BillEtAl2025: experimental results (generated)

Auto-generated from Linglib/Data/Experiments/BillEtAl2025.json by scripts/gen_experiments.py. Do not edit by hand: edit the JSON and re-run the generator.

An act-out comprehension study of the three conjunctive expressions of Georgian and of Hungarian, J, MU and J-MU, with children and adults. Each trial showed three objects and a sentence saying that two of them are on the table; the two measures were accuracy, whether the end state matched the exhaustified sentence, and sentence-played-n, how often the sentence was replayed. Tables 1, 2, 4 and 5 print the likelihood-ratio tests of the fixed effects, Table 3 the Tukey follow-up contrasts among the Georgian sentence types, and footnote 12 the kinds of error the Georgian children made.

Raw data

• https://doi.org/10.5281/zenodo.15225998: materials, trial-level data and analysis scripts of both experiments
• https://doi.org/10.17605/OSF.IO/VE9N8: preregistration of the Georgian experiment
• https://doi.org/10.17605/OSF.IO/29UFG: preregistration of the Hungarian experiment

References

• [BGD+25]

inductive BillEtAl2025.Language : Type

The language of an experiment.

• georgian : Language

  Georgian: Georgian, §3.1

• hungarian : Language

  Hungarian: Hungarian, §3.2

@[instance_reducible]

instance BillEtAl2025.instDecidableEqLanguage : DecidableEq Language

Equations

• BillEtAl2025.instDecidableEqLanguage x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprLanguage.repr : Language → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprLanguage : Repr Language

Equations

• BillEtAl2025.instReprLanguage = { reprPrec := BillEtAl2025.instReprLanguage.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeLanguage : Fintype Language

Equations

• BillEtAl2025.instFintypeLanguage = { elems := { val := ↑BillEtAl2025.Language.enumList, nodup := BillEtAl2025.Language.enumList_nodup }, complete := BillEtAl2025.instFintypeLanguage._proof_1 }

inductive BillEtAl2025.Group : Type

The participant group, the fixed effect group.

• adult : Group

  Adult: adults

• child : Group

  Child: children

@[instance_reducible]

instance BillEtAl2025.instDecidableEqGroup : DecidableEq Group

Equations

• BillEtAl2025.instDecidableEqGroup x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprGroup.repr : Group → ℕ → Std.Format

Equations

• BillEtAl2025.instReprGroup.repr BillEtAl2025.Group.adult prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Group.adult")).group prec✝
• BillEtAl2025.instReprGroup.repr BillEtAl2025.Group.child prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Group.child")).group prec✝

@[instance_reducible]

instance BillEtAl2025.instReprGroup : Repr Group

Equations

• BillEtAl2025.instReprGroup = { reprPrec := BillEtAl2025.instReprGroup.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeGroup : Fintype Group

Equations

• BillEtAl2025.instFintypeGroup = { elems := { val := ↑BillEtAl2025.Group.enumList, nodup := BillEtAl2025.Group.enumList_nodup }, complete := BillEtAl2025.instFintypeGroup._proof_1 }

inductive BillEtAl2025.Sentence : Type

The sentence type, the fixed effect sentence-type.

• j : Sentence

  j: only a J particle, (5a) and (6a)

• mu : Sentence

  mu: only MU particles, (5b) and (6b)

• jMu : Sentence

  j-mu: a J particle and two MU particles, (5c) and (6c)

@[instance_reducible]

instance BillEtAl2025.instDecidableEqSentence : DecidableEq Sentence

Equations

• BillEtAl2025.instDecidableEqSentence x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance BillEtAl2025.instReprSentence : Repr Sentence

Equations

• BillEtAl2025.instReprSentence = { reprPrec := BillEtAl2025.instReprSentence.repr }

def BillEtAl2025.instReprSentence.repr : Sentence → ℕ → Std.Format

Equations

• BillEtAl2025.instReprSentence.repr BillEtAl2025.Sentence.j prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Sentence.j")).group prec✝
• BillEtAl2025.instReprSentence.repr BillEtAl2025.Sentence.mu prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Sentence.mu")).group prec✝
• BillEtAl2025.instReprSentence.repr BillEtAl2025.Sentence.jMu prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Sentence.jMu")).group prec✝

