1. Motivation

pairwiseLLM uses large language models (LLMs) to compare pairs of writing samples and decide which sample is better on a given trait (for example, Overall Quality).

If a prompt template systematically nudges the model toward the first or second position, then scores derived from these comparisons may be biased. This vignette documents how we:

• Designed and tested several prompt templates for positional bias
  
• Quantified both reverse-order consistency and preference for SAMPLE_1
  
• Recorded descriptive results for several historical provider configurations

The vignette also shows how to:

• Retrieve the tested templates from the package
  
• Inspect their full text
  
• Access summary statistics from the experiments

For basic function usage, see:

• Getting Started with pairwiseLLM

For advanced batch processing workflows, see:

• Advanced: Submitting and Polling Multiple Batches

2. Testing Process Summary

This section describes an archived 2025 experiment bundled with pairwiseLLM 1.3.0. The result artifact was added to the repository on 2025-12-10; the exact dates on which its provider calls ran were not recorded. It is not a catalog of currently available models. In particular, gemini-3-pro-preview is retired, and the old Together identifiers below are retained only to identify archived result rows.

At a high level, the testing pipeline works as follows:

1. Trait and samples

   • Choose a trait (here: "overall_quality") and obtain its description with trait_description().
   • Use example_writing_samples or your own dataset of writing samples.

2. Generate forward and reverse pairs

   • Use make_pairs() to generate all unordered pairs.
   • Use alternate_pair_order() to build a deterministic “forward” set.
   • Use sample_reverse_pairs() with reverse_pct = 1 to build a fully “reversed” set, where SAMPLE_1 and SAMPLE_2 are swapped for all pairs.

3. Prompt templates

   • Define multiple templates (e.g., "test1"–"test5") and register them in the template registry.
   • Each template is a text file shipped with the package and accessed via get_prompt_template("testX").

4. Batch calls to LLM providers

   • For each combination of:

     • Template (test1–test5)
     • Backend (Anthropic, Gemini, OpenAI, TogetherAI)
     • Historical model recorded in the bundled experiment
     • Thinking configuration ("no_thinking" vs "with_thinking", where applicable)
     • Direction (forward vs reverse)

   • Submit the forward and reverse pairs. You can do this using the package’s Batch API helpers (for large-scale jobs) or the live API wrapper submit_llm_pairs() with parallel = TRUE (for faster turnaround on smaller test sets).

   • Store responses as CSVs, including the model’s <BETTER_SAMPLE> decision and derived better_id.

5. Reverse-order consistency

   • Within each (template, backend, model, thinking) condition, compare:

     • The model’s decisions for a pair in the forward set
     • The decisions for the same pair in the reverse set (where positions are swapped)

   • Use compute_reverse_consistency() to compute:

     • prop_consistent: proportion of comparisons where reversing the order yields the same underlying winner.

6. Positional bias statistics

   • Use check_positional_bias() on the reverse-consistency results to quantify:

     • the descriptive proportion of valid forward and reverse outcomes where SAMPLE_1 is chosen as better; and
     • p_sample1_overall: the current paired exact test comparing inconsistent pairs where position 1 wins both presentations with those where position 2 wins both presentations.

7. Summarize and interpret

   • Aggregate the results across templates and models into a summary table.
   • Look for templates with:
     • High prop_consistent (close to 1).
     • prop_pos1 close to 0.5.
     • Directional preference estimates and their uncertainty, without treating a non-significant test as evidence that positional preference is absent.

In the sections below we show how to retrieve the templates, how they are intended to be used, and how to examine the summary statistics for the experiment.

3. Trait descriptions and custom traits

In the tests, we evaluated samples for overall quality.

td <- trait_description("overall_quality")
td
#> $name
#> [1] "Overall Quality"
#> 
#> $description
#> [1] "Overall quality of the writing, considering how well ideas are expressed,\nhow clearly the writing is organized, and how effective the language and\nconventions are."

