 Hello, my name is Shinji Nakagawa. Today, I'd like to tell you about our new method on log-response ratio and some standard deviations are missing. First, I'd like to acknowledge my lab members at UNSW Sydney, Australia, and my co-authors, Vex, Russia, Dan Alistar, and Wolfgang the Cat. He sometimes takes human form. It looks like this. OK, I think some of you may be familiar with log-response ratio, but everybody probably knows. Co-NZD, HGZG, this is just a small sample-sized collection version of the Co-NZD. More generally, they are known as the standardized mean difference. And for the reason I'm going to show, so d equal mean minus another mean divided by full standard deviation. Log-response ratio is a ratio of two means, and it's long. And it turns out to be the most standardized or a unique less defect size in ecology and evolution. So it's important defect size for evolutionary biologists like myself. OK, so the missing data everywhere and the meta-nike data are no exception. And generally, it looks like this. When we try to collect descriptive statistics from papers, so you get mean, standard deviation, sample size for the control, and the same thing for the treatment group or experimental group, and quite often, standard deviation missing. Sometimes, occasionally, and I'm missing, but that's very rare. So when that happens, what we usually do is just delete those rows or cases because you can't calculate log-response ratio sampling variance, which we will see the reason why a bit later on. So when we delete these cases, it's called the complete cases approach because we just use the cases where SD are not missing. But this will lead to some biases overall mean estimate or other meta-nike parameters. And this paper points out this. And this paper says we should use multiple invitations otherwise or the meta-nike results are biased often. I guess. And another interesting thing is a survey included in this study showed 75% of meta-nike data in a collogen evolution have missing SD. So it's a very common problem. And multiple invitations are certainly a solution, but problem is when we run the complex meta-analysis, multiple invitations are very difficult to implement. For example, when you have effects size, multiple effects size from the same studies or a collogen evolution, we often have multiple species on the top of multiple effects size per study. Then we have to account for what we call phylogenetic relatedness. That gets very complex model. In this case, multiple invitations technique is very hard to implement. So I was kind of looking for the easier solution compared to multiple invitations. And I couldn't come up with tell. I came across this paper by Donkastan Spake and Rebecca Spake-Zabeks. You saw in the second acknowledgement slide. In this study, they conducted simulation study. And they proposed this formula there with CB. And I'd like to explain this. So this is log-response ratio. You've seen this before. Important thing is meta-analysis. You need the sampling variance. Inverse of this is going to be a weight for each case or each study. And this has a SD mean sample size. And you can see the SD divided mean can be written as a CB coefficient of variation. And they propose rather than using the CB specific to study, we can calculate overall CB, average CB, across all available study. And you can use that. And that would lead to less biased or more accurate overall meta-analytic mean. And you are wondering why is that? And the reason being, they showed this in the simulation is when n's are small, and quite often many studies in the ecology revolution, lots of study has a small n's or sample sizes. SD are estimates so inaccurately. Yes, those are estimate, not true SD. This will result some bias or an inaccuracy over all mean. So that's quite cool. But Fenaro reading this paper toward the end of this paper, they said, actually, this CB, average CB can be calculated. There's missing data because average CB can be calculated without or excluding those missing cases. And you can use average CB for those missing cases. And I thought, oh, this will solve everything. This is why we conducted this new study and the proposed four different new methods, which I'm going to tell you about. So as you have already seen, this is a Doncaster spec estimator. And they use, for sampling variance or log response ratio, they use average CB. We made two improvements for this. We actually used, it looks scary, but it's just a weighted average CB, giving more weights on the study with higher sample size. Another one is that those two latter terms, it's a small sample size correction. It's a bit like a HGG to the Cohen's D. So what's the study? So we had a four method, but I want to just share with you the two method, the missing cases, all cases. So you've seen this before, grades are missing data. And we use this sampling variance. Let's call it the V-Calder. That's our estimator. Those missing a standard deviation, we replace with our V-Calder or all cases method. We use all, for all regardless it's missing SB or not, use this V-Calder for all the studies or all cases, I guess. So we conducted simulation. And this is our simulation. Actually, we vary the degree of missingness from 5% to up to 30%. It's surprising thing is bias. Logical response ratio here is a bias in the overall mean, overall meta-analytic mean. And all cases performs really well, close to zero, zero bias. Next are missing cases. What really surprising, so full data, one is the family simulated, that data set didn't have any missing data. That's really counterintuitive because that should, this should perform least bias, with least bias. But you may remember this Don Castan's fake paper. What they showed is, sometimes each study has a two few sample size, and that affects the accuracy of the meta-analytic mean estimate. So that's what's happening. So actually turns out to be using that new estimator, our estimators for the sampling variance would perform the best. And we don't show this here. It performs in like estimating heterogeneity, coverage, everything is better for all cases. And the missing cases compared to full data, which is surprising. So conclusion, all cases mess with the best one, but we should also probably run the missing cases as a sort of sensitivity analysis. See, you get consistent result. And what we can say, the biggest conclusion is all future meta-analysis can use our method because regardless of how complex or how complex your meta-analysis models are, you can use this method easily because only you need to get weighted average of CV, then you can plug in. One thing I didn't tell you about is assumptions and normality, log response ratio is passed and proposed by hedges. That's the same hedges for the hedges D. And this formulas seem to fail when there's a lot of counter data or non-normal. Yes, so lots of counter data in ecological evolution. So we need to be careful. In such case, we propose several different, couple of different solutions for this all in this webpage, it's connected to paper. You can find this in the webpage for the paper or it's here and thank you.