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Agreed, though if their model isn't correctly specified to identify the causal effect on meat (which I agree is tough here), then presumably the effects on plant-based sales would also be suspect.

Good point. This does provide a bit more evidence that it's not just due to other January shocks that were happening regularly before Veganuary started.

There's this in the abstract:

"Average weekly unit sales of plant-based products increased significantly (57 %) during the intervention period (incidence rate ratio (IRR) 1·52 (95 % CI1·51, 1·55)). Plant-based product sales decreased post-intervention but remained 15 % higher than pre-intervention (IRR 1·13 (95 % CI 1·12, 1·14)). There was no significant change in meat sales according to time period. The increase in plant-based product sales was greatest at superstores (58 %), especially those located in below average affluence areas (64 %)."

I think this is pretty bad news, actually.

Here we have an intervention that apparently increases sales of plant-based products by 57% and yet *does not *decrease sales of meat products at all. Unfortunately, this corroborates a growing body of evidence suggesting that plant-based products often fail to displace meat products, even when they gain their own (orthogonal) market share.

As an aside, even with the effects on plant-based products, it's also hard to attribute causation to Veganuary specifically, since it always occurs during a month that we know is associated with unusual recurring "shocks" (e.g., the end of holiday dinner parties; the beginning of New Year's resolutions).

Thanks for putting together this excellent list, Martin and Emma. This is just in time for my lab's upcoming brainstorming session on future research priorities.

No worries. Effect-size conversions are very confusing. Thanks for doing this important project and for the exchange!

Hi Seth,

Thanks so much for the thoughtful and interesting response, and I’m honored to hear that the 2021 papers helped lead into this. Cumulative science at work!

- I fully agree. Our study was at best comparing a measure with presumably less social desirability bias to one with presumably more, and lacked any gold-standard benchmark. In any case, it was also only one particular intervention and setting. I think your proposed exercise of coding attitude and intention measures for each study would be very valuable. A while back, we had tossed around some similar ideas in my lab. I’d be happy to chat offline about how we could try to help support you in this project, if that would be helpful.
- Makes sense.
- For binary outcomes, yes, I think your analog to delta is reasonable. Often these proportion-involving estimates are not normal across studies, but that’s easy enough to deal with using robust meta-analysis or log-transforms, etc. I guess you approximated the variance of this estimate with the delta method or similar, which makes sense. For continuous outcomes, this actually was the case I was referring to (a binary treatment X and continuous outcome Y), since that is the setting where the d-to-r conversion I cited holds. Below is an MWE in R, and please do let me know if I’ve misinterpreted what you were proposing. I hope not to give the impression of harping on a very minor point – again, I found your analysis very thoughtful and rigorous throughout; I’m just indulging a personal interest in effect-size conversions.

Thanks again, Seth!

Maya

library(dplyr)

# sample size

N = 10^5

# population parameter

delta = .3

# assume same SD conditional on X=0 and X=1 so that Glass = Cohen

sd.within = .5

# E[Y | X=0] and E[Y | X=1]

m0 = .5

m1 = m0 + delta*sd.within

# generate data

d = data.frame( X = c( rep(0, N/2), rep(1, N/2) ) )

d$Y[ d$X == 0 ] = rnorm(n = sum(d$X == 0), mean = m0, sd = sd.within )

d$Y[ d$X == 1 ] = rnorm(n = sum(d$X == 1), mean = m1, sd = sd.within )

# sanity check

d %>% group_by(X) %>%

summarise( mean(Y) )

hist(d$Y)

# check the conversion

r = cor(d$Y, d$X)

(2*r) / sqrt(1 - r^2); delta

# proportion of variance explained

r^2

# percent reduction in E[Y] itself

# note this is not 1-1 with delta; change m0 and this will change

100*( abs(m1 - m0) / m0 )

Seth and Benny, many thanks for this extremely interesting and thought-provoking piece. This is a major contribution to the field. It is especially helpful to have the quantitative meta-analyses and meta-regressions; the typically low within-study power in this literature can obscure the picture in some other reviews that just count significant studies. It's also heartening to see how far this literature has come in the past few years in terms of measuring objective outcomes.

A few thoughts and questions:

1.) The meta-regression on self-reported vs. objectively measured outcomes is very interesting and, as you say, a little counter-intuitive. In a previous set of RCTs (Mathur 2021 in the forest plot), we found suggestive evidence of strong social desirability bias in the context of an online-administered documentary intervention. There, we only considered self-reported outcomes, but compared two types of outcomes: (1) stated intentions measured immediately (high potential for social desirability bias); vs. (2) reported consumption measured after 2 weeks (lower potential for social desirability bias). In light of your results, it could be that ours primarily reflected effects decaying over time, or genuine differences between intentions and behavior, more than pure social desirability bias. Methodologically, I think your findings point to the importance of head-to-head comparisons of self-reported vs. objective outcomes in studies that are capable of measuring both. If these findings continue to suggest little difference between these modes of outcome measurement, that would be great news for interpreting the existing literature using self-report measures and for doing future studies on the cheap, using self-report.

2.) Was there a systematic database search in addition to the thorough snowballing and manual searches? I kind of doubt that you would have found many additional studies this way, but this seems likely to come up in peer review if the paper is described as a systematic review.

3.) Very minor point: I think the argument about Glass delta = 0.3 corresponding to a 10% reduction in MAP consumption is not quite right. For a binary treatment X and continuous outcome Y, the relationship between Cohen’s d (not quite the same as Glass, as you say) and Pearson’s r is given by d = 2r / sqrt(1-r^2), such that d = 0.3 corresponds to r^2 (proportion of variance explained) = 0.02. Even so, the 2% of variation explained does not necessarily mean a 2% reduction in Y itself. Since Glass standardizes by only the control group SD, the same relationship will hold under equal SDs between the treatment and control group, and otherwise I do not think there will be a 1-1 relationship between delta and r.

Again, congratulations on this very well-conducted analysis, and best of luck with the journal submissions. I am very glad you are pursuing that.

Yes, good point