

Worked example: a knockout with no real effect

Constructed data (the simulation’s design, not a recommended sample size): 10 wild-type and 10 knockout mice, each tested for 5 min in the EPM and 10 min in the open field. Each mouse has an anxiety level and an activity level; percentage measures depend only on anxiety in this model (an assumption: in real mice they can shift a little with activity), while counts (open-arm entries, centre entries) and distance also depend on activity. The composite averages % open-arm time, % open-arm entries (EPM) and % centre time (open field). All differences are knockout − wild-type; the example has no mouse with zero open-arm entries. By design, the knockout changes neither anxiety nor activity. The data’s random seed was the first one tried and was not chosen for its result. Stored code and data: anxiety.csv, model.py, make_data.py, analysis.py, analysis.R and the analysis output; analysis.py and analysis.R print the same output.

Measure	Wild-type mean	Knockout mean	Welch p
EPM: % time in open arms (primary)	20.1	17.0	0.54
EPM: % entries into open arms	31.0	26.2	0.56
EPM: open-arm entries	5.8	5.9	0.95
Open field: % time in centre	7.9	8.6	0.72
Open field: centre entries	7.1	7.3	0.94
EPM: closed-arm entries (activity)	12.3	18.3	0.06
Open field: distance, m (activity)	30.7	29.6	0.70
Open field: rearing (activity)	40.1	42.1	0.61

Conclusion about anxiety	Result
A. Any of the 5 anxiety measures with p < 0.05 (not valid without correction)	none (0 of 5)
B. Holm correction over the 5 anxiety measures	smallest adjusted p = 1
C. Primary outcome, % time in open arms	difference −3.1 percentage points (95% CI −13.7 to 7.5), p = 0.54
D. Composite: mean z-score of the three percentage measures	difference −0.16 SD (95% CI −0.90 to 0.59), p = 0.67

With this data set no approach found a difference; the simulation shows how often the approaches disagree. Closed-arm entries came close to p = 0.05 by chance (p = 0.06), a reminder that activity measures vary too and should be reported. Across 5,000 simulated studies of this design, 10 mice per group, with the percentages below giving how often each approach reported an anxiety effect (simulation.py, the simulation output):

Scenario	A. Any of 5 anxiety measures (invalid)	B. Holm over 5	C. Primary: % open-arm time	D. Composite of 3 percentages	Either count measure, uncorrected (invalid)
No effect (false positives)	14.1%	2.6%	4.0%	4.9%	7.7%
Less anxious by 0.8 SD (power)	46.2%	17.6%	26.5%	32.6%	22.9%
Less anxious by 1.2 SD (power)	70.4%	37.7%	50.2%	59.1%	40.0%
30% more active, anxiety unchanged (“less anxious” by mistake)	23.7%	5.1%	4.5%	5.1%	17.0%

These percentages describe this simulated design (10 mice per group, the model in model.py), not every anxiety study. With 10 mice per group even a 1.2 SD change in the underlying anxiety level was detected only about half the time by the primary outcome; for a power calculation, use the effect you expect on the primary measure itself, from pilot data. Taking any of five measures as evidence gives five chances for a false positive; its high power is the other face of that. Holm over all five (B) kept false positives low but lost power, because the five measures largely repeat each other; the recommended plan tests one primary outcome uncorrected and applies Holm only to the secondary measures. A primary outcome chosen in advance kept false positives near 5% (4.0%; percentages near 0 make the t-test slightly cautious), and the composite of three percentage measures kept them at 5% and gained power by averaging out measurement noise. When the knockout was only 30% more active, count measures (open-arm or centre entries) rose with activity and suggested less anxiety in 17.0% of studies; the percentage-based primary outcome and composite stayed near 5%.

For sample size, use the effect you expect on the primary measure in a standard two-sample power calculation (sample size); for zero open-arm entries, compare the proportion of mice entering with Fisher’s exact test (percentages). The code compares two groups (for three or more, see Welch’s ANOVA). It expects one row per mouse with a genotype column whose labels are exactly wild-type and knockout (check that each group has the expected number of mice; other labels give empty groups) and one column per measure, named as in anxiety.csv (pct_open_time, pct_open_entries = 100 × open ÷ all arm entries, open_entries, closed_entries, pct_centre_time, centre_entries, distance_m, rearing); the snippets are condensed, and the full scripts print every measure and approach A–D; rename your columns and labels to match, and run the code in the folder that holds the CSV file. Python needs NumPy, pandas and SciPy; the R code uses base R only.

