The p-value is the probability that a result like that could have happened if only chance were at work. That this is not the same as the probability that the result is due to chance is easily seen from the fact that the p-value is inversely correlated with sample size. Surely sample size has no influence on whether there’s a real effect to be measured; it only affects how likely we are to detect the effect. There may be other reasons for thinking that chance is more or less likely; e.g. because there is an extremely plausible causal mechanism, or conversely because there are independent grounds to doubt any meaningful relationship could be present. If so, that can give you good reason for thinking the probability of the chance hypothesis remains lower or higher than the p-value, possibly much lower or much higher. If a study linked prayer and earthquakes with a .001 p-value (and fraud were ruled out as an explanation), it would still surely be most reasonable to think that chance produced an unlikely result (as of course it sometimes does). The current analysis may include instances of the converse situation, where it seems very unlikely that there is no connection, so it may be more reasonable to think that a small, skewed sample has inflated the p-value, rather than thinking that only chance is at work. I suppose I tend to think it probably does include such cases; I can easily believe that some of the effects of ethical theory on behavior could be very small, small enough to require a very large sample to reliably detect, but zero effect seems a priori unlikely in many of the examples.
Connected to Stuff that maes Stuff happen. A null hypothesis could be one where obesity, exercise and internet are not connected, or alternatively that exercise (or lack thereof) causes obesity, and internet is unrelated to both of these. Then, you can conduct an experiment and collect evidence for or against the null hypothesis. If p=P(data | null hypothesis is true)<0.05, a winner is you.
The p-value is the probability that a result like that could have happened if only chance were at work. That this is not the same as the probability that the result is due to chance is easily seen from the fact that the p-value is inversely correlated with sample size. Surely sample size has no influence on whether there’s a real effect to be measured; it only affects how likely we are to detect the effect. There may be other reasons for thinking that chance is more or less likely; e.g. because there is an extremely plausible causal mechanism, or conversely because there are independent grounds to doubt any meaningful relationship could be present. If so, that can give you good reason for thinking the probability of the chance hypothesis remains lower or higher than the p-value, possibly much lower or much higher. If a study linked prayer and earthquakes with a .001 p-value (and fraud were ruled out as an explanation), it would still surely be most reasonable to think that chance produced an unlikely result (as of course it sometimes does). The current analysis may include instances of the converse situation, where it seems very unlikely that there is no connection, so it may be more reasonable to think that a small, skewed sample has inflated the p-value, rather than thinking that only chance is at work. I suppose I tend to think it probably does include such cases; I can easily believe that some of the effects of ethical theory on behavior could be very small, small enough to require a very large sample to reliably detect, but zero effect seems a priori unlikely in many of the examples.
Connected to Stuff that maes Stuff happen. A null hypothesis could be one where obesity, exercise and internet are not connected, or alternatively that exercise (or lack thereof) causes obesity, and internet is unrelated to both of these. Then, you can conduct an experiment and collect evidence for or against the null hypothesis. If p=P(data | null hypothesis is true)<0.05, a winner is you.