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copy_SPI_EA_impact_make_book.Rmd
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---
title: "Empathic and Numerate Giving: Donor responses to charity effectiveness and impact information"
date: "`r format(Sys.time(), '%d/%m/%Y')`"
author: "David Reinstein (Exeter, innovationsinfundraising.org), Robin Bergh (Harvard), Donor's Voice advisory board"
output:
revealjs::revealjs_presentation:
self_contained: false
reveal_plugins: ["notes", "chalkboard","zoom"]
theme: white
highlight: pygments
transition: fade
smart: true
css: reveal.css
center: true
options: knitr.table.format = "html"
classoption: table
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<script>
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// add the button and a wrapping container to each of them...
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```{r setup_S, include=FALSE, warning=FALSE}
library(here)
here <- here::here
library(knitr)
source(here("dr-rstuff","functions","baseoptions.R"))
source(here("dr-rstuff","functions","functions.R"))
purl(here("analysis","analysis_dp.Rmd"), output = here("code","analysis_dp.R"))
source(here("code","analysis_dp.R"))
```
```{r somefunctions, echo=FALSE, results='hide'}
#possibly move these to a separate file
#multi-output text color
#https://dr-harper.github.io/rmarkdown-cookbook/changing-font-colour.html#multi-output-text-colour
#We can then use the code as an inline R expression format_with_col("my text", "red")
format_with_col = function(x, color){
if(knitr::is_latex_output())
paste("\\textcolor{",color,"}{",x,"}",sep="")
else if(knitr::is_html_output())
paste("<font color='",color,"'>",x,"</font>",sep="")
else
x
}
#do the same for centering etc
```
# Outline
## Outline
0. [Definition of 'effective giving' for our purposes, motivation](#intro)
1. [Barriers to effectiveness in giving (very brief taxonomy/outline)](#barriers)
<!--
2. [Focus: 'Processing of effectiveness information' & dual-system](#effect-info-dual)
<small> [(Concepts/theory)](#concepts) </small>
-->
3. [Prior evidence and gaps](#prior-evidence), [our empirical approach](#empirical-approach)
<!-- Naturalistic, Robustness across setups/frames, Honestly present evidence, allow integration -->
5. [DonorsVoice mailing experiment](#dv-experiment) <small> (many co-authors) i) Setup ii) Results iii) Proposed follow-up </small>
6. [Bergh project (Mturk)](#bergh-mturk-experiment) <small> Setups, Results </small>
7. [Bergh/Reinstein (Essex piggyback)](#essex-piggyback) <small> Setups, [Results](#bergh-results) </small>
8. [Preliminary conclusions, proposed future directions](#conclusion) (time permitting)
<aside class="notes">
This is partially accreted to the work Robin Bergh presented at the 2017 SPI: "Doing the Most Good How and When to Reason about Charity Efficiency"
</aside>
## SPI/AFE abstract
`r format_with_col("Puzzle:","blue")` inefficient giving/little to highest-impact causes
- Conceptual breakdown of 'barriers'
- 'Innumerate empathy': key barrier to promoting effective giving?
- Previous: emotional reactions to suffering $\rightarrow$ helping; but it "doesn't scale" with need (and few ppl 'research effectiveness before giving')
- Dual process: *analytical* impact info may disrupt empathic giving
*7 giving experiments, various contexts*, 2x2, between-subject treatments
- Measures of charity efficiency/effectiveness
- Emotional-empathy-inducing images
*Results:* <small> Analytical info doesn't seem to disrupt emotional-empathic giving (but some lack of power), and may enhance it. The 'right' empathic images can drive effective giving. </small>
<aside class="notes">
A small share of charitable giving goes towards “highly-effective” charities as measured by GiveWell (or to charities in this category: health interventions in poor countries).
*Innumerate empathy* may constitute a major barrier to (promoting) effective giving.
Previous work finds that helping behaviors are strongly driven by emotional reactions to individual suffering, but these do not scale with the magnitude of need. From a dual-process perspective, presenting analytical impact information may even disrupt empathic giving, shifting potential donors towards a system-II deliberative mode. We report on seven charitable giving experiments. Treatments (between subjects, mainly 2x2) present (i) measures of charity efficiency/effectiveness and (ii) empathy-inducing images. Variations across experiments include: subject pools (MTurk, UK students, US regular donors via direct mail), separate vs. joint evaluation, the nature of the effectiveness information, and treatment ordering/timing.
