ClausWalch2024: experimental results (generated)

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Three web-based experiments in German on how numeral modification bears on framing effects. Each offers a risky-choice framing scenario (a war zone with 600 lives at stake and a sure and a risky response plan, after Mandel 2014; participants choose a plan) or an attribute framing scenario (a project team asking for more funding after 50 projects, after Duchon et al. 1989; participants approve or reject), with the sure outcome or the team's record stated in a positive frame (lives saved, successful projects) or a negative one (lives lost, unsuccessful projects). Experiment 1 modifies the numerals with genau 'exactly', frame within subjects, both scenarios. Experiments 2 (risky choice) and 3 (attribute) cross frame, within subjects, with the modifier of the critical numeral, bis zu 'up to' or höchstens 'at most', between subjects. The tables print the share of sure-option choices or of approvals per cell; the generalized linear mixed models are reported in the text.

References

• [CW24]

inductive ClausWalch2024.Frame : Type

How the outcome is stated.

• positive : Frame

  Positive: as lives saved or successful projects

• negative : Frame

  Negative: as lives lost or unsuccessful projects

@[instance_reducible]

instance ClausWalch2024.instDecidableEqFrame : DecidableEq Frame

Equations

• ClausWalch2024.instDecidableEqFrame x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def ClausWalch2024.instReprFrame.repr : Frame → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprFrame : Repr Frame

Equations

• ClausWalch2024.instReprFrame = { reprPrec := ClausWalch2024.instReprFrame.repr }

@[instance_reducible]

instance ClausWalch2024.instFintypeFrame : Fintype Frame

Equations

• ClausWalch2024.instFintypeFrame = { elems := { val := ↑ClausWalch2024.Frame.enumList, nodup := ClausWalch2024.Frame.enumList_nodup }, complete := ClausWalch2024.instFintypeFrame._proof_1 }

inductive ClausWalch2024.Modifier : Type

The upper-bounding modifier of the critical numeral in Experiments 2 and 3.

• bisZu : Modifier

  Bis zu 'up to': the directional modifier bis zu

• hoechstens : Modifier

  Höchstens 'at most': the superlative modifier höchstens

@[instance_reducible]

instance ClausWalch2024.instDecidableEqModifier : DecidableEq Modifier

Equations

• ClausWalch2024.instDecidableEqModifier x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def ClausWalch2024.instReprModifier.repr : Modifier → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprModifier : Repr Modifier

Equations

• ClausWalch2024.instReprModifier = { reprPrec := ClausWalch2024.instReprModifier.repr }

@[instance_reducible]

instance ClausWalch2024.instFintypeModifier : Fintype Modifier

Equations

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

inductive ClausWalch2024.Experiment : Type

The experiment, by scenario.

• exp1RiskyChoice : Experiment

  Experiment 1, risky-choice framing: genau, the risky-choice scenario

• exp1Attribute : Experiment

  Experiment 1, attribute framing: genau, the attribute framing scenario

• exp2 : Experiment

  Experiment 2: bis zu and höchstens, the risky-choice scenario

• exp3 : Experiment

  Experiment 3: bis zu and höchstens, the attribute framing scenario

@[instance_reducible]

instance ClausWalch2024.instDecidableEqExperiment : DecidableEq Experiment

Equations

• ClausWalch2024.instDecidableEqExperiment x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance ClausWalch2024.instReprExperiment : Repr Experiment

Equations

• ClausWalch2024.instReprExperiment = { reprPrec := ClausWalch2024.instReprExperiment.repr }

def ClausWalch2024.instReprExperiment.repr : Experiment → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instFintypeExperiment : Fintype Experiment

Equations

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

inductive ClausWalch2024.Effect : Type

A fixed effect of the mixed model, with deviation coding (+.5, -.5).

