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So I'm just starting to learn some proper statistics and recently learned about FP, FN, TP, TN.

I'm a little confused as to how that works.

Firstly lets say I have a way to predict whether a variable X is either 1 or 0 considering 1 to be positive and 0 to be negative. The quirk is that it is only correct some of the time

So lets say I have these values

The model is correct 40% of the time

The model is wrong 60% of the time

It predicts that X = 1 20% of the time

It predicts that X = 0 80% of the time

So that means:

True Positive : 40% * 20% = 8%

True Negative : 40% * 80% = 32%

False Positive: 60% * 20% = 12%

False Negative: 60% * 80% = 48%

Now my question is whether it would be correct to assume to say that the probability for a positive result using the model would be 56% (True Positive + False Negative) and the probability for a negative result using the model would be 44%(True Negative + False Positive).

Luis F Hernandez
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  • Yes. Something particular puzzles you ? – brumar Jul 03 '15 at 20:03
  • I was just unsure whether it would be correct to say if I have a method that is right 40% of the time then I could just add the false positive and true negative numbers to get how a prediction of the negative outcome. It just seemed a bit odd. It seems logical but I wasn't sure if there was any specific differentiation between a false positive and a true negative other than that one is just the opposite way of expressing it. – Luis F Hernandez Jul 03 '15 at 20:06
  • I see. I don't know what your current state of mind about it is but I think that you should no be mistaken about the fact that In this case Positive result is just "reporting Positive result" that is to say "The model think X=1". It can be right or wrong this is why False Negative or True Positive are not the same thing : in the first case (FN) the model is wrong in the later (TP) he is right. – brumar Jul 03 '15 at 20:22
  • When you say the model is correct 40% of the time, do you mean the model is equally correct when the situation is really 0 as when the situation is really 1? Do your calculations for the probability for a positive result consider base rates for 0's and 1's? – Joel W. Jul 03 '15 at 21:13
  • I'm just wondering if I could extrapolate a probability of X=1 from the sum of FN and TP? So assuming that the model is right 40% of the time and wrong 60% of the time(aka the opposite of the prediction happened) would it be sound to say when the model predicts that X=1 (assuming X=0 the only other possibility) has a 20% probability of happening, then the real probability of X=1 is 40% * 20% + 60% * 80% = 56% = (probability of model predicting correctly) * ( probability of X =1 according to model) + (probability of model predicting incorrectly) * ( probability of X = 0 according to the model) – Luis F Hernandez Jul 03 '15 at 21:42
  • @JoelW. yes, whether the model predicts X=0 or X=1 it's equally correct if the outcome is X=0 or X=1 respectively. But using my example 40% of the time that the model predicts X=1, the outcome will be X=0. And vice versa. aka the model will predict incorrectly.

    What do you mean by base rates for 0's and 1's?

     – Luis F Hernandez Jul 03 '15 at 21:45
  • @LuisFHernandez Let's say that in the real world there were only 1s. Zeros never occurred. What would that do to your calculation of what you call the probability for a positive result? – Joel W. Jul 03 '15 at 22:11
  • @JoelW. Well assuming the model was still predicting as it always had, it would make that probability 68%, because the model would still predict 20% X=1, and 80% X=0, but since the model would be wrong 80% of the time (because X=0 never comes up) that means that what I've called "Probability for a Positive Result" would be 20% * 20% + 80% * 80% = 68% . I think? Not sure if that all makes sense. – Luis F Hernandez Jul 04 '15 at 00:38

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