Is there an industry standard for the power section of the power.prop.test?
I am using the function to find p2 but not sure what is the standard for power.
power.prop.test(
n= 6289195,
p1=0.004,
power=0.8,
sig.level=0.05,
tol=.Machine$double.eps^.8)
For example, should it be 0.8 or 0.9?
This is a practical statistics question rather than an R question, but a power of 0.8, i.e. 80%, is common. Since it is common (rather like 95% confidence), people think they understand what it is saying and do not query its choice as much as they might another values.
You need to remember that it is an arbitrary target: if you changed it in your example, then the main impact would be to give you a different result for p2. Really you should be explicitly balancing the cost of increasing the sample size with against the different costs of Type I and particular Type II errors
A common reference is to Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic, section 2.4, which says:
It is proposed here as a convention that, when the investigator has no other basis for setting the desired power value, the value .80 be used. This means that b is set at .20. This arbitrary but reasonable value is offered for several reasons (Cohen, 1965, pp. 98-99). The chief among them takes into consideration the implicit convention for a of .05. The b of .20 is chosen with the idea that the general relative seriousness of these two kinds of errors is of the order of .20/.05, i.e., that Type I errors are of the order of four times as serious as Type II errors. This .80 desired power convention is offered with the hope that it will be ignored whenever an investigator can find a basis in his substantive concerns in his specific research investigation to choose a value ad hoc.
Other examples of 0.8 found in a quick search:
The R stats reference page for power.prop.test uses power=0.8 as an example
A University of Ottawa medicine page says "A power of 80% is often chosen; hence a true difference will be missed 20% of the time. This is a compromise because raising power to 90% power will require increasing the sample size by about 30%"
The Statistics Done Wrong site and book says "A scientist might want to know how many patients are needed to test if a new medication improves survival by more than 10%, and a quick calculation of statistical power would provide the answer. Scientists are usually satisfied when the statistical power is 0.8 or higher, corresponding to an 80% chance of concluding there’s a real effect. However, few scientists ever perform this calculation, and few journal articles ever mention the statistical power of their tests."
Related
I am a university student working on a research project, because of our local lockdown I cannot go into the field to collect observation data, I am therefore looking for an R package that will allow me to model the effects of competition when testing for ideal free distribution (IFD).
To give you a better idea of what I am looking for I have described the project in more detail below.
In my original dataset (which I received i.e., I did not collect the data myself) I have two patches (A,B) which received random treatments of food input (1:1, 2:1, 5:1). Under the ideal free distribution hypothesis species should distribute into the patches in accordance with the treatment ratios. This is not the case.
Under normal circumstances I would go into the field and observe behaviour of individuals in the patches to see if dominance affects distribution. Since we are in a lockdown I am unable to do so. I am hoping that there is a package out there that would allow me to model this scenario and help me investigate how competition affects IFD.
I have already found two packages called coexist and EcoVirtual but they model coexistence and extinction dynamics, whereas I want to investigate how competition might alter distribution between profitable patches when there is variation in the level of competition.
I am fairly new to R and creating my own package is beyond my skillset at this point, so I would appreciate the help.
I hope this makes sense and thanks in advance.
Wow, that's an odd place to find another researcher of IFD. I do not believe there are packages on R specifically about IFD. Its too specific and most models are relatively simple to estimate using common tests. For example, the input-matching rule you mentioned can be tested using a simple run-of-the-mill t-test, already included in base R.
What you have is not a coding problem per say, or even an statistical one. It is a biological problem. What ratio would you expect when animals are ideal (full knowledge of the environment), free (no movement costs), but with the presence of competition? Is this ratio equal to the ratio in your dataset? Sutherland,1983 suggests animals would undermatch.
I would love to discuss this at depth, given my PhD was in IFD, but I fear you hit the wrong forum.
What is the difference between the Maximal Information Coefficient and Hierarchical Agglomerative Clustering in identifying functional and non functional dependencies.
Which of them can identify duplicates better?
This question doesn't make a lot of sense, sorry.
The MIC and HAC have close to zero in common.
The MIC is a crippled form of "correlation" with a very crude heuristic search, and plenty of promotion video and news announcements, and received some pretty harsh reviews from statisticians. You can file it in the category "if it had been submitted to an appropriate journal (rather than the quite unspecific and overrated Science which probably shouldn't publish such topics at all - or at least, get better reviewers from the subject domains. It's not the first Science article of this quality....), it would have been rejected (as-is - better expert reviewers would have demanded major changes)". See, e.g.,
Noah Simon and Robert Tibshirani, Comment on “Detecting Novel Associations in Large Data Sets” by Reshef et al., Science Dec. 16, 2011
"As one can see from the Figure, MIC has lower power than dcor, in every case except the somewhat pathological high-frequency sine wave. MIC is sometimes less powerful than Pearson correlation as well, the linear case being particularly worrisome."
And "tibs" is a highly respected author. And this is just one of many surprised that such things get accepted in such a high reputation journal. IIRC, the MIC authors even failed to compare to "ancient" alternatives such as Spearman, to modern alternatives like dCor, or to properly conduct a test of statistical power of their method.
