How can bucketing a prediction variable make it significant? Recently, I read a research report that said that
"When academic achievement (first-year GPA) was treated as a continuous variable the relationship between academic achievement and emotional intelligence variables was non-significant or quite weak. "  
But, when they bucketed the academic variable (i.e. into people who scored above and below 3.0 as a cut-off), they found that variable was significant. 
"When academic achievement (first-year GPA) was treated as a continuous variable the relationship between academic achievement and emotional intelligence variables was non-significant or quite weak. "
Why would bucketing make a variable significant? Wouldn't you just lose information by bucketing? (i.e. why would you ever convert a continuous variable into a ordinal variable?) 
Thanks for your help! 
 A: If there is a linear relationship between the variables then "bucketing" will lose information and, all else being equal, you would expect that bucketing would lead to a higher (less-significant) p-value. 
However, in this example a linear relationship is unlikely. We might expect that an "average" student may get a lift in their marks due to their higher emotional intelligence. But, at the top end of GPA, perhaps the people with poor emotional intelligence will have an advantage (less friends = more time to study). Similarly, at the bottom end of GPA, students may be trying to get by with a minimum of effort, so the students with low emotional intelligence will try harder, which will offset the effect of emotional intelligence on grades.
More generally, this issue is at the heart of why many people like non-parametric statistics: while they throw away some information they make less stringent assumptions.
A: One scenario is that the continuous predictor is actually a noisy report of a discrete variable. For example, I do a lot of work with maritime data where the size of a ship is reported in dead weight tonnes. However, the important part of this data is whether the weight has crossed the threshold from one weight class to the next (Panamax versus Suezmax etc.) So the underlying relationship has natural 'steps'.
