Statistics has always been a stumbling block for me (when the going gets tough, the tough get empirical). Can anyone explain this in practical terms? Maybe I am asking what lm does in the given...
To adjust for a variable X means to look at relationships in data that contain only a subset or single value of X. It can also mean to look at relationships for all the values of X separately. Adjustment goes by a number of different names in the sciences, including “control for”, “condition on”, “hold constant”, “stratify”, “select”, etc.
Statistics has always been a stumbling block for me (when the going gets tough, the tough get empirical). Can anyone explain this in practical terms? Maybe I am asking what lm does in the given examples, but maybe I am misunderstanding/asking the wrong question.
Looks like you’re asking about Rule 8? So there, a and b are unrelated, except for the fact that they’re both influenced by c. So the idea is to control for the effect of the c on each, and then...
Looks like you’re asking about Rule 8? So there, a and b are unrelated, except for the fact that they’re both influenced by c. So the idea is to control for the effect of the c on each, and then see what relationship remains (here, none).
In the code, lm() fits a simple linear regression - a straight line describing the relationship. So you fit a line for a predicted by c and a line for b predicted by c. Then you calculate whatever is left in each - the residuals. That is, the distance of each point from the line. This is the part of a that isn’t related to c, and the part of b that isn’t related to c. Then lastly, they plot those residuals against each other. Since both a and b were defined above as 2c + noise, we see it’s just noise left over with no relationship between a and b.
In practical terms, say I’m measuring growth rate of rabbits on two different diets. I have 40 rabbits in each group. You might expect that - in addition to diet - growth rate is also impacted by starting weight. So I would include starting weight in the statistical model, and then the effect of diet is estimated while controlling for starting weight. Otherwise, any difference due to diet might be masked by differences due to starting weight.
You could also flip that and say you’re interested in the effect of starting weight on growth rate, but you have data from rabbits in two different diets. You’d do the same to control for diet - you can then estimate the effect of starting weight on growth rate, given a particular diet.
Thank you, the explanation is helpful. I'm still in "believe it because Prof. WeAreWaves tells you so even though you have no intuition", but it is clearer, and I appreciate the explanation of...
Thank you, the explanation is helpful. I'm still in "believe it because Prof. WeAreWaves tells you so even though you have no intuition", but it is clearer, and I appreciate the explanation of lm() as well.
Here’s a nice summary of the rules from The Book of Why.
(Headline says seven, but there are actually eight.)
Statistics has always been a stumbling block for me (when the going gets tough, the tough get empirical). Can anyone explain this in practical terms? Maybe I am asking what
lmdoes in the given examples, but maybe I am misunderstanding/asking the wrong question.Looks like you’re asking about Rule 8? So there, a and b are unrelated, except for the fact that they’re both influenced by c. So the idea is to control for the effect of the c on each, and then see what relationship remains (here, none).
In the code, lm() fits a simple linear regression - a straight line describing the relationship. So you fit a line for a predicted by c and a line for b predicted by c. Then you calculate whatever is left in each - the residuals. That is, the distance of each point from the line. This is the part of a that isn’t related to c, and the part of b that isn’t related to c. Then lastly, they plot those residuals against each other. Since both a and b were defined above as 2c + noise, we see it’s just noise left over with no relationship between a and b.
In practical terms, say I’m measuring growth rate of rabbits on two different diets. I have 40 rabbits in each group. You might expect that - in addition to diet - growth rate is also impacted by starting weight. So I would include starting weight in the statistical model, and then the effect of diet is estimated while controlling for starting weight. Otherwise, any difference due to diet might be masked by differences due to starting weight.
You could also flip that and say you’re interested in the effect of starting weight on growth rate, but you have data from rabbits in two different diets. You’d do the same to control for diet - you can then estimate the effect of starting weight on growth rate, given a particular diet.
Thank you, the explanation is helpful. I'm still in "believe it because Prof. WeAreWaves tells you so even though you have no intuition", but it is clearer, and I appreciate the explanation of lm() as well.