@[instance_reducible]

instance BillEtAl2025.instFintypeSentence : Fintype Sentence

Equations

• BillEtAl2025.instFintypeSentence = { elems := { val := ↑BillEtAl2025.Sentence.enumList, nodup := BillEtAl2025.Sentence.enumList_nodup }, complete := BillEtAl2025.instFintypeSentence._proof_1 }

inductive BillEtAl2025.Measure : Type

The response variable.

• accuracy : Measure

  accuracy: whether the end state matched the exhaustified sentence

• playedN : Measure

  sentence-played-n: how many times the sentence was played, log-transformed, over the responses satisfying the basic truth conditions

@[instance_reducible]

instance BillEtAl2025.instDecidableEqMeasure : DecidableEq Measure

Equations

• BillEtAl2025.instDecidableEqMeasure x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprMeasure.repr : Measure → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprMeasure : Repr Measure

Equations

• BillEtAl2025.instReprMeasure = { reprPrec := BillEtAl2025.instReprMeasure.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeMeasure : Fintype Measure

Equations

• BillEtAl2025.instFintypeMeasure = { elems := { val := ↑BillEtAl2025.Measure.enumList, nodup := BillEtAl2025.Measure.enumList_nodup }, complete := BillEtAl2025.instFintypeMeasure._proof_1 }

inductive BillEtAl2025.Effect : Type

A fixed effect of the mixed-effects models.

• group : Effect

  group: adult or child

• sentence : Effect

  sentence: the sentence type

• interaction : Effect

  group:sentence: the interaction of group and sentence type

@[instance_reducible]

instance BillEtAl2025.instDecidableEqEffect : DecidableEq Effect

Equations

• BillEtAl2025.instDecidableEqEffect x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprEffect.repr : Effect → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.
• BillEtAl2025.instReprEffect.repr BillEtAl2025.Effect.group prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Effect.group")).group prec✝

@[instance_reducible]

instance BillEtAl2025.instReprEffect : Repr Effect

Equations

• BillEtAl2025.instReprEffect = { reprPrec := BillEtAl2025.instReprEffect.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeEffect : Fintype Effect

Equations

• BillEtAl2025.instFintypeEffect = { elems := { val := ↑BillEtAl2025.Effect.enumList, nodup := BillEtAl2025.Effect.enumList_nodup }, complete := BillEtAl2025.instFintypeEffect._proof_1 }

inductive BillEtAl2025.Contrast : Type

A pairwise contrast between sentence types, in the paper's order and orientation.

• jVsJMu : Contrast

  j vs. j-mu: J against J-MU

• jVsMu : Contrast

  j vs. mu: J against MU

• jMuVsMu : Contrast

  j-mu vs. mu: J-MU against MU

@[instance_reducible]

instance BillEtAl2025.instDecidableEqContrast : DecidableEq Contrast

Equations

• BillEtAl2025.instDecidableEqContrast x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprContrast.repr : Contrast → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprContrast : Repr Contrast

Equations

• BillEtAl2025.instReprContrast = { reprPrec := BillEtAl2025.instReprContrast.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeContrast : Fintype Contrast

Equations

• BillEtAl2025.instFintypeContrast = { elems := { val := ↑BillEtAl2025.Contrast.enumList, nodup := BillEtAl2025.Contrast.enumList_nodup }, complete := BillEtAl2025.instFintypeContrast._proof_1 }

inductive BillEtAl2025.Bound : Type

How a p-value is printed.

