Allow me to translate.
"Using established scientific methods..."
Translation:
"Using statistical tests that were never meant to be used in the way we're going to use them, we will produce a large number of false positive results to convince people they're psychic".
Hi there, totally understandable response. However I am going to direct you to a few of the academic journal articles which I based the app upon. I hope you read them 
1. goo.gl/P7nYwG
Correlations of Random Binary Sequences with Pre-Stated Operator Intention: A Review of a 12-Year Program (1997). J. Scientific Exploration, 11, No.3, pp.345-367.
2. goo.gl/QC3jbY
Correlations of Continuous Random Data with Major World Events (2002). Foundations of Physics Letters, Vol. 15, No. 6, pp. 537-550.
3. goo.gl/irrBrg
Consciousness, Information, and Living Systems (2005). Cellular & Molecular Biology, 51, pp.703-714.
4. goo.gl/b14wuqcontent_copyCopy short URL
Biological Utilisation of Quantum NonLocality (1991). Foundations of Physics, Vol. 21, pp. 197-207
Interesting articles. I didn't actually claim psychic abilities don't exist, although I personally don't believe in them. I was claiming that your app won't be able to determine their existence on an individual with any kind of accuracy.
Since psychic ability is largely shunned by the mainstream, we can take it that at least one of two things is true: psychic ability is "small", and/or it is rare. If it were "large" or commonplace it would be accepted by the mainstream.
If psychic abilities are "small" then you'll need thousands of tests to determine if an individual has them. See your first reference for a perfect example - in table 1, column HI, they had 839,800 repetitions of 200 Bernoulli trials to get a mean difference of 0.026 in the number of successes. They couldn't even achieve a mean difference of 1.
If psychic abilities are rare then your app will suffer from the notorious problem of having very poor positive predictive value. This article describes it: http://www.badscience.net/2006/12/crystal-balls-and-positive-predictive-values/
I can explain how the app can correctly determine whether psychic ability is present. For individual users, after each test is completed, the app transitions into a results screen which shows the deviation from chance, albeit not using a p-value (I wanted to make the results screen easy to read for those without a statistical background). While one test deviating from chance does not mean the user is psychic, if the user is able to consistently achieve a deviation from chance, that would be something to explore further.
Having said that, the big picture in determining if psychic ability is present is that within the "cloud" of the app there is an anonymous database where the information from each test is stored. Once a large enough body of data has been accumulated, a meta-analysis of the data can be made which would then mathematically determine whether or not psychic ability is being demonstrated.
To your point of psychic ability being a "small" effect. You are correct. Research shows that these abilities are not of a sufficient magnitude to normally be detectable. While there have been many instances of dramatic demonstrations of psychic ability in the literature, in general psychic ability is a small effect. Having said that, while the effect may be "small", an effect is still present. Which is why in the studies I previously cited meta-analysis was used. The effect would be undetectable otherwise. Once a large enough body of data has been accumulated, then we can see whether the results from the app is demonstrating an effect.
Finally, just as an aside, the app is registered with the IRB, and is a legitimate parapsychological experiment. The idea was to create something fun that anyone could play, while the real science was going on in the background.
I appreciate your skepticism. I'm not sure whether or not the app will show that psychic ability exists, only time will tell on that.