In pairwiseLLM, every pairwise comparison evaluates writing samples on a trait — a specific dimension of writing quality, such as:

• Overall Quality
• Organization
• IRRC, an overall-writing rubric spanning prompt task, development of explanation, organization, and language use

The trait determines what the model should focus on when choosing which sample is better. Each trait has:

• a short name (e.g., "overall_quality")
• a human-readable name (e.g., "Overall Quality")
• a textual description used inside prompts

The function that supplies these definitions is:

trait_description(name, custom_name = NULL, custom_description = NULL)

trait_description("overall_quality")
trait_description("organization")
trait_description("IRRC")

$name         # human-friendly name
$description  # the textual rubric used in prompts

td <- trait_description("organization")
td$name
td$description

td <- trait_description("organization")

prompt <- build_prompt(
  template   = get_prompt_template("test1"),
  trait_name = td$name,
  trait_desc = td$description,
  text1      = sample1,
  text2      = sample2
)

td <- trait_description(
  custom_name        = "Clarity",
  custom_description = "Clarity refers to how easily a reader can understand the writer's ideas, wording, and structure."
)

td$name
#> [1] "Clarity"

td$description
#> [1] "Clarity refers to how easily ..."

prompt <- build_prompt(
  template   = get_prompt_template("test2"),
  trait_name = td$name,
  trait_desc = td$description,
  text1      = sample1,
  text2      = sample2
)

4. Example data used in tests

The positional-bias experiments in this vignette use the example_writing_samples dataset that ships with the package.

Each row represents a student writing sample and includes:

• an identifying ID,
• a text field containing the full written response.

Below we print the 20 writing samples included in the file.
This dataset provides a reproducible testing base; in real applications, you would use your own writing samples.

data("example_writing_samples", package = "pairwiseLLM")

# Inspect the structure
glimpse(example_writing_samples)
#> Rows: 20
#> Columns: 3
#> $ ID            <chr> "S01", "S02", "S03", "S04", "S05", "S06", "S07", "S08", …
#> $ text          <chr> "Writing assessment is hard. People write different thin…
#> $ quality_score <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1…

# Print the 20 samples (full text)
example_writing_samples |>
  kable(
    caption = "20 example writing samples included with pairwiseLLM."
  )

handwriting is bad or the grammar is wrong, and that makes it hard to give
a score.                                                                                                                                                                                                                                           |             4|

|S05 |Writing assessment is challenging because teachers must judge ideas, organization, grammar, and style all at once. Different raters may focus on different things. | 5| |S06 |It is difficult to assess writing because it is subjective. One teacher might like a creative style while another teacher wants a strict structure. This makes the scores unfair sometimes. | 6| |S07 |Writing assessment is difficult because writing is a complex skill. Raters must consider ideas, organization, style, and conventions, and these features do not always align. | 7| |S08 |A paper with strong ideas might have weak grammar, while another has flawless sentences but no clear argument. Deciding which one deserves a higher score is a major challenge in assessment. | 8| |S09 |Assessing writing is difficult because the construct is multidimensional. Even with detailed rubrics, raters interpret criteria differently, and their judgments can be influenced by fatigue or expectations. | 9| |S10 |The difficulty in writing assessment lies in consistency. Because raters bring their own background knowledge and preferences to the task, achieving high inter-rater reliability requires extensive training and calibration. | 10| |S11 |Writing assessment is difficult because we are trying to compress a rich, multi-dimensional performance into a single score. Raters must weigh content, organization, style, and mechanics, while also dealing with time pressure. | 11| |S12 |Evaluating writing is challenging because no rubric can fully capture what makes a text effective for a particular audience. Two essays might receive the same score for completely different reasons, obscuring the feedback loop. | 12| |S13 |Writing assessment is difficult because it is context-dependent. A style that works for a narrative is inappropriate for a report. Raters must constantly adjust their internal standard based on the specific purpose of the prompt. | 13| |S14 |The challenge of writing assessment is distinguishing between surface-level errors and deep structural flaws. Raters often over-penalize mechanical mistakes while missing more significant issues in logic or argumentation due to cognitive load. | 14| |S15 |Writing assessment is difficult because it sits at the intersection of measurement and interpretation. Raters must translate complex judgments about ideas, voice, and language into discrete rubric categories, often losing nuance in the process. | 15| |S16 |Assessing writing is inherently difficult because it requires balancing consistency with sensitivity. A rubric describes general qualities, but individual texts vary in genre and voice. Raters must decide if an unconventional choice is a mistake or a stylistic innovation. | 16| |S17 |Writing assessment is challenging because of the trade-off between validity and reliability. Highly standardized scoring protocols often strip away the subjective appreciation of voice and creativity, while holistic scoring captures the ‘whole’ but risks being unreliable. | 17| |S18 |The fundamental difficulty in writing assessment is cognitive complexity. The rater must construct a mental model of the writer’s argument while simultaneously evaluating against specific criteria. This dual processing makes the task prone to bias and halo effects. | 18| |S19 |Writing assessment is difficult because it asks us to quantify something fundamentally qualitative. To evaluate a piece of writing, raters integrate judgments about content, organization, and style, while also considering task demands. Scores often reflect both the text and the rater’s implicit theory of writing. | 19| |S20 |Writing assessment is inherently problematic because it attempts to standardize a socially situated act. The assessment process often decontextualizes the writing, stripping it of its communicative purpose. Consequently, the score represents a construct of ‘school writing’ rather than authentic communication, creating a validity gap that simple psychometrics cannot resolve. | 20|