import numpy as np, pandas as pd
from scipy import stats

d = pd.read_csv("anxiety.csv"); print(d.genotype.value_counts())                 # check both groups are there
wt = d[d.genotype == "wild-type"]; ko = d.genotype == "knockout"; is_wt = d.genotype == "wild-type"
Z = ["pct_open_time", "pct_open_entries", "pct_centre_time"]                  # composite chosen in advance
z = sum((d[c] - wt[c].mean()) / wt[c].std() for c in Z) / len(Z)            # mean z-score against wild-type
for name, y in (("primary", d.pct_open_time), ("composite", z)):
    t = stats.ttest_ind(y[ko], y[is_wt], equal_var=False); ci = t.confidence_interval()   # knockout - wild-type
    print(f"{name}: difference {y[ko].mean() - y[is_wt].mean():.2f} (95% CI {ci.low:.2f} to {ci.high:.2f}), p = {t.pvalue:.2g}")
# primary: -3.13 (-13.74 to 7.48), p = 0.54; composite: -0.16 (-0.90 to 0.59), p = 0.67

d <- read.csv("anxiety.csv"); table(d$genotype)                # check both groups are there
t.test(pct_open_time ~ genotype, data = d)                     # primary outcome, Welch: p = 0.54
sec <- c("pct_open_entries", "open_entries", "pct_centre_time", "centre_entries")   # the 4 secondary measures
p <- sapply(sec, function(v) t.test(d[[v]] ~ d$genotype)$p.value)
round(p.adjust(p, method = "holm"), 2)                        # secondary measures, Holm-adjusted (row B instead corrects all 5)

Before you analyse

1. Name the primary outcome (or the composite and its parts) before testing, and size the study for it.
2. Record activity in every test (closed-arm entries, distance) and report it next to the anxiety measures.
3. Prefer percentage measures for anxiety, such as % open-arm time and % open-arm entries, over counts that rise with activity.
4. Keep test conditions fixed: time of day, light level, handling, test order when one mouse does both tests, and blind scoring or automated tracking.
5. Report how many animals never entered the open arms or fell off, and analyse both sexes with sex in the model (sex as a biological variable).

Check what an AI assistant ran

1. The assistant tested every measure and reported the ones with p < 0.05. Ask which outcome was primary, and for the correction applied to the rest.
2. The assistant called fewer open-arm entries “more anxiety” without checking total entries or distance. Ask for the activity measures and the percentage measures.
3. The assistant built a composite after seeing which measures differed. Ask for a composite defined in advance.
4. The assistant treated two tests on the same mouse as independent samples. Ask for one row per mouse.

Report it

Anxiety-like behaviour was tested in the elevated plus maze ([5] min) and the open field ([10] min) in [10] wild-type and [10] knockout mice, [in that order, at the same time of day], with automated tracking. The primary outcome, chosen before testing, was the percentage of time in the open arms; the [4] secondary anxiety measures were compared with Welch t-tests and Holm’s correction for the familywise error rate, and distance travelled and closed-arm entries were reported as activity measures (R [4.3.3]).

In the constructed example, which has no effect built in, the knockout did not clearly change the percentage of time in the open arms (difference [−3.1] percentage points, 95% CI [−13.7] to [7.5]; p = [0.54]; n = [10] per genotype). Distance travelled was similar ([30.7] vs [29.6] m; p = [0.70]); closed-arm entries were higher in knockouts ([18.3] vs [12.3]; p = [0.06]), so a difference in activity remains possible.

Replace the bracketed values with your own.

References

• Pellow S, Chopin P, File SE, Briley M (1985). Validation of open:closed arm entries in an elevated plus-maze as a measure of anxiety in the rat. Journal of Neuroscience Methods 14:149–167. doi:10.1016/0165-0270(85)90031-7
• Walf AA, Frye CA (2007). The use of the elevated plus maze as an assay of anxiety-related behavior in rodents. Nature Protocols 2:322–328. doi:10.1038/nprot.2007.44
• Seibenhener ML, Wooten MC (2015). Use of the open field maze to measure locomotor and anxiety-like behavior in mice. Journal of Visualized Experiments (96):e52434. doi:10.3791/52434
• Percie du Sert N, Hurst V, Ahluwalia A, et al. (2020). The ARRIVE guidelines 2.0: updated guidelines for reporting animal research. PLOS Biology 18:e3000410. doi:10.1371/journal.pbio.3000410