• frame : Effect

  FRAME: the main effect of frame

• modifier : Effect

  MODIFIER: the main effect of modifier

• interaction : Effect

  MODIFIER x FRAME: the interaction of modifier and frame

@[instance_reducible]

instance ClausWalch2024.instDecidableEqEffect : DecidableEq Effect

Equations

• ClausWalch2024.instDecidableEqEffect x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def ClausWalch2024.instReprEffect.repr : Effect → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprEffect : Repr Effect

Equations

• ClausWalch2024.instReprEffect = { reprPrec := ClausWalch2024.instReprEffect.repr }

@[instance_reducible]

instance ClausWalch2024.instFintypeEffect : Fintype Effect

Equations

• ClausWalch2024.instFintypeEffect = { elems := { val := ↑ClausWalch2024.Effect.enumList, nodup := ClausWalch2024.Effect.enumList_nodup }, complete := ClausWalch2024.instFintypeEffect._proof_1 }

inductive ClausWalch2024.Bound : Type

How a p-value is printed.

• below : Bound

  <: as an upper bound

• exact : Bound

  =: as a value

@[instance_reducible]

instance ClausWalch2024.instDecidableEqBound : DecidableEq Bound

Equations

• ClausWalch2024.instDecidableEqBound x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def ClausWalch2024.instReprBound.repr : Bound → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprBound : Repr Bound

Equations

• ClausWalch2024.instReprBound = { reprPrec := ClausWalch2024.instReprBound.repr }

@[instance_reducible]

instance ClausWalch2024.instFintypeBound : Fintype Bound

Equations

• ClausWalch2024.instFintypeBound = { elems := { val := ↑ClausWalch2024.Bound.enumList, nodup := ClausWalch2024.Bound.enumList_nodup }, complete := ClausWalch2024.instFintypeBound._proof_1 }

def ClausWalch2024.livesAtStake : ℕ

The lives at stake in the risky-choice scenario. (Experiment 1, Materials and (3), p. 4146; checked against the page images.)

Equations

• ClausWalch2024.livesAtStake = 600

def ClausWalch2024.livesSaved : ℕ

The lives the sure option saves in the positive frame. ((3), p. 4146; checked against the page images.)

Equations

• ClausWalch2024.livesSaved = 200

def ClausWalch2024.livesLost : ℕ

The lives lost under the sure option in the negative frame. ((3), p. 4146; checked against the page images.)

Equations

• ClausWalch2024.livesLost = 400

def ClausWalch2024.projects : ℕ

The team's last projects in the attribute framing scenario. ((4), p. 4146; checked against the page images.)

Equations

• ClausWalch2024.projects = 50

def ClausWalch2024.successfulProjects : ℕ

The successful projects, in the positive frame. ((4), p. 4146; checked against the page images.)

Equations

• ClausWalch2024.successfulProjects = 30

def ClausWalch2024.unsuccessfulProjects : ℕ

The unsuccessful projects, in the negative frame. ((4), p. 4146; checked against the page images.)

Equations

• ClausWalch2024.unsuccessfulProjects = 20

def ClausWalch2024.exp1Participants : ℕ

The participants analysed in Experiment 1. (Experiment 1, Participants, p. 4146; checked against the page images.)

Equations

• ClausWalch2024.exp1Participants = 52

def ClausWalch2024.exp2Participants : ℕ

The participants analysed in Experiment 2. (Experiment 2, Participants, p. 4147; checked against the page images.)

Equations

• ClausWalch2024.exp2Participants = 101

def ClausWalch2024.exp3Participants : ℕ

The participants analysed in Experiment 3. (Experiment 3, Participants, p. 4148; checked against the page images.)

Equations

• ClausWalch2024.exp3Participants = 94

structure ClausWalch2024.SureChoices1 : Type

A row of Table 1, p. 4147: the proportion of sure-option choices in the risky-choice framing trials of Experiment 1, by frame.

• percent : Data.Experiments.Decimal

  The percentage of sure-option choices.