5. Built-in prompt templates

The tested templates are stored as plain-text files in the package and exposed via the template registry. You can retrieve them with get_prompt_template():

template_ids <- paste0("test", 1:5)
template_ids
#> [1] "test1" "test2" "test3" "test4" "test5"

Use get_prompt_template() to view the text:

cat(substr(get_prompt_template("test1"), 1, 500), "...\n")
#> You are a debate adjudicator. Your task is to weigh the comparative strengths of two writing samples regarding a specific trait.
#> 
#> TRAIT: {TRAIT_NAME}
#> DEFINITION: {TRAIT_DESCRIPTION}
#> 
#> SAMPLES:
#> 
#> === SAMPLE_1 ===
#> {SAMPLE_1}
#> 
#> === SAMPLE_2 ===
#> {SAMPLE_2}
#> 
#> EVALUATION PROCESS (Mental Simulation):
#> 
#> 1.  **Advocate for SAMPLE_1**: Mentally list the single strongest point of evidence that makes SAMPLE_1 the winner.
#> 2.  **Advocate for SAMPLE_2**: Mentally list the single strongest point of evidence that mak ...

The same pattern works for all templates:

# Retrieve another template
tmpl_test3 <- get_prompt_template("test3")

# Use it to build a concrete prompt for a single comparison
pairs <- example_writing_samples |>
  make_pairs() |>
  head(1)

prompt_text <- build_prompt(
  template   = tmpl_test3,
  trait_name = td$name,
  trait_desc = td$description,
  text1      = pairs$text1[1],
  text2      = pairs$text2[1]
)

cat(prompt_text)

6. Forward and reverse pairs

Here is a small example of how we constructed forward and reverse datasets for each experiment:

pairs_all <- example_writing_samples |>
  make_pairs()

pairs_forward <- pairs_all |>
  alternate_pair_order()

pairs_reverse <- sample_reverse_pairs(
  pairs_forward,
  reverse_pct = 1.0,
  seed        = 2002
)

pairs_forward[1:3, c("ID1", "ID2")]
#> # A tibble: 3 × 2
#>   ID1   ID2  
#>   <chr> <chr>
#> 1 S01   S02  
#> 2 S03   S01  
#> 3 S01   S04
pairs_reverse[1:3, c("ID1", "ID2")]
#> # A tibble: 3 × 2
#>   ID1   ID2  
#>   <chr> <chr>
#> 1 S18   S02  
#> 2 S18   S06  
#> 3 S07   S08

In pairs_reverse, SAMPLE_1 and SAMPLE_2 are swapped for every pair relative to pairs_forward. Analyze each model, template, trait, and reasoning condition separately: compute_reverse_consistency() does not group on those columns and would otherwise pool duplicate votes within each unordered pair.

7. Thinking / Reasoning Configurations Used in Testing

The archived artifact uses a thinking column to distinguish two historical request configurations:

thinking = "no_thinking"   # archived grouping label
thinking = "with_thinking" # archived grouping label

These strings are labels in the result artifact, not arguments accepted by the current public wrappers. The underlying request fields were backend-specific. Below we describe the historical configurations recorded with the experiment; consult current provider documentation and the package’s dated compatibility registry before constructing a new request.