</aside>
# Definition of 'effective giving' for our purposes, motivation {#intro .flexbox .vcenter}
## Definition {#def-impact}
*Impact* aka *effectiveness* of a charity
$B(G_i)$: Beneficial *outcome* achieved by charity $i$ with total donations $G_i$
<br>
- *Ultimate outcome* -- Lives saved, QALY added, etc.
- Not *'output'* -- 'nets provided' nor 'paintings purchased'
<aside class="notes">
(Total or marginal) impact per dollar = output per dollar $\times$ impact per output
</aside>
----
*Impact* of a donation:
$B'(G_i)$ for the marginal donor
- GiveWell and others attempt to measure this
<br>
<center>
*We know:*
$B'(G_i)$ is much larger for most *impactful* vs. most *popular* charities.
</center>
<aside class="notes">
Trust me on this, or at least accept that this seems likely in many cases.
Steinberg & Morris, 2010 wrote about marginal vs average effectiveness.
</aside>
----
## Raises questions {.build}
1. “Why don’t we give more to the most effective charities and to those most in need?”,
<br>
<center> *and* </center>
<br>
2. “Why are we not more efficient with our giving choices?”
<br>
<center>
`r format_with_col("*A 'Puzzle'?*","blue")`
</center>
<aside class="notes">
Ben:
... although people have their pet charity causes (e.g. blindness), even if you buy an argument of incommensurability between causes (which we shouldn’t imo), there are more effective charities within these subsets.
</aside>
# Barriers to effectiveness in giving (very brief taxonomy/outline) {#barriers}
<br>
<center>
<small>
Review/mini-meta-analyses, extending from innovationsinfundraising.org
Collaborators: David Reinstein, Robin Bergh, Nick Fitz, Ben Grodeck, Ari Kagan, Janek Kretschmer, Jason Nemirow
</small>
</canter>
## Barriers: a workable categorization
0. No moral-utilitarian concerns
1. (Psychological) distance $\rightarrow$ (lack of) emotional arousal/awareness
{width=40%} {width=55%}
----
```{r measuringpov, out.width='33%', fig.align='center', fig.cap='2. Identity & self-perception; 3. Inertia and systemic factors; 4. Quantitative biases', echo=FALSE, fig.show='hold'}
knitr::include_graphics(rep(c('rather-fight-than-switch.jpg','fb_supoprtmydaughter.jpg','measuring-poverty.jpg')))
```
<center>
... and...
</center>
<aside class="notes">
*This is a project with many authors: Myself, Robin Bergh, Nick Fitz, Ari Kagan, Jason Nemirow, Paul Smeets, Janek Kretschmer, Ben Grodeck, and others*
1. Psychological distance/emotional arousal: Whether a cause/charity is something people are aware of, feel is important/salient, and feel close to
2. Identity: Things that run against one's self-perception and how one believes others will will see you. (e.g., signaling emotional empathy; avoiding cognitive dissonance from previous ineffective giving)
3. Inertia and systemic/institutional "Factors limiting individual & social *change* in behavior
4. Quantitative biases : Problems dealing with numbers and making logical evaluations involving numbers, values and amounts. Common cognitive errors *or* intuitive and emotional reactions triggered in these contexts. (E.g., Overhead aversion; Proportional dominance)
</aside>
----
5. **Obstacles/aversion to doing evaluations; analytical/empathetic clash**
<center>
{width=35%} {width=35%}
</center>
<br>
> - Reluctant to evaluate (taboo tradeoffs, 'social v. market norm', ...)
> - The evaluation process switches off empathy $\rightarrow$ **the present focus**
<aside class="notes">
5. Aversion to *doing* evaluations: "Things that make people reluctant to evaluate and consider the effectiveness of charities, and ways that doing these evaluations reduce generosity." (E.g., taboo tradeoffs; market vs social norm; dual-system)
</aside>
## 'Processing of effectiveness information' and spontaneous/deliberate responses {#effect-info-dual}
<br>
- Heuristic (fast) $\rightarrow$ spontaneous generosity?