• below : Bound

  <: as an upper bound

• exact : Bound

  =: as a value

@[instance_reducible]

instance BillEtAl2025.instDecidableEqBound : DecidableEq Bound

Equations

• BillEtAl2025.instDecidableEqBound x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprBound.repr : Bound → ℕ → Std.Format

Equations

• BillEtAl2025.instReprBound.repr BillEtAl2025.Bound.below prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Bound.below")).group prec✝
• BillEtAl2025.instReprBound.repr BillEtAl2025.Bound.exact prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Bound.exact")).group prec✝

@[instance_reducible]

instance BillEtAl2025.instReprBound : Repr Bound

Equations

• BillEtAl2025.instReprBound = { reprPrec := BillEtAl2025.instReprBound.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeBound : Fintype Bound

Equations

• BillEtAl2025.instFintypeBound = { elems := { val := ↑BillEtAl2025.Bound.enumList, nodup := BillEtAl2025.Bound.enumList_nodup }, complete := BillEtAl2025.instFintypeBound._proof_1 }

inductive BillEtAl2025.Mark : Type

Whether the authors star the p-value.

• starred : Mark

  *: starred

• plain : Mark

  none: not starred

@[instance_reducible]

instance BillEtAl2025.instDecidableEqMark : DecidableEq Mark

Equations

• BillEtAl2025.instDecidableEqMark x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprMark.repr : Mark → ℕ → Std.Format

Equations

• BillEtAl2025.instReprMark.repr BillEtAl2025.Mark.starred prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Mark.starred")).group prec✝
• BillEtAl2025.instReprMark.repr BillEtAl2025.Mark.plain prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "BillEtAl2025.Mark.plain")).group prec✝

@[instance_reducible]

instance BillEtAl2025.instReprMark : Repr Mark

Equations

• BillEtAl2025.instReprMark = { reprPrec := BillEtAl2025.instReprMark.repr }

@[instance_reducible]

instance BillEtAl2025.instFintypeMark : Fintype Mark

Equations

• BillEtAl2025.instFintypeMark = { elems := { val := ↑BillEtAl2025.Mark.enumList, nodup := BillEtAl2025.Mark.enumList_nodup }, complete := BillEtAl2025.instFintypeMark._proof_1 }

inductive BillEtAl2025.ErrorKind : Type

The kinds of inaccurate end state among the Georgian children's responses, footnote 12.

• unmentioned : ErrorKind

  unmentioned objects: an unmentioned object was placed on the table

• oneMentioned : ErrorKind

  only one of the mentioned objects: only one of the two mentioned objects was placed on the table

• neitherMentioned : ErrorKind

  neither of the mentioned objects: neither mentioned object was placed on the table

@[instance_reducible]

instance BillEtAl2025.instDecidableEqErrorKind : DecidableEq ErrorKind

Equations

• BillEtAl2025.instDecidableEqErrorKind x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance BillEtAl2025.instReprErrorKind : Repr ErrorKind

Equations

• BillEtAl2025.instReprErrorKind = { reprPrec := BillEtAl2025.instReprErrorKind.repr }

def BillEtAl2025.instReprErrorKind.repr : ErrorKind → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instFintypeErrorKind : Fintype ErrorKind

Equations

• One or more equations did not get rendered due to their size.

def BillEtAl2025.objectsPerTrial : ℕ

The objects shown in a trial, of which the sentence mentions two. (§2.2, 5:5; checked against the page images.)

Equations

• BillEtAl2025.objectsPerTrial = 3

def BillEtAl2025.startingPictures : ℕ

The starting pictures: none, one or both mentioned objects already on the table. (§2.3, Fig. 3, 5:6; checked against the PDF text layer only.)

Equations

• BillEtAl2025.startingPictures = 3

def BillEtAl2025.versionsPerPicture : ℕ

The versions of each starting picture for each sentence type. (§2.3, 5:7; checked against the page images.)

Equations

• BillEtAl2025.versionsPerPicture = 2

def BillEtAl2025.items : ℕ

The experimental items, six per sentence type. (§2.3, 5:7; checked against the page images.)

Equations

• BillEtAl2025.items = 18

def BillEtAl2025.removedItems : ℕ

Item 2, removed from both datasets because two objects of its picture looked like cakes. (§3.1, 5:8; §3.2, 5:12; checked against the PDF text layer only.)

