How should I objectively test my program results? I have developed two differing methods in MATLAB which aim to analyse a pop song and then automatically create a 30 second audio thumbnail (a preview clip) containing part of the chorus section.
Both methods have varying results:


*

*The first method can create a thumbnail for each track, managing to find a chorus section in 40 out of 50 tested songs

*The second method only managed to work on 30 out of the 50 songs, and it found the chorus section 21 times out the 30.


Obviously I know which method is superior, but I need to describe and explain the results in a report which requires the demonstration of proper statistical testing.
Other academic papers have previously used an f-test to do this, but because their methods are vastly superior, their aims are usually involve the detection of chorus onset times with 100% accuracy.
My aim is more relaxed as I am just looking for the generated thumbnails to contain any part of the chorus, regardless of onset.
Can anyone suggest some objective tests that I could possibly explore with regards to my project? This is my first time conducting an investigation like this so my experience/knowledge is incredibly low.
Thank you!
edit: Can I possibly conduct an f-test?
Recall = Number of thumbnails produced / Total number of tested songs
Precision = Number of choruses detected / Total number of thumbnails
Would this work or am I completely wrong?
 A: You can count the recognition of a chorus track as a 'Success' and the lack of recognition as a 'Failure'. Thus, you have the following data:
Method 1: Proportion of success (say, $p_1$) =  $\frac{40}{50}$
Method 2: Proportion of success (say, $p_2$) =  $\frac{21}{50}$
It seems that method 2 fails completely for 20 music tracks and hence I am assuming that they should be counted as a failure. 
Let:
$\pi_1$ and $\pi_2$ be the true proportions of successes for the two methods. Then you wish to assess if method 1 is superior to method 2. Thus, you would assume that:
Null Hypothesis: $\pi_1 = \pi_2$ 
Your alternative hypothesis is $\pi_1 \ne \pi_2$. 
(Note: Your alternative hypothesis could also be framed as $\pi_1 \ge \pi_2$ which would impact how you would do the testing but that is a nuance that you probably need not worry about.)
And attempt to see to what extent the data is consistent with the null hypothesis. The way to test for the null hypothesis is to use a Two-proportion z-test (See the 7th row of Common Test Statistics on wiki titled "Two-proportion z-test, pooled for d0 = 0". The symbols used in the table are explained at the bottom of the table.)
If the calculated Z value as per the formula is greater than 1.96 or less than -1.96 then you would reject the null in favor of the alternative hypothesis.