- Deliberative (slow) $\rightarrow$ thoughtful giving ... or 'calculated greed'
- Also: relational models theory <small> (Fisk, '91)</small>; Motivated reasoning <small> (e.g., Exley '19) </small> $\rightarrow$ all suggests analytical information $\rightarrow$ less giving
<!-- ## Concepts/theory {#concepts}
-->
<aside class="notes">
Spontaneous Emotions and Deliberation: Dual-Process Perspectives
What happens when we combine emotional and reasoning appeals?
Dual process models of prosocial behaviors:
theoretical arguments for this perspective comes from other research on generosity and cooperativeness, suggesting that people are spontaneously prosocial and more self-serving when they think longer/more (e.g., Rand et al., 2012, Rand, 2016).
cf Fisk: Relational models theory (x1991 ) ... all thinking about social relationships is based on four elementary mental models: communal sharing, authority ranking, equality matching, and market pricing.
Alt. channel: Exley, Motivated reasoning: ' ...if participants desire to keep money for themselves and to think of themselves as generous, they may overweight their dislike of less-than-perfect performance metrics as an excuse not to give.'
Note: these
</aside>
# Prior evidence and gaps {#prior-evidence}
## Evidence brief: key findings
- **Small, Lowenstein, Slovic, '07** (Lab char'l giving), prime analytic (vs emotion): `r format_with_col("NEGATIVE","blue")`
<aside class="notes">
S3: Identifiable victim $>$ donation stats, S4: Priming analytic (maths) vs. priming feelings ('impressions') $\rightarrow$ less giving to identifiable victims
</aside>
- **Karlan \& Wood, '17**, field mailing, scientific impact info: NULL, tight-ish bounds; (`r format_with_col("+","red")`/`r format_with_col("-","blue")` for 'prior large/small donors'
- **Parson, '07**, field mailing, numeric overhead info: `r format_with_col("POSITIVE","red")` effect for previous donor subset
- Mixed/null/positive evidence of 'real-world ratings' <small> (Yoruk '16; Brown ea '17; Gordon 'ea '19) </small>
- Mixed evidence (lab; charity/non) of 'excuse-driven information seeking' <small> (Exley '16b; Fong & O, '10; Metzger & G '19) </small>
<aside class="notes">
Karlan & W bounds, table 2: column 1 incidence near-0, se under 1\%, baseline incidence 14\%
Amount donated +2.35, se 1.98, mean 14.17; windsorised -0.074, se 0.82, mean 11.30
</aside>
<!-- Add work on framing of market and social in economics experiments (e.g., Public goods)
Incorporate Sandra Goff's work ... field experiment in Maine)
'Market framing e.g., Cohn ea 2014
Market interactions erode moral values Falk and Sczech '13 .. Mouse study
-->
## Identifiable victims effect/ deservingness vs deliberation
<br>
Claim: Better to portray an individual (child) than convey the total affected <small> Small & Loewenstein (03); Small et al (07); Kogut & R (05) </small>
- Driven by System-1 empathy, switched off by analytic thinking
----
**Small, Lowenstein, Slovic (2007):**
<br>
[Study 3] "individuals who faced an identifiable victim donated more..."
<br>
> - "...than those who faced victim statistics, p < .01,"
<br>
> - ..."than those who faced [both] an identifiable victim [and] statistics, p < .05.""
----
**Small et al, '07, Study 4**
<br>
> Priming analytic thinking reduced donations to an identifiable victim relative to a feeling-based thinking prime.
<br>
> Yet, the primes had no distinct effect on donations to statistical victims, which is symptomatic of the difficulty in generating feelings for these victims.
<br>
<center> <small> `r format_with_col("*Tightly bounded null, but ... nonlinearity?*","blue")` </small> </center>
<aside class="notes">
Note, the latter non-effect appears tightly bounded; but this could simply be driven by nonlinearity. If people gave little to statistical victims, there is less room for this to decrease further. A classic problem when considering interactions.