Equations

• BillEtAl2025.removedItems = 1

def BillEtAl2025.childErrors : ℕ

The inaccurate responses of the Georgian children. (fn. 12, 5:14; checked against the page images.)

Equations

• BillEtAl2025.childErrors = 103

structure BillEtAl2025.Participants : Type

A row of §2.1, 5:5: the participants of each experiment by group.

• count : ℕ

  The number of participants.

@[instance_reducible]

instance BillEtAl2025.instDecidableEqParticipants : DecidableEq Participants

Equations

• BillEtAl2025.instDecidableEqParticipants = BillEtAl2025.instDecidableEqParticipants.decEq

def BillEtAl2025.instDecidableEqParticipants.decEq (x✝ x✝¹ : Participants) : Decidable (x✝ = x✝¹)

Equations

• BillEtAl2025.instDecidableEqParticipants.decEq { count := a } { count := b } = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprParticipants.repr : Participants → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprParticipants : Repr Participants

Equations

• BillEtAl2025.instReprParticipants = { reprPrec := BillEtAl2025.instReprParticipants.repr }

def BillEtAl2025.participants : Language → Group → Participants

The cells of §2.1, 5:5, by language and group; checked against the page images.

Equations

• BillEtAl2025.participants BillEtAl2025.Language.georgian BillEtAl2025.Group.child = { count := 31 }
• BillEtAl2025.participants BillEtAl2025.Language.georgian BillEtAl2025.Group.adult = { count := 41 }
• BillEtAl2025.participants BillEtAl2025.Language.hungarian BillEtAl2025.Group.child = { count := 25 }
• BillEtAl2025.participants BillEtAl2025.Language.hungarian BillEtAl2025.Group.adult = { count := 30 }

structure BillEtAl2025.PlayedPoints : Type

A row of §3.1.2, 5:10: the Georgian data points entering the sentence-played-n analysis, the responses satisfying the basic truth conditions of the sentence.

• count : ℕ

  The number of data points.

@[instance_reducible]

instance BillEtAl2025.instDecidableEqPlayedPoints : DecidableEq PlayedPoints

Equations

• BillEtAl2025.instDecidableEqPlayedPoints = BillEtAl2025.instDecidableEqPlayedPoints.decEq

def BillEtAl2025.instDecidableEqPlayedPoints.decEq (x✝ x✝¹ : PlayedPoints) : Decidable (x✝ = x✝¹)

Equations

• BillEtAl2025.instDecidableEqPlayedPoints.decEq { count := a } { count := b } = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

def BillEtAl2025.instReprPlayedPoints.repr : PlayedPoints → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprPlayedPoints : Repr PlayedPoints

Equations

• BillEtAl2025.instReprPlayedPoints = { reprPrec := BillEtAl2025.instReprPlayedPoints.repr }

def BillEtAl2025.playedPoints : Group → PlayedPoints

The cells of §3.1.2, 5:10, by group; checked against the page images.

Equations

• BillEtAl2025.playedPoints BillEtAl2025.Group.adult = { count := 689 }
• BillEtAl2025.playedPoints BillEtAl2025.Group.child = { count := 499 }

structure BillEtAl2025.Lrt : Type

A row of Tables 1 and 2, 5:9 and 5:11 (Georgian); Tables 4 and 5, 5:13 (Hungarian): a likelihood-ratio test of a fixed effect of the model of a response measure, against the model without it.

• df : ℕ

  The degrees of freedom.

• chiSq : Data.Experiments.Decimal

  The chi-square statistic.

• bound : Bound

  How the p-value is printed.

• p : Data.Experiments.Decimal

  The p-value.

• mark : Mark

  Whether the authors star the p-value.

