Why is F-measure more popular than accuracy? F-measure, the harmonic mean of recall and precision, and accuracy, the ratio of true positives and negatives to all instances, are two ways of evaluating the quality of a dichotomous model.
It seems that whenever there is a 2x2 contingency table to evaluate, theoretically or in practical use, the first thing to use is F-measure, and accuracy, if ever mentioned, is secondary.
Despite always using F-measure, I feel like accuracy is both more telling about a model (naturally balanced between the test and the ground truth for both positive and negative) and more easily interpreted.
Here is a 2x2 contingency table for reference:
$$
\begin{array}{ccc}
   &\rm{Ground\ Truth}& \\
   &\rm{True}         & \rm{False} \\
\rm{Model} &&\\
\rm{Positive} & TP & FP \\
\rm{Negative} & FN & TN 
\end{array}
$$
The F-measure looks like a balance between recall and precision:
$$F_1 = \frac{2}{\frac{1}{\rm{recall}} + \frac{1}{\rm{precision}}}$$
Since this is somewhat opaque (when looking at a 2x2 table), when can derive the simpler computation:
$$ F_1 = \frac{2}{\frac{1}{\frac{TP}{TP+FN}} + \frac{1}{\frac{TP}{TP+FP}}} = \frac{2 TP}{2TP+FN+FP} $$
which shows that $F_1$ ignores entirely $TN$ in the numerator and arbitrarily doubles $TP$.
But accuracy already has the balance right at the top; no matter how lopsided the incidence is, accuracy just counts what is correct:
$$\rm{acc} = \frac{TP+TN}{TP+FP+FN+TN}.$$ 
Is there a good reason why F-measure is favored over accuracy, why True Positives are favored over True either Positive or Negative? $F_1$ seems unbalanced. Is it that TP is just that much more important? Is it mostly culture (people just have used it more)? What are the properties of a model that would lead to ignoring accuracy and favoring F-measure for most things? Is it simply because of the usual lack of available instances for True Negatives?
 A: $F_1$ works better when you care most for classification of rare positives. $F_\beta$ is just a weighted harmonic mean of two positive focused measures, i.e. precision and recall. When $\beta=1$ precision and recall are equally weighted in $F_1$, which is used most in practice. When positive incidence rate is low in the sample the predictive performance metrics such as accuracy can get overwhelmed by high rates of prediction in negatives, which can be accomplished by overpredicting them in expense of positives.
Suppose that you're classifying rare events, i.e. positives rate in the sample is low. So, you make your model mark everything negative. What will be the performance scores?
Let's look at the case where the positive are 10% of the sample of size 100. Your "model" always outputs negative. It's not really a model, of course, but let's see what happens : TP = 0, FP = 0, TN = 90 and FN = 10.
$$
\begin{array}{|c|c|}
\hline
              & \rm{True} & \rm{False} \\
\hline
\rm{Positive} & TP = 0 & FP = 0 \\
\hline 
\rm{Negative} & FN = 10 & TN = 90 \\
\hline
\end{array}
$$
Obviously, this "model" missed all positives, but it's accuracy is 90/100 = 90%! Luckily, F1 = 0/10 = 0%. 
Now compare this performance to a completely random marking of outputs with $(5+45)/100 =$ 50% positive: TP = 5, FP =5, TN = 45 and FN = 45. 
$$
\begin{array}{|c|c|}
\hline
              & \rm{True} & \rm{False} \\
\hline
\rm{Positive} & TP = 5 & FP = 5 \\
\hline 
\rm{Negative} & FN = 45 & TN = 45 \\
\hline
\end{array}
$$
You get accuracy = 50/100 = 50%, and F1 = 10/60 = 17%. Oh, what happened? The random marking is less accurate, despite marking half of positives right according "accuracy" measure, but F1 measure indicates that it's better than "always neg model."
A dummy model that marks everything positive in this sample will produce TP = 10, FP =90, TN = 0 and FN = 0. 
$$
\begin{array}{|c|c|}
\hline
              & \rm{True} & \rm{False} \\
\hline
\rm{Positive} & TP = 10 & FP = 90 \\
\hline 
\rm{Negative} & FN = 0 & TN = 0 \\
\hline
\end{array}
$$
So, its accuracy = 10/100 = 10%, while F1 = 20/110 = 18%.
All three models are not really models at all. They can be used as benchmarks when comparing to actual models.

Here's another comparison, between two models.
Suppose that you built a real model A and it produced the following metrics: TP = 9, FP =5, TN = 85 and FN = 1. 
$$
\begin{array}{|c|c|}
\hline
              & \rm{True} & \rm{False} \\
\hline
\rm{Positive} & TP = 9 & FP = 5 \\
\hline 
\rm{Negative} & FN = 1 & TN = 85 \\
\hline
\end{array}
$$
This model will have accuracy = 94/100 = 94% and F1= 18/24 = 75%.
Then you build another model B: TP = 8, FP =4, TN = 86 and FN = 2. 
$$
\begin{array}{|c|c|}
\hline
              & \rm{True} & \rm{False} \\
\hline
\rm{Positive} & TP = 8 & FP = 4 \\
\hline 
\rm{Negative} & FN = 2 & TN = 86 \\
\hline
\end{array}
$$
The accuracy= 94/100 = 94% and F1= 16/22 = 73%.
Accuracy doesn't catch the difference between A and B because it cares equally for TP and TN, model B missed one more positive, but picked up one correct negative, so its accuracy is the same. F1 "doesn't care" for correct negatives, so it catches the lower rate of positives in model B.