</aside>
----
**Verkaik (2016)**
<br>
> While previous studies have convincingly shown that providing output information, informing donors of how their donation is used, increases generosity <small> (Cryder & L, '10; Cryder ea '13; Aknin ea '13) </small>
<aside class="notes">
Robin: I personally wouldn't count the Cryder studies as examples of studies demonstrating that effectiveness has a positive effect on giving. There's a fundamental difference between psychological perceptions of impact (and "tweaks" of info to make it seem more impactful to donate) versus evaluating actual evidence of effectiveness. For instance, the fact that donors are more willing to donate when a fundraiser is close to reaching a goal tells us something about how people feel about donating, but it tells us absolutely nothing about the actual effectiveness of a charity and how people process such information. Effectiveness is an attribute of the charity, not a perception of making a difference (if we reduce effectiveness to a subjective impact belief then guide dogs could also argued to be highly effective).
DR: True; But I wouldn't say it is completely unrelated. For actual cost-effectiveness/impact information to be used to increase/improve giving we presumably need both
1. Individuals care about their own impact per \$, as they perceive it (Cryder speaks to this),2. Individuals can reasonably draw conclusions about effectiveness per \$ from the information properly presented, and 3. The presentation of this information does not itself substantially reduce the actualized motivation to give,
</aside>
<br>
> ...the evidence on the effects of impact information are more mixed, with mainly null effects <small> (Metzger & G '15; Karlan & W, '14; Baron & S, '10; Caviola ea '14, Berman ea '15) </small>
<aside class="notes">
</aside>
<!-- Check more closely
See also Frumkin & Kim, 2001
[MORE on how this is claimed to be via system 1/2]
Some limitations/caveats: (Ein-Gar and L, '12; Kogut and R '07)
-->
## Ratings and information in general: mixed evidence
- Yörük (2016, JEMS): RD w/ Charity Navigator; significant for 'small' charities only
- See also Brown ea (2017), Gordon ea (2009)
<aside class="notes">
- Charity Navigator stars based on continuous score across categories (not EA criteria)
- Identification via RD: Impact of crossing a 'star' threshold on amounts raised
*Results:* Significant impact for small charities only: finds a nearly 20\% effect of a one star increase
</aside>
## "Effectiveness" info
**Karlan and Wood (2017)**
Add scientific impact text to appeal (& remove emotional text):
$\rightarrow$ little net effect
$\rightarrow$ reduced (increased) giving among small (large) prior donors `r format_with_col("(not a preregistered hypothesis)","grey") `
<br>
`r format_with_col("*Potential confounds, specificity*","blue")`
<aside class="notes">
- Yale/institution effect (seemed negative)
- Nature of 'impact' information (not exactly quantitative)
- ex-post splitting
- two things changed at once (impact in, emotional out)
</aside>
----
**Details of Karlan first wave: SCIENCE vs EMOTION**
> According to studies on our programs in Peru that used rigorous scientific methodologies, women who have received both loans and business education saw their profits grow, even when compared to women who just received loans for their businesses. But the real difference comes when times are slow. The study showed that women in Freedom from Hunger's Credit with Education program kept their profits strong–ensuring that their families would not suffer, but thrive.
<br>
> Because of caring people like you, Freedom from Hunger was able to offer Sebastiana a self-help path toward achieving her dream of getting “a little land to farm” and pass down to her children. As Sebastiana's young son, Aurelio, runs up to hug her, she says, “I do whatever I can for my children.”
----
**Parsons (2007)**
2 x 2 mailing appeal for People with Aids Coalition-Houston,
- Add "Service efforts and accomplishment info"(SEA)
- Add favorable "FINANCIAL" spending/overhead ratio info
FINANCIAL (alone) $\rightarrow$ 180\% increase in odds of donating *among prior donors* ($p<0.05$)
(Other effects mainly insignificant, underpowered)
<aside class="notes">
Unsure if it's a logit or LPM -- confusing writing
Not effect-coded; no measure of *overall* impact of FINANCIAL across both SEA treatments
Probably not preregistered
I'd like to see CI's
</aside>
----
<small> Details from Parsons </small>
```{r parsons, out.width='40%', fig.align='center', echo=FALSE}
knitr::include_graphics(c('parsons_fin_treat.png'))
```
```{r parsons_logit, out.width='40%', fig.align='center', echo=FALSE}
knitr::include_graphics(c('parsons_logit.png'))
```
## Information as an 'excuse' not to give; allows motivated reasoning
**Exley, 2016b:** Greater discounting of 'less-efficient' charity in charity-charity decision-making than in charity-self d-m
<br>
**Fong & O, '10:**
> "Dictators [charitable giving] who acquire information mostly use it to withhold resources from less-preferred types, leading to a drastic decline in aggregate transfers"
`r format_with_col("But...","blue")`
<br>
<aside class="notes">
Exley issues: Experimenter demand (M-turk focus), not really 'impact' information
Fong: Selection effects. In their tables, exogenous provision of information seems to *increase* donations overall.
