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Cliff AB
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What we call P-hacking is applying a significance test multiple times and only reporting the significance results. Whether this is good or bad is situationally dependent.

To explain, let's think about true effects in Bayesian terms, rather than null and alternative hypotheses. As long as we believe our effects of interest come from a continuous distribution, then we know the null hypothesis is false. However, in the case of a two-sided test, we don't know whether it is positive or negative. Under this light, we can think of p-values for two sided tests as a measure of how strong the evidence is that our estimate has the correct direction (i.e., positive or negative effect).

Under this interpretation, any significance test can have three possible outcomes: we see enough evidence to conclude the direction of the effect and we are correct, we see enough evidence to conclude the direction of the effect but we are wrong, or we don't see enough evidence to conclude the direction of the effect. Note that conditional that you have enough evidence (i.e., $p < \alpha$), the probability of getting the direction correct should be greater than the probability of getting it incorrect (unless you have some really crazy, really bad test), although as the true effect size approaches zero, the conditional probability of getting the direction correct given sufficient evidence approaches 0.5.

Now, consider what happens when you keep going back to get more data. Each time you get more data, your probability of getting the direction correct conditional on sufficient data only goes up. So under in this scenario, we should realize that by getting more data, although we are in fact increasing the probability of a type I error, we are also reducing the probability of mistakenly concluding the wrong direction.

Take this in contrast the more typical abuse of P-hacking; we test 100's of effect sizes that have good probability of being very small and only report the significant ones. Note that in this case, if all the effects are small, we have a near 50% chance of getting the direction wrong when we declare significance.

Of course, the produced p-values from this data-double-down should still come with a grain of salt. While, in general, you shouldn't have a problem with people collecting more data to be more certain about an effect size, this could be abused in other ways. For example, a clever PI might realize that instead of collecting all 100 data points at once, they could save a bunch of money and increase power by first collecting 50 data points, analyzing the data, and then collecting the next 50 if it's not significant. In this scenario, they increase the probability of getting the direction of the effect wrong conditional on declaring significance, since they are more likely to get the direction of the effect wrong with 50 data points than with 100 data points.

And finally, consider the implications of not getting more data when we have an insignificant result. That would imply never collecting more information on the topic, which won't really push the science forward, would it? One underpowered study would kill a whole field.

What we call P-hacking is applying a significance test multiple times and only reporting the significance results. Whether this is good or bad is situationally dependent.

To explain, let's think about true effects in Bayesian terms, rather than null and alternative hypotheses. As long as we believe our effects of interest come from a continuous distribution, then we know the null hypothesis is false. However, in the case of a two-sided test, we don't know whether it is positive or negative. Under this light, we can think of p-values for two sided tests as a measure of how strong the evidence is that our estimate has the correct direction (i.e., positive or negative effect).

Under this interpretation, any significance test can have three possible outcomes: we see enough evidence to conclude the direction of the effect and we are correct, we see enough evidence to conclude the direction of the effect but we are wrong, or we don't see enough evidence to conclude the direction of the effect. Note that conditional that you have enough evidence (i.e., $p < \alpha$), the probability of getting the direction correct should be greater than the probability of getting it incorrect (unless you have some really crazy, really bad test), although as the true effect size approaches zero, the conditional probability of getting the direction correct given sufficient evidence approaches 0.5.

Now, consider what happens when you keep going back to get more data. Each time you get more data, your probability of getting the direction correct conditional on sufficient data only goes up. So under in this scenario, we should realize that by getting more data, although we are in fact increasing the probability of a type I error, we are also reducing the probability of mistakenly concluding the wrong direction.

Take this in contrast the more typical abuse of P-hacking; we test 100's of effect sizes that have good probability of being very small and only report the significant ones. Note that in this case, if all the effects are small, we have a near 50% chance of getting the direction wrong when we declare significance.

And finally, consider the implications of not getting more data when we have an insignificant result. That would imply never collecting more information on the topic, which won't really push the science forward, would it? One underpowered study would kill a whole field.

