Since the usual claim is that cooperation has decreased drastically, showing any scatterplot with cooperation rates flat/increasing (and definitely not decreasing drastically) is food for thought. That the temporal trend is small in whatever unit is to miss the point there: it shouldn't be small! At the least, it should make you think about how it can be possible to have both drastically decreasing cooperation as measured by things like going to your local Kiwanis and also have people being just as nice as ever to each other in artificial lab experiments.
They don't specify why the predictive interval, but that should be obvious given that it's a random-effects meta-analysis: it's the interval of interest for the parameter relevant to individual studies, the within-study cooperation rate. There is substantial heterogeneity between each lab experiment (lab, experimenter, experiment/test, local population, recruitment...), so in planning a well-powered experiment, the global mean is unhelpful - oh, there's a global mean cooperation rate across all possible combinations of variables of 50% but also basically zero probability the exact cooperation rate will be 50% when you go to run it in your own particular lab? That's, uh, good to know...? But if you do your power analysis based on that, you will be over-optimistic because you are ignoring that uncertainty due to heterogeneity. Much better to know how wide the spread on your actual cooperation rate will be: plotting the *predictive* interval tells you your realized cooperation rate could be anywhere from 25% to 75%, and you will base your power analysis on that. (So you wouldn't assume optimistically that you'll get the nice 50%, which maximizes information from binary comparisons/outcomes, you'd assume your rate would be high/low by 25%, which usually means you'll need substantially more _n_.)
I bet my bottom dollar that if the authors presented the yearly weighted averages, these people would be soyfacing over their results. The rank-order correlation between year and weighted cooperation rate would be yuuuge. The increase from 1971 to 2002 is roughly 6 times as large as the standard error. For a given 15 year interval, there should be a 95% chance that the studies at the last end of the interval are higher in cooperation than the studies at the first end of the interval.
Since the usual claim is that cooperation has decreased drastically, showing any scatterplot with cooperation rates flat/increasing (and definitely not decreasing drastically) is food for thought. That the temporal trend is small in whatever unit is to miss the point there: it shouldn't be small! At the least, it should make you think about how it can be possible to have both drastically decreasing cooperation as measured by things like going to your local Kiwanis and also have people being just as nice as ever to each other in artificial lab experiments.
They don't specify why the predictive interval, but that should be obvious given that it's a random-effects meta-analysis: it's the interval of interest for the parameter relevant to individual studies, the within-study cooperation rate. There is substantial heterogeneity between each lab experiment (lab, experimenter, experiment/test, local population, recruitment...), so in planning a well-powered experiment, the global mean is unhelpful - oh, there's a global mean cooperation rate across all possible combinations of variables of 50% but also basically zero probability the exact cooperation rate will be 50% when you go to run it in your own particular lab? That's, uh, good to know...? But if you do your power analysis based on that, you will be over-optimistic because you are ignoring that uncertainty due to heterogeneity. Much better to know how wide the spread on your actual cooperation rate will be: plotting the *predictive* interval tells you your realized cooperation rate could be anywhere from 25% to 75%, and you will base your power analysis on that. (So you wouldn't assume optimistically that you'll get the nice 50%, which maximizes information from binary comparisons/outcomes, you'd assume your rate would be high/low by 25%, which usually means you'll need substantially more _n_.)
I bet my bottom dollar that if the authors presented the yearly weighted averages, these people would be soyfacing over their results. The rank-order correlation between year and weighted cooperation rate would be yuuuge. The increase from 1971 to 2002 is roughly 6 times as large as the standard error. For a given 15 year interval, there should be a 95% chance that the studies at the last end of the interval are higher in cooperation than the studies at the first end of the interval.