Also ... it's evidence on the deservingness of the recipients, not on impact of a charity itself.
</aside>
<br>
----
**Metzger & G, '19 **
Lab donations to high/low-performing NGO
- More purchasing of 'recipient type' than 'impact' info
- Mixed & weak evidence on excuse-driven information-seeking
<br>
<center>`r format_with_col("Caveats...","blue")` </center>
<aside class="notes">
Opportunity to buy info on 'recipient type' increased giving, on 'admin costs' decreased giving (marginal significance for both), no effect of 'aid impact' but wide CI
'Free info' on each of these had insignificant effects (underpowered!)
Lots of caveats; e.g., recipient type (artists vs children) may have been seen as a proxy for impact
</aside>
<!--
In a laboratory experiment, we analyze individuals’ demand for information about a donation’s welfare impact, and compare it with demand for information on recipient types and administrative costs. We find the least demand for information about aid impact, indicating that individuals either do not understand, do not trust, or do not care about the specific information we provide. Average donations increase in response to information about the recipient type and decrease in response to information about administrative costs. Information about aid impact does not significantly change average donations: donors who demand information respond positively to high impact projects and negatively to low impact projects, resulting in a zero net effect on donation levels. Our results further show that information has the same effect on donation behavior regardless of whether it is provided for free or at a cost.
-->
<!-- "Making an impact? The relevance of information on aid effectiveness for charitable giving. A laboratory experiment.":
>...the demand for information about aid impact is lowest, and it is highest for information about the recipient type.
> ... exact information about aid impact did not lead to a significant change in average donation levels, while information about the exact recipient type and administrative costs led to a significant change in donation levels.
> In the recipient type group, informed participants donated significantly more than uninformed participants because they "rewarded" the preferred recipient with higher-than-average transfers. In the administration costs group, informed participants donated significantly less than uninformed participants because they used the information to "punish" NGOs with high administration costs.
DR: It is not clear to me when they are reporting on the self-selected groups and when they report on the sample overall, or in a way that deals with the self-selection.
Looking at their one clearer result, we see a lack of power.
Average don: 2.45 CHF
Aid impact group coef: -.231 (.45)
This looks like an underpowered study. They can perhaps rule out an effect greater than around half of the average donation, but no more precisely.
-->
## Our empirical approach {#empirical-approach}
- Naturalistic environments
- Robustness across setups/frames
- Honest presentation of evidence, allowing integration
<aside class="notes">
This is a project and not just a (set of) papers.
The general project is a practical one (although Bergh's project aims to explore into specific mechanisms).
By measuring the impact of several types of efficiency information, across several contexts, we aim to produce a fairly robust picture. We expect heterogeneity and sensitivity to frames; thus results may vary, and we will carefully examine the overall picture as well as this variation in a 'mini-meta-analysis'.
To limit various types of experimenter demand and arbitrary coherence, these experiments are *between* participant, and (largely) run in contexts where the donation is not the focus of the interaction.
We have preregistered our studies, hypotheses and analyses.
We will share all of our data to enable future reanalyses.
</aside>
# DonorsVoice mailing experiment {#dv-experiment}
<small>
Co-authors: David Reinstein, Elizabeth Keenan, Ayelet Gneezy, Hengchen Dai, Enrico Rubaltelli, Stephan Dickert, Kiki Koutmeridou, and Peter Ayton
</small>
## Plans from prereg [OSF---link](https://osf.io/ucwm3):
> What is the impact of including 'information about the per-dollar impact' of a charity (in terms of services provided) on the average donation (equivalently, total amount raised) and the donation incidence rate?
----
> We are running this subject to the final say of the charity. We have proposed that the Treatment emails (but not the control emails) will include a sentence/fragment such as the following in both a captioned photo in the email, and the email text:
> "Last year, we were able to provide [general provision of an outcome here relevant to the charity] to a [recipient unit] with just $[small amount of money]."