8. Loading summary results

The archived results are stored in inst/extdata/template_test_summary_all.csv. Only aggregate rows remain, so the raw judgments cannot be reanalyzed with the current paired test.

summary_path <- system.file("extdata", "template_test_summary_all.csv", package = "pairwiseLLM")
if (!nzchar(summary_path)) stop("Data file not found in installed package.")

summary_tbl <- readr::read_csv(summary_path, show_col_types = FALSE)
head(summary_tbl)
#> # A tibble: 6 × 7
#>   template_id backend model thinking prop_consistent prop_pos1 p_sample1_overall
#>   <chr>       <chr>   <chr> <chr>              <dbl>     <dbl>             <dbl>
#> 1 test1       anthro… clau… no_thin…           0.895     0.505            0.878 
#> 2 test1       anthro… clau… with_th…           0.932     0.497            0.959 
#> 3 test1       anthro… clau… no_thin…           0.884     0.516            0.573 
#> 4 test1       anthro… clau… with_th…           0.905     0.484            0.573 
#> 5 test1       anthro… clau… no_thin…           0.884     0.442            0.0273
#> 6 test1       anthro… clau… with_th…           0.884     0.447            0.0453

9. Summary results by prompt

In this section we present, for each template:

1. The full template text (as used in the experiments).
   

2. A simple summary table with one row per (backend, model, thinking) configuration and columns:

   • Backend
     
   • Model
     
   • Thinking
     
   • Prop_Consistent
     
   • Prop_SAMPLE_1
     
   • Binomial_Test_p

cat(get_prompt_template("test1"))
#> You are a debate adjudicator. Your task is to weigh the comparative strengths of two writing samples regarding a specific trait.
#> 
#> TRAIT: {TRAIT_NAME}
#> DEFINITION: {TRAIT_DESCRIPTION}
#> 
#> SAMPLES:
#> 
#> === SAMPLE_1 ===
#> {SAMPLE_1}
#> 
#> === SAMPLE_2 ===
#> {SAMPLE_2}
#> 
#> EVALUATION PROCESS (Mental Simulation):
#> 
#> 1.  **Advocate for SAMPLE_1**: Mentally list the single strongest point of evidence that makes SAMPLE_1 the winner.
#> 2.  **Advocate for SAMPLE_2**: Mentally list the single strongest point of evidence that makes SAMPLE_2 the winner.
#> 3.  **Adjudicate**: Compare the *strength of the evidence* identified in steps 1 and 2. Which sample provided the more compelling demonstration of the definition above?
#> 
#> CRITICAL:
#> - You must construct a mental argument for BOTH samples before deciding.
#> - Do not default to the first sample read.
#> - If the samples are close, strictly follow the trait definition to break the tie.
#> 
#> FINAL DECISION:
#> Output your decision based on the stronger evidence.
#> 
#> <BETTER_SAMPLE>SAMPLE_1</BETTER_SAMPLE>
#> OR
#> <BETTER_SAMPLE>SAMPLE_2</BETTER_SAMPLE>
#> 
#> (Provide only the XML tag).

summary_tbl |>
  filter(template_id == "test1") |>
  arrange(backend, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Backend = backend,
    Model = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    align = c("l", "l", "l", "r", "r", "r")
  )

cat(get_prompt_template("test2"))
#> You are an impartial, expert writing evaluator. You will be provided with two student writing samples.
#> 
#> YOUR GOAL: Identify which sample is better regarding {TRAIT_NAME}.
#> 
#> ***
#> SAMPLE_1 START
#> ***
#> {SAMPLE_1}
#> ***
#> SAMPLE_1 END
#> ***
#> 
#> ***
#> SAMPLE_2 START
#> ***
#> {SAMPLE_2}
#> ***
#> SAMPLE_2 END
#> ***
#> 
#> EVALUATION CRITERIA:
#> Trait: {TRAIT_NAME}
#> Definition: {TRAIT_DESCRIPTION}
#> 
#> DECISION PROTOCOL:
#> 1. Ignore the order in which the samples appeared.
#> 2. Mentally 'shuffle' the samples. If Sample 1 was read second, would it still be better/worse?
#> 3. Focus STRICTLY on the definition above. Ignore length, vocabulary complexity, or style unless explicitly mentioned in the definition.
#> 4. If the samples are effectively tied, scrutinize them for the slightest advantage in {TRAIT_NAME} to break the tie.
#> 
#> OUTPUT FORMAT:
#> You must output ONLY one of the following tags. Do not produce any other text, reasoning, or preamble.
#> 
#> <BETTER_SAMPLE>SAMPLE_1</BETTER_SAMPLE>
#> or
#> <BETTER_SAMPLE>SAMPLE_2</BETTER_SAMPLE>

