---
title: "Do 95% Confidence Intervals Make Readers Overconfident? A One-Sample Test"
shorttitle: "Reading Confidence Intervals"
author:
  - name: YOUR NAME HERE
    email: your.email@colostate.edu
    corresponding: true
    affiliations:
      - name: Colorado State University
        department: Department of Psychology
abstract: "REPLACE THIS with your own abstract, written in your own words. One paragraph, roughly 150 words: what question you asked, what data you used, what you found, and what it means."
keywords: [keyword1, keyword2, keyword3]
bibliography: ../documentation/references.bib
format:
  apaquarto-docx: default
---

```{r}
#| label: setup
#| include: false

library(tidyverse)
library(here)

# This manuscript does NOT re-run the analysis. It reads the results your
# analysis notebook saved, so there is exactly one place where the numbers
# are computed. Change m08_lab.qmd, re-run it, and this paper updates.
#
# Note what is missing: no raw data is loaded here. That is deliberate --
# a manuscript that reads only saved results can be rendered by a co-author
# who does not have (and may not be permitted to have) the underlying data.
results <- read_rds(here("output", "m08_results.Rds"))

res <- results$res   # the t_test() output: statistic, t_df, p_value, estimate, CI
d   <- results$d     # the cohens_d() output: Cohens_d, CI_low, CI_high
```

# Introduction

Communicating uncertainty is hard, and the choice of display can change what a reader concludes
XXX. Hofman, Goldstein, and Hullman asked whether the *kind* of interval an author draws changes how
accurately readers judge an outcome XXX.

REPLACE THIS PARAGRAPH with 2–3 sentences framing the question in your own words: why does it matter
whether people read a 95% confidence interval accurately, and what would it mean if they
systematically got it wrong?

# Method

Participants viewed a 95% confidence interval display of a competition between two boulders and reported
their perceived probability that the special boulder would win. We analyzed the
`r res$t_df + 1` participants in the large-effect, 95% confidence interval condition.

REPLACE THIS PARAGRAPH with a description of the design and the benchmark. State where the
comparison value of 0.76 comes from — it is not an arbitrary number. Also state the SCOPE of this
analysis: it examines a single condition of a larger between-subjects experiment, so it addresses
calibration within that condition and not comparisons between display types.

# Results

REPLACE THIS PARAGRAPH with a formal description of the result, written the way it would appear in a
journal article. Use the inline-R values below rather than typing numbers by hand, and refer to
@fig-results in your prose.

A one-sample *t* test compared perceived probability against the true value of .76,
*t*(`r res$t_df`) = `r sprintf("%.2f", res$statistic)`,
*p* `r if (res$p_value < .001) "< .001" else paste("=", sub("^0", "", sprintf("%.3f", res$p_value)))`,
95% CI [`r sprintf("%.3f", res$lower_ci)`, `r sprintf("%.3f", res$upper_ci)`],
Cohen's *d* = `r sprintf("%.2f", d$Cohens_d)`.

```{r}
#| label: fig-results
#| fig-cap: "Perceived probability of winning under a 95% confidence interval display, against the true probability of .76."
#| echo: false

# This imports the figure your LAB NOTEBOOK saved with ggsave().
# Run the lab notebook first — this chunk will error if the file is not there yet.
knitr::include_graphics(here("output", "m08_results_figure.png"))
```

# Discussion

REPLACE THIS PARAGRAPH with 2–3 sentences: what does the result mean for the question you posed in
the Introduction? Say what you may and may not conclude. Two traps to avoid: (1) if the test was not
significant, do not write that there is no effect — say what the data could and could not establish;
(2) do not claim this display is WORSE than another one. You tested one condition against a
benchmark; you did not compare conditions.

REPLACE THIS PARAGRAPH with one limitation worth naming.

# References

::: {#refs}
:::