----
<center> (from prereg) </center>
> We plan to perform standard nonparametric statistical tests of the effect of this treatment on
- Average gift amount (including zeroes)
- Incidence/number of people making a gift, [and]
- Incidence of gifts of exactly $10.
> In particular, we will focus on Fisher's exact test (for incidence) and the standard rank sum and t-tests for the donation amounts.
----
**Power calculations**
> Response rates in previous such emails were extremely low: approximately 1 per 3,000 emails. Our power calculations suggest that we have .29 power to detect a 50% effect, and 0.90 power to detect approximately a 100% (doubling) on incidence...
> Because of this limited power, we will ask the charity to run this trial a second time with an equivalent-sized sample.
----
**Stopping rule**
> We aim to continue this treatment in future charity appeals until we can statistically bound (with 95% confidence) the impact of the treatment on both incidence and average donation within a margin of 1/3 of the incidence and average donation in the control condition.
----
## Context
*Charity:* A large US religiously-associated international poverty relief charity
*Timing:* All emails sent out at the same time, 21-Nov-2018 'Thanksgiving email'
Sample size and composition:
- Charity's standard email list (previous donors with emails)
- Approx 182,600 emails sent out, 91.3k in each condition
<!--
----
<center>
{width=1000px}
</center>
-->
## Setup
<div id="left">
``` {r crs_ctrl_top, out.width='140%', echo=FALSE}
knitr::include_graphics('crs_ctrl_top.png')
```
</div>
<div id="right">
``` {r crs_test_top, out.width='140%', echo=FALSE}
knitr::include_graphics('crs_test_top.png')
```
</div>
----
<div id="left">
```{r crs_ctrl_bottom, out.width='140%', echo=FALSE}
knitr::include_graphics('crs_ctrl_bottom.png')
```
</div>
<div id="right">
```{r crs_test_bottom, out.width='140%', echo=FALSE}
knitr::include_graphics('crs_test_bottom.png')
```
</div>
## Results
<!-- summarised data input
-->
```{r dv-input-cross, echo=FALSE, results='hide'}
#input donation crosstabs (summary data we can analyse)
dv_cross <- read_excel("other_experimental_data/DV_work/Stats-for-DV-Formula_TYVid_dr_editing.xlsx",range="moved_from...!R11:V41") %>%
mutate(
range = ordered(range, levels = c("<$50", "$50-$99", "$100-$499","$500-$999", "$1000+")),
mode = ordered(mode, levels = c("email-link", "not-email","any" ))
)
```
```{r dv-input-ranks, echo=FALSE, results='hide'}
#input rank data and add zeroes
dv_ranks <- read_excel("other_experimental_data/DV_work/Stats-for-DV-Formula_TYVid_dr_editing.xlsx",sheet="ty_video_ranks")
dv_ranks_pos <- dv_ranks %>%
mutate(
treatment=as.factor(Treatment),
rev_rank = rank(-Rank)
) %>%
rename(rank=Rank) %>%
select(-Treatment)
#Add 91298-27 zeroes for control, add 91296-71 zeroes for treatment
zcontrol <- as_tibble(dv_ranks_pos[1,]) %>%
mutate(
rank=max(dv_ranks_pos$rank)+1,
rev_rank=min(dv_ranks_pos$rev_rank)-1,
treatment=as.factor("Control")
) %>%
slice(rep(1:n(), each = 91298-27))
ztreat <- as_tibble(dv_ranks_pos[1,]) %>%
mutate(
rank=max(dv_ranks_pos$rank)+1,
rev_rank=min(dv_ranks_pos$rev_rank)-1,
treatment=as.factor("Test")
) %>%
slice(rep(1:n(), each = 91296-71))
dv_ranks_all_em <- as_tibble(bind_rows(dv_ranks_pos,zcontrol,ztreat))
```
```{r fisher-dv, echo=FALSE, results='hide'}
#Fisher tests (could adjust to integrate input data i.e. softcode)
