# False Positives, False negatives, true positives, true negatives

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).

• Yes. Something particular puzzles you ? – brumar Jul 3 '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 3 '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 3 '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 3 '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 3 '15 at 21:42