summary_tbl |>
  filter(template_id == "test2") |>
  arrange(backend, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Backend = backend,
    Model = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    align = c("l", "l", "l", "r", "r", "r")
  )

cat(get_prompt_template("test3"))
#> You are an expert writing assessor.
#> 
#> Your task: Determine which of two writing samples demonstrates superior {TRAIT_NAME}.
#> 
#> {TRAIT_NAME} is defined as:
#> {TRAIT_DESCRIPTION}
#> 
#> Below are two samples. They appear in arbitrary order—neither position indicates quality.
#> 
#> ═══════════════════════════════════════
#> FIRST SAMPLE:
#> {SAMPLE_1}
#> 
#> ═══════════════════════════════════════
#> SECOND SAMPLE:
#> {SAMPLE_2}
#> 
#> ═══════════════════════════════════════
#> 
#> ASSESSMENT PROTOCOL:
#> 
#> Step 1: Read both samples in their entirety.
#> 
#> Step 2: For each sample independently, assess the degree to which it demonstrates {TRAIT_NAME} based solely on the definition provided.
#> 
#> Step 3: Compare your assessments. Determine which sample shows stronger {TRAIT_NAME}.
#> 
#> Step 4: Select the sample with better {TRAIT_NAME}. If extremely close, choose the one with any detectable advantage. No ties are allowed.
#> 
#> Step 5: Verify your selection reflects the CONTENT quality, not the presentation order.
#> 
#> RESPONSE FORMAT:
#> 
#> Respond with exactly one line using this format:
#> 
#> <BETTER_SAMPLE>SAMPLE_1</BETTER_SAMPLE>
#> 
#> if the first sample is better, OR
#> 
#> <BETTER_SAMPLE>SAMPLE_2</BETTER_SAMPLE>
#> 
#> if the second sample is better.
#> 
#> Output only the XML tag with your choice. No explanations or additional text.

summary_tbl |>
  filter(template_id == "test3") |>
  arrange(backend, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Backend = backend,
    Model = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    align = c("l", "l", "l", "r", "r", "r")
  )

cat(get_prompt_template("test4"))
#> You are an expert writing assessor.
#> 
#> Evaluate which sample better demonstrates {TRAIT_NAME}.
#> 
#> {TRAIT_NAME}: {TRAIT_DESCRIPTION}
#> 
#> ---
#> SAMPLE 1:
#> {SAMPLE_1}
#> 
#> ---
#> SAMPLE 2:
#> {SAMPLE_2}
#> 
#> ---
#> 
#> TASK:
#> - Assess both samples on {TRAIT_NAME} only
#> - Choose the sample with stronger {TRAIT_NAME}
#> - If nearly equal, select the marginally better one
#> 
#> The samples above appear in random order. Base your judgment only on which content better demonstrates {TRAIT_NAME}, not on position.
#> 
#> Respond with only one line:
#> 
#> <BETTER_SAMPLE>SAMPLE_1</BETTER_SAMPLE> if Sample 1 is better
#> 
#> <BETTER_SAMPLE>SAMPLE_2</BETTER_SAMPLE> if Sample 2 is better

summary_tbl |>
  filter(template_id == "test4") |>
  arrange(backend, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Backend = backend,
    Model = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    align = c("l", "l", "l", "r", "r", "r")
  )