@[instance_reducible]

instance ClausWalch2024.instDecidableEqSureChoices1 : DecidableEq SureChoices1

Equations

• ClausWalch2024.instDecidableEqSureChoices1 = ClausWalch2024.instDecidableEqSureChoices1.decEq

def ClausWalch2024.instDecidableEqSureChoices1.decEq (x✝ x✝¹ : SureChoices1) : Decidable (x✝ = x✝¹)

Equations

• ClausWalch2024.instDecidableEqSureChoices1.decEq { percent := a } { percent := b } = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance ClausWalch2024.instReprSureChoices1 : Repr SureChoices1

Equations

• ClausWalch2024.instReprSureChoices1 = { reprPrec := ClausWalch2024.instReprSureChoices1.repr }

def ClausWalch2024.instReprSureChoices1.repr : SureChoices1 → ℕ → Std.Format

Equations

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

def ClausWalch2024.table1 : Frame → SureChoices1

The cells of Table 1, p. 4147, by frame; checked against the page images.

Equations

• ClausWalch2024.table1 ClausWalch2024.Frame.positive = { percent := { mantissa := 519, exponent := 1 } }
• ClausWalch2024.table1 ClausWalch2024.Frame.negative = { percent := { mantissa := 346, exponent := 1 } }

structure ClausWalch2024.Approvals2 : Type

A row of Table 2, p. 4147: the proportion of approvals in the attribute framing trials of Experiment 1, by frame.

• percent : Data.Experiments.Decimal

  The percentage of approvals.

def ClausWalch2024.instDecidableEqApprovals2.decEq (x✝ x✝¹ : Approvals2) : Decidable (x✝ = x✝¹)

Equations

• ClausWalch2024.instDecidableEqApprovals2.decEq { percent := a } { percent := b } = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance ClausWalch2024.instDecidableEqApprovals2 : DecidableEq Approvals2

Equations

• ClausWalch2024.instDecidableEqApprovals2 = ClausWalch2024.instDecidableEqApprovals2.decEq

@[instance_reducible]

instance ClausWalch2024.instReprApprovals2 : Repr Approvals2

Equations

• ClausWalch2024.instReprApprovals2 = { reprPrec := ClausWalch2024.instReprApprovals2.repr }

def ClausWalch2024.instReprApprovals2.repr : Approvals2 → ℕ → Std.Format

Equations

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

def ClausWalch2024.table2 : Frame → Approvals2

The cells of Table 2, p. 4147, by frame; checked against the page images.

Equations

• ClausWalch2024.table2 ClausWalch2024.Frame.positive = { percent := { mantissa := 923, exponent := 1 } }
• ClausWalch2024.table2 ClausWalch2024.Frame.negative = { percent := { mantissa := 654, exponent := 1 } }

structure ClausWalch2024.SureChoices3 : Type

A row of Table 3, p. 4148: the proportion of sure-option choices in the risky-choice framing trials of Experiment 2, by modifier and frame.

• percent : Data.Experiments.Decimal

  The percentage of sure-option choices.

def ClausWalch2024.instDecidableEqSureChoices3.decEq (x✝ x✝¹ : SureChoices3) : Decidable (x✝ = x✝¹)

Equations

• ClausWalch2024.instDecidableEqSureChoices3.decEq { percent := a } { percent := b } = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance ClausWalch2024.instDecidableEqSureChoices3 : DecidableEq SureChoices3

Equations

• ClausWalch2024.instDecidableEqSureChoices3 = ClausWalch2024.instDecidableEqSureChoices3.decEq

def ClausWalch2024.instReprSureChoices3.repr : SureChoices3 → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprSureChoices3 : Repr SureChoices3

Equations

• ClausWalch2024.instReprSureChoices3 = { reprPrec := ClausWalch2024.instReprSureChoices3.repr }

def ClausWalch2024.table3 : Modifier → Frame → SureChoices3

The cells of Table 3, p. 4148, by modifier and frame; checked against the page images.