@[instance_reducible]

instance BillEtAl2025.instDecidableEqLrt : DecidableEq Lrt

Equations

• BillEtAl2025.instDecidableEqLrt = BillEtAl2025.instDecidableEqLrt.decEq

def BillEtAl2025.instDecidableEqLrt.decEq (x✝ x✝¹ : Lrt) : Decidable (x✝ = x✝¹)

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprLrt : Repr Lrt

Equations

• BillEtAl2025.instReprLrt = { reprPrec := BillEtAl2025.instReprLrt.repr }

def BillEtAl2025.instReprLrt.repr : Lrt → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def BillEtAl2025.lrt : Language → Measure → Effect → Lrt

The cells of Tables 1 and 2, 5:9 and 5:11 (Georgian); Tables 4 and 5, 5:13 (Hungarian), by language and measure and effect; checked against the page images.

Equations

• One or more equations did not get rendered due to their size.

structure BillEtAl2025.ContrastTest : Type

A row of Table 3, 5:11: a Tukey-adjusted follow-up contrast between two sentence types in the Georgian sentence-played-n model, on the log scale: a negative estimate means the first sentence type was played less.

• estimate : Data.Experiments.Decimal

  The estimated difference, first minus second, on the log scale.

• se : Data.Experiments.Decimal

  The standard error.

• df : ℕ

  The degrees of freedom.

• t : Data.Experiments.Decimal

  The t ratio.

• bound : Bound

  How the p-value is printed.

• p : Data.Experiments.Decimal

  The Tukey-adjusted p-value.

• mark : Mark

  Whether the authors star the p-value.

def BillEtAl2025.instDecidableEqContrastTest.decEq (x✝ x✝¹ : ContrastTest) : Decidable (x✝ = x✝¹)

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instDecidableEqContrastTest : DecidableEq ContrastTest

Equations

• BillEtAl2025.instDecidableEqContrastTest = BillEtAl2025.instDecidableEqContrastTest.decEq

@[instance_reducible]

instance BillEtAl2025.instReprContrastTest : Repr ContrastTest

Equations

• BillEtAl2025.instReprContrastTest = { reprPrec := BillEtAl2025.instReprContrastTest.repr }

def BillEtAl2025.instReprContrastTest.repr : ContrastTest → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def BillEtAl2025.contrasts : Group → Contrast → ContrastTest

The cells of Table 3, 5:11, by group and contrast; checked against the page images.

Equations

• One or more equations did not get rendered due to their size.

structure BillEtAl2025.ErrorCount : Type

A row of fn. 12, 5:14: the Georgian children's inaccurate responses by kind, with the percentage of all 103 errors as printed.

• count : ℕ

  The number of errors of the kind.

• percent : Data.Experiments.Decimal

  The printed percentage of all errors.

@[instance_reducible]

instance BillEtAl2025.instDecidableEqErrorCount : DecidableEq ErrorCount

Equations

• BillEtAl2025.instDecidableEqErrorCount = BillEtAl2025.instDecidableEqErrorCount.decEq

def BillEtAl2025.instDecidableEqErrorCount.decEq (x✝ x✝¹ : ErrorCount) : Decidable (x✝ = x✝¹)

Equations

• BillEtAl2025.instDecidableEqErrorCount.decEq { count := a, percent := a_1 } { count := b, percent := b_1 } = if h : a = b then h ▸ if h : a_1 = b_1 then h ▸ isTrue ⋯ else isFalse ⋯ else isFalse ⋯

def BillEtAl2025.instReprErrorCount.repr : ErrorCount → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance BillEtAl2025.instReprErrorCount : Repr ErrorCount

Equations

• BillEtAl2025.instReprErrorCount = { reprPrec := BillEtAl2025.instReprErrorCount.repr }

def BillEtAl2025.childErrorKinds : ErrorKind → ErrorCount

The cells of fn. 12, 5:14, by kind; checked against the page images.

Equations

• BillEtAl2025.childErrorKinds BillEtAl2025.ErrorKind.unmentioned = { count := 75, percent := { mantissa := 73, exponent := 0 } }
• BillEtAl2025.childErrorKinds BillEtAl2025.ErrorKind.oneMentioned = { count := 21, percent := { mantissa := 20, exponent := 0 } }
• BillEtAl2025.childErrorKinds BillEtAl2025.ErrorKind.neitherMentioned = { count := 7, percent := { mantissa := 7, exponent := 0 } }