What we call P-hacking is applying a significance test multiple times and only reporting the significance results. Whether this is good or bad is situationally dependent.

To explain, let's think about true effects in Bayesian terms, rather than null and alternative hypotheses. As long as we believe our effects of interest come from a continuous distribution, then we know the null hypothesis is false. However, in the case of a two-sided test, we don't know whether it is positive or negative. Under this light, we can think of p-values for two sided tests as a measure of how strong the evidence is that our estimate has the correct direction (i.e., positive or negative effect).

Under this interpretation, any significance test can have three possible outcomes: we see enough evidence to conclude the direction of the effect and we are correct, we see enough evidence to conclude the direction of the effect but we are wrong, or we don't see enough evidence to conclude the direction of the effect. Note that conditional that you have enough evidence (i.e., $p < \alpha$), the probability of getting the direction correct should be greater than the probability of getting it incorrect (unless you have some really crazy, really bad test), although as the true effect size approaches zero, the conditional probability of getting the direction correct given sufficient evidence approaches 0.5.

Now, consider what happens when you keep going back to get more data. Each time you get more data, your probability of getting the direction correct conditional on sufficient data only goes up. So under in this scenario, we should realize that by getting more data, although we are in fact increasing the probability of a type I error, we are also reducing the probability of mistakenly concluding the wrong direction.

Take this in contrast the more typical abuse of P-hacking; we test 100's of effect sizes that have good probability of being very small and only report the significant ones. Note that in this case, if all the effects are small, we have a near 50% chance of getting the direction wrong when we declare significance.

Of course, the produced p-values from this data-double-down should still come with a grain of salt. While, in general, you shouldn't have a problem with people collecting more data to be more certain about an effect size, this could be abused in other ways. For example, a clever PI might realize that instead of collecting all 100 data points at once, they could save a bunch of money and increase power by first collecting 50 data points, analyzing the data, and then collecting the next 50 if it's not significant. In this scenario, they increase the probability of getting the direction of the effect wrong conditional on declaring significance, since they are more likely to get the direction of the effect wrong with 50 data points than with 100 data points.

And finally, consider the implications of not getting more data when we have an insignificant result. That would imply never collecting more information on the topic, which won't really push the science forward, would it? One underpowered study would kill a whole field.

Source Link
Cliff AB
  • 21.6k
  • 1
  • 51
  • 104

What we call P-hacking is applying a significance test multiple times and only reporting the significance results. Whether this is good or bad is situationally dependent.

To explain, let's think about true effects in Bayesian terms, rather than null and alternative hypotheses. As long as we believe our effects of interest come from a continuous distribution, then we know the null hypothesis is false. However, in the case of a two-sided test, we don't know whether it is positive or negative. Under this light, we can think of p-values for two sided tests as a measure of how strong the evidence is that our estimate has the correct direction (i.e., positive or negative effect).

Under this interpretation, any significance test can have three possible outcomes: we see enough evidence to conclude the direction of the effect and we are correct, we see enough evidence to conclude the direction of the effect but we are wrong, or we don't see enough evidence to conclude the direction of the effect. Note that conditional that you have enough evidence (i.e., $p < \alpha$), the probability of getting the direction correct should be greater than the probability of getting it incorrect (unless you have some really crazy, really bad test), although as the true effect size approaches zero, the conditional probability of getting the direction correct given sufficient evidence approaches 0.5.

Now, consider what happens when you keep going back to get more data. Each time you get more data, your probability of getting the direction correct conditional on sufficient data only goes up. So under in this scenario, we should realize that by getting more data, although we are in fact increasing the probability of a type I error, we are also reducing the probability of mistakenly concluding the wrong direction.

Take this in contrast the more typical abuse of P-hacking; we test 100's of effect sizes that have good probability of being very small and only report the significant ones. Note that in this case, if all the effects are small, we have a near 50% chance of getting the direction wrong when we declare significance.

And finally, consider the implications of not getting more data when we have an insignificant result. That would imply never collecting more information on the topic, which won't really push the science forward, would it? One underpowered study would kill a whole field.