cat(get_prompt_template("test5"))
#> You are a critique-focused evaluator. Instead of looking for general quality, you will look for deviations from the ideal.
#> 
#> Target Trait: {TRAIT_NAME}
#> Ideal Standard: {TRAIT_DESCRIPTION}
#> 
#> SAMPLES:
#> 
#> >>> TEXT_BLOCK_1 (Refers to SAMPLE_1)
#> {SAMPLE_1}
#> 
#> >>> TEXT_BLOCK_2 (Refers to SAMPLE_2)
#> {SAMPLE_2}
#> 
#> EVALUATION METHOD (Gap Analysis):
#> 
#> 1. Scrutinize TEXT_BLOCK_1. Where does it fail, hesitate, or deviate from the Ideal Standard?
#> 2. Scrutinize TEXT_BLOCK_2. Where does it fail, hesitate, or deviate from the Ideal Standard?
#> 3. Compare the 'Distance from Ideal'. Which sample is closer to the definition provided?
#> 4. Select the sample with the FEWEST or LEAST SEVERE deficits regarding {TRAIT_NAME}.
#> 
#> IMPORTANT:
#> - Ignore the order of presentation.
#> - Focus purely on which text adheres more tightly to the definition.
#> - If both are excellent, select the one with the higher 'ceiling' (stronger peak performance).
#> 
#> FINAL SELECTION:
#> <BETTER_SAMPLE>SAMPLE_1</BETTER_SAMPLE>
#> or
#> <BETTER_SAMPLE>SAMPLE_2</BETTER_SAMPLE>

summary_tbl |>
  filter(template_id == "test5") |>
  arrange(backend, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Backend = backend,
    Model = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    align = c("l", "l", "l", "r", "r", "r")
  )

10. Per-backend summary

It is often useful to examine positional-bias metrics within each backend to see whether:

• certain models exhibit more positional bias than others,
• reasoning mode makes a difference,
• a backend shows overall higher or lower reverse-order consistency.

The tables below show, for each provider, the key statistics:

• Prop_Consistent — proportion of consistent decisions under pair reversal
  
• Prop_SAMPLE_1 — proportion of comparisons selecting SAMPLE_1
  
• Binomial_Test_p — significance level for deviation from 0.5

Each row corresponds to a (template, model, thinking) configuration used in testing.

summary_tbl |>
  filter(backend == "anthropic") |>
  arrange(template_id, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Template = template_id,
    Model    = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    caption = "Anthropic: Positional-bias summary by template, model, and thinking configuration.",
    align = c("l", "l", "l", "r", "r", "r")
  )

summary_tbl |>
  filter(backend == "gemini") |>
  arrange(template_id, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Template = template_id,
    Model    = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    caption = "Gemini: Positional-bias summary by template, model, and thinking configuration.",
    align = c("l", "l", "l", "r", "r", "r")
  )

summary_tbl |>
  filter(backend == "openai") |>
  arrange(template_id, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Template = template_id,
    Model    = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    caption = "OpenAI: Positional-bias summary by template, model, and thinking configuration.",
    align = c("l", "l", "l", "r", "r", "r")
  )

summary_tbl |>
  filter(backend == "together") |>
  arrange(template_id, model, thinking) |>
  mutate(
    Prop_Consistent = round(prop_consistent, 3),
    Prop_SAMPLE_1   = round(prop_pos1, 3),
    Binomial_Test_p = formatC(p_sample1_overall, format = "f", digits = 3)
  ) |>
  select(
    Template = template_id,
    Model    = model,
    Thinking = thinking,
    Prop_Consistent,
    Prop_SAMPLE_1,
    Binomial_Test_p
  ) |>
  kable(
    caption = "TogetherAI: Positional-bias summary by template, model, and thinking configuration.",
    align = c("l", "l", "l", "r", "r", "r")
  )

11. Conclusion

This vignette demonstrates a workflow for describing reversal agreement and testing directional positional preference in prompt templates.

Use the archived tables to inspect the 2025 experiment, not to infer current provider availability or certify a template for production. For a new study, retain raw forward/reverse judgments, analyze each configuration separately, report agreement and position preference as distinct quantities, and review effect sizes and study design alongside the paired p-value. Because unordered pairs commonly share items, statistical review is appropriate when formal inference is required.

12. Citation

Mercer, S. H. (2026). Prompt template positional bias testing [R package vignette]. Comprehensive R Archive Network. https://doi.org/10.32614/CRAN.package.pairwiseLLM