contrast / pairs

Linear contrasts and pairwise comparisons on estimated marginal means.

contrast() applies a set of linear contrasts to an emmeans result. pairs() is a convenience wrapper for all pairwise differences with Tukey HSD adjustment, matching R’s pairs() ergonomics.

contrast(emm, method='pairwise', adjust='none')

Apply linear contrasts to estimated marginal means.

Parameters:

• emm – An EmmResult returned by emmeans().

• method – How to form the contrasts:

  'pairwise'

  All pairwise differences i - j for i < j (alphabetical level order). Produces n*(n-1)//2 rows.

  'trt.vs.ctrl'

  Each non-first level minus the first (control) level. Produces n-1 rows.

  list of np.ndarray

  Each array is a contrast vector of length n (number of EMM rows). Generic names contrast1, contrast2, … are used.

  dict mapping str → np.ndarray

  Same as a list but uses the dict keys as contrast names.

• adjust – Multiple-comparison p-value adjustment: 'none' (default), 'bonferroni', 'holm', 'fdr', or 'tukey'.

Return type:

Any

Returns:

pandas.DataFrame – Columns: ["contrast", "estimate", "SE", "df", "t.ratio", "p.value"].

Raises:

ValueError – If method is a string other than 'pairwise' or 'trt.vs.ctrl', or if adjust is not a recognised method.

Parameters:

• emm (EmmResult)

• method (str | list[ndarray] | dict[str, ndarray])

• adjust (str)

Examples

>>> emm = interlace.emmeans(result, specs="treatment")
>>> interlace.contrast(emm, method="pairwise")

pairs(emm, adjust='tukey')

All pairwise comparisons of estimated marginal means.

Convenience wrapper for contrast(emm, method='pairwise', adjust=adjust). Matches R’s pairs() ergonomics with Tukey HSD adjustment by default.

Parameters:

• emm – An EmmResult returned by emmeans().

• adjust – Multiple-comparison adjustment (default 'tukey'). Any value accepted by contrast() is valid.

Return type:

Any

Returns:

pandas.DataFrame – Columns: ["contrast", "estimate", "SE", "df", "t.ratio", "p.value"].

Parameters:

• emm (EmmResult)

• adjust (str)

Examples

>>> emm = interlace.emmeans(result, specs="treatment")
>>> interlace.pairs(emm)

Built-in contrast methods

method	Description	Rows produced
'pairwise'	All pairwise differences i − j (alphabetical order)	n*(n-1)//2
'trt.vs.ctrl'	Each non-first level minus the first (control) level	n-1
list of np.ndarray	Custom contrast vectors of length n (number of EMM rows)	one per vector
dict str → np.ndarray	Same as list, using the dict keys as contrast names	one per entry

p-value adjustment methods

adjust	Method
'none'	No adjustment (raw p-values)
'bonferroni'	Bonferroni correction (p * n)
'holm'	Step-down Bonferroni (Holm 1979)
'fdr'	Benjamini-Hochberg false discovery rate
'tukey'	Tukey HSD via the studentized range distribution

Returned columns

Column	Description
contrast	Name of the contrast (e.g. "high - control")
estimate	Contrast estimate
SE	Standard error
df	Satterthwaite denominator degrees of freedom
t.ratio	t-statistic (estimate / SE)
p.value	Adjusted p-value

Examples

Pairwise comparisons (no adjustment)

import interlace

result = interlace.fit("rt ~ condition", data=df, groups=["subject", "item"])
emm = interlace.emmeans(result, specs="condition")

pw = interlace.contrast(emm, method="pairwise")
print(pw)
#         contrast  estimate    SE    df  t.ratio  p.value
# 0  high - control    46.4  8.3  41.2     5.59   0.0001

All pairwise with Tukey HSD via pairs()

pw_tukey = interlace.pairs(emm)           # adjust='tukey' by default
pw_bonf  = interlace.pairs(emm, adjust="bonferroni")

Treatment vs. control

# First level (alphabetically) is treated as control
tvc = interlace.contrast(emm, method="trt.vs.ctrl", adjust="holm")

Custom contrast vectors

import numpy as np

# 3-level factor: [control, low, high]
# Custom: average of treatments vs. control
custom = interlace.contrast(emm, method={
    "avg(low,high) - control": np.array([-1.0, 0.5, 0.5]),
})

See also

• emmeans — computing the EMMs that contrast operates on

• Anova — omnibus F-tests for fixed effects