fisherme <- function(g1=91298, g1pos = 16816, g2 = 91296, g2pos= 16105) {
mat <- matrix(c(g1-g1pos, g1pos, g2-g2pos, g2pos),
nrow = 2,
dimnames = list(control = c("no", "yes"), treat = c("no", "yes")))
fisher.test(mat, or=1, alternative="t", conf.int)
}
dv_d_don_gte_100 <-
matrix(c(91298-241-72-63, 241-72-63, 91296-267-69-67, 267-69-67),
nrow = 2, dimnames = list(control = c("no", "yes"), treat = c("no", "yes")))
dv_d_don_open_gte_100 <-
matrix(c(16816-241-72-63, 241-72-63, 16105-267-69-67, 267-69-67),
nrow = 2, dimnames = list(control = c("no", "yes"), treat = c("no", "yes")))
(ft_dv_d_open <- fisherme())
(ft_dv_d_click <- fisherme(16816,412,16105,371))
(ft_dv_d_don_all <- fisherme(91298,26,91296,71))
(ft_dv_d_don_open <- fisherme(16816,26,16105,71))
(ft_dv_d_don_7day <- fisherme(91298,241,91296,267))
(ft_dv_d_don_open_7day <- fisherme(16816,241,16105,267))
(ft_dv_don_gte100 <- fisherme(91298,241-72-63,91296,267-69-67))
(ft_dv_don_open_gte100 <- fisherme(16816,241-72-63,16105,267-69-67))
```
```{r input-dv-ranks, echo=FALSE, results='hide'}
dv_ranks_all_em %>% group_by(treatment) %>% summarise(mn = mean(rank))
dv_ranks_pos %>% group_by(treatment) %>% summarise(mn = mean(rank))
#dv_ranks %>
#liftedWilcox(rev_rank,treatment)
#Ranksum test - CoP
(dv_ranksum <- wilcox.test(rev_rank ~ treatment, data = dv_ranks_pos, exact = FALSE, conf.int=TRUE))
#Ranksum test - include zeroes
(dv_ranks_all_em_t <- wilcox.test(rev_rank ~ treatment, data = dv_ranks_all_em, exact = FALSE, conf.int=TRUE))
```
```{r input-don, echo=FALSE, results='hide'}
#FOR ALL (email openers?) donations over 7 days; see fullcomp_DR
```
<!-- dv-ttest-ranksum-all -- see fullcomp branch -->
**Cost (Impact/\$) information treatment $\rightarrow$**
1. Slightly lower rate of opened emails:
- 16816/91298 (18.4%) in control vs 16105/91296 in treatment (17.6%)
- Highly significant in Fisher's exact test ($p<0.001$)
<br>
2. Slightly (insignificantly) lower rate of click-through after opening
- 2.3% vs 2.5% (95% OR: 0.81, 1.08)
<aside class="notes">
Headers were identical but people may 'peek' at content in some email systems, I believe.
Spam filtering may have also been affected by the different messages.
See 'https://www.hipb2b.com/blog/email-opens-measuring-actually' for the issue of how email opens are tracked.
<\aside>
----
... Cost info $\rightarrow$
**3. Greater donation incidence:**
*Via email click-through:* **66 > 25**
- Highly significant in Fisher's exact test ($p<0.001$, 95% CI OR: (1.7, 4.5); (1.8,4.5) conditional on opening email)
<br>
*Next 7 days, all channels, for email-openers:* **267 > 241 **
- "Marginally insignificant" in Fisher's exact ($p=0.1$, 95\% CI OR: (0.97,1.39))
<aside class="notes">
Some intertemporal substitution?
But I'm not sure yet whether the latter is 'all modes' or 'modes other than the original email'.
</aside>
----
```{r dv-histo, echo=FALSE, results='hide'}
smalltext <- element_text(size = 7)
dv_hist_email <- dv_cross %>%
dplyr::arrange(desc(mode)) %>%
ggplot() + geom_col(aes(x=range, y=gifts, fill=treatment), position = position_dodge(width=.5), width=.5) + facet_grid(mode ~ .) + theme(axis.text.x = smalltext)
dv_hist_email_stack <- dv_cross %>%
filter(mode!="any") %>%
dplyr::arrange(desc(mode)) %>%
ggplot() + geom_col(aes(x=range, y=gifts, fill=mode), position = position_stack(reverse = TRUE)) + facet_grid(. ~ treatment)
```
4. **Mixed results on avg. donation (overall \& CoP), amount raised**