Equations

• ClausWalch2024.table3 ClausWalch2024.Modifier.bisZu ClausWalch2024.Frame.positive = { percent := { mantissa := 592, exponent := 1 } }
• ClausWalch2024.table3 ClausWalch2024.Modifier.bisZu ClausWalch2024.Frame.negative = { percent := { mantissa := 449, exponent := 1 } }
• ClausWalch2024.table3 ClausWalch2024.Modifier.hoechstens ClausWalch2024.Frame.positive = { percent := { mantissa := 423, exponent := 1 } }
• ClausWalch2024.table3 ClausWalch2024.Modifier.hoechstens ClausWalch2024.Frame.negative = { percent := { mantissa := 558, exponent := 1 } }

structure ClausWalch2024.Approvals4 : Type

A row of Table 4, p. 4148: the proportion of approvals in the attribute framing trials of Experiment 3, by modifier and frame.

• percent : Data.Experiments.Decimal

  The percentage of approvals.

def ClausWalch2024.instDecidableEqApprovals4.decEq (x✝ x✝¹ : Approvals4) : Decidable (x✝ = x✝¹)

Equations

• ClausWalch2024.instDecidableEqApprovals4.decEq { percent := a } { percent := b } = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance ClausWalch2024.instDecidableEqApprovals4 : DecidableEq Approvals4

Equations

• ClausWalch2024.instDecidableEqApprovals4 = ClausWalch2024.instDecidableEqApprovals4.decEq

def ClausWalch2024.instReprApprovals4.repr : Approvals4 → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprApprovals4 : Repr Approvals4

Equations

• ClausWalch2024.instReprApprovals4 = { reprPrec := ClausWalch2024.instReprApprovals4.repr }

def ClausWalch2024.table4 : Modifier → Frame → Approvals4

The cells of Table 4, p. 4148, by modifier and frame; checked against the page images.

Equations

• ClausWalch2024.table4 ClausWalch2024.Modifier.bisZu ClausWalch2024.Frame.positive = { percent := { mantissa := 889, exponent := 1 } }
• ClausWalch2024.table4 ClausWalch2024.Modifier.bisZu ClausWalch2024.Frame.negative = { percent := { mantissa := 689, exponent := 1 } }
• ClausWalch2024.table4 ClausWalch2024.Modifier.hoechstens ClausWalch2024.Frame.positive = { percent := { mantissa := 673, exponent := 1 } }
• ClausWalch2024.table4 ClausWalch2024.Modifier.hoechstens ClausWalch2024.Frame.negative = { percent := { mantissa := 714, exponent := 1 } }

structure ClausWalch2024.MixedModelEffect : Type

A row of Results and Discussion of Experiments 1–3, pp. 4146–4148: a fixed effect of the generalized linear mixed model (binomial logit, participants as random factor) fitted to an experiment's choices.

• experiment : Experiment

  The experiment and scenario.

• effect : Effect

  The fixed effect.

• b : Data.Experiments.Decimal

  The estimate.

• se : Data.Experiments.Decimal

  The standard error.

• z : Data.Experiments.Decimal

  The z statistic.

• bound : Bound

  How the p-value is printed.

• p : Data.Experiments.Decimal

  The p-value or its bound.

@[instance_reducible]

instance ClausWalch2024.instDecidableEqMixedModelEffect : DecidableEq MixedModelEffect

Equations

• ClausWalch2024.instDecidableEqMixedModelEffect = ClausWalch2024.instDecidableEqMixedModelEffect.decEq

def ClausWalch2024.instDecidableEqMixedModelEffect.decEq (x✝ x✝¹ : MixedModelEffect) : Decidable (x✝ = x✝¹)

Equations

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

def ClausWalch2024.instReprMixedModelEffect.repr : MixedModelEffect → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance ClausWalch2024.instReprMixedModelEffect : Repr MixedModelEffect

Equations

• ClausWalch2024.instReprMixedModelEffect = { reprPrec := ClausWalch2024.instReprMixedModelEffect.repr }

def ClausWalch2024.mixedModels : List MixedModelEffect

The 8 rows of Results and Discussion of Experiments 1–3, pp. 4146–4148, in the paper's order; checked against the page images.

Equations

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