MIC works much worse than advertised when studied with statistical scrunity:
Gorfine, M., Heller, R., & Heller, Y. (2012). Comment on "detecting novel associations in large data sets"
"under the majority of the noisy functionals and non-functional settings, the HHG and dCor tests hold very large power advantages over the MIC test, under practical sample sizes; "
As a matter of fact, MIC gives wildly inappropriate results on some trivial data sets such as a checkerboard uniform distribution ▄▀, which it considers maximally correlated (as correlated as y=x); by design. Their grid-based design is overfitted to the rather special scenario with the sine curve. It has some interesting properties, but these are IMHO captured better by earlier approaches such as Spearman and dCor).
The failure by the MIC authors to compare to Spearman is IMHO a severe omission, because their own method is also purely rank-based if I recall correctly. Spearman is Pearson-on-ranks, yet they compare only to Pearson. The favorite example of MIC (another questionable choice) is the sine wave - which after rank transformation actually is busy a zigzag curve, not a sine anymore). I consider this to be "cheating" to make Pearson look bad, by not using the rank transformation with Pearson, too. Good reviewers would have demanded such a comparison.
Now all of these complaints are essentially unrelated to HAC. HAC is not trying to define any form if "correlation", but it can be used with any distance or similarity (including correlation similarity).
HAC is something completely different: a clustering algorithm. It analyzes a larger rows, not two (!) columns.
You could even combine them: if you compute the MIC foe every pair of variables (but I'd rather use Pearson correlation, Spearman correlation, or distance correlation dCor instead), you can use HAC to cluster variables.
For finding aftual duplicates, neither is a good choice. Just sort your data, and duplicates will follow each other. (Or, if you sort columns, next to each other).
I would like to compare the "death penalty method" with other penalty methods proposed in the Genetic Algorithms' literature.
I'm using the R software, so I need to write the codes of these penalty methods. I've finding lots of difficulties because I have not understood one thing about the death penalty function: how I have to handle the infeasible offsprings since the population size usually is fixed in genetic algorithms?
I mean, I understand that, in order to use appropriately the death penalty, I have to initialize the genetic algorithm with all feasible solutions. But even if I have all feasible solutions in the first population (t=0), I could have infeasible solutions in the next generation since the crossover and the mutations are "blind" operators.
So, since the death penalty rejects all the infeasible solutions, then what happen?
Will the next generation have a population side smaller (original dim size - number of infeasible solutions) or I have to select more parents to put in the mating pool for reproduction until the next generation is composed by "original dim size" feasible offsprings or I have to try again the genetic operators until all the individuals in t+1 are feasible?
I do not know R, but the theory of the death penalty implies that you should generate more offspring.
I would generate do the following pseudo-code (translate to R):
n=<desired_population_size>;
while (n>0) {
generate n offspring;
eliminate the non feasible ones
add the feasible ones to the new generation
n=<desired population size> - <current new generation population size>
}
The only problem with this loop is the risk that it may go on forever (if we never generate feasible solutions). Even though it is quite small, if you want to protect yourself from it, you can limit the number of iterations allowed in the while loop, using a simple counter.
There is a pretty interesting article on this by Michalewicz. Have a look.
I am trying to understand how neural network can predict different outputs by learning different input/output patterns..I know that weights changes are the mode of learning...but if an input brings about weight adjustments to achieve a particular output in back propagtion algorithm.. won't this knowledge(weight updates) be knocked of when presented with a different set of input pattern...thus making the network forget what it had previously learnt..
The key to avoid "destroying" the networks current knowledge is to set the learning rate to a sufficiently low value.
Lets take a look at the mathmatics for a perceptron:
The learning rate is always specified to be < 1. This forces the backpropagation algorithm to take many small steps towards the correct setting, rather than jumping in large steps. The smaller the steps, the easier it will be to "jitter" the weight values into the perfect settings.
If, on the other hand, used a learning rate = 1, we could start to experience trouble with converging as you mentioned. A high learning rate would imply that the backpropagation should always prefer to satisfy the currently observed input pattern.
Trying to adjust the learning rate to a "perfect value" is unfortunately more of an art, than science. There are of course implementations with adaptive learning rate values, refer to this tutorial from Willamette University. Personally, I've just used a static learning rate in the range [0.03, 0.1].
I am designing a RPG game like final fantasy.
I have the programming part done but what I lack is the maths. I am ok at maths but I am having trouble incorporating the players stas into mu sums.
How can I make an action timer that is based on the players speed?
How can I use attack and defence so that it is not always exactly the same damage?
How can I add randomness into the equations?
Can anyone point me to some resources that I can read to learn this sort of stuff.
EDIT: Clarification Of what I am looking for
for the damage I have (player attack x move strength) / enemy defence.
This works and scales well but i got a look at the algorithms from final fantasy 4 a while a got and this sum alone was over 15 steps. mine has only 2.
I am looking for real game examples if possible but would settle for papers or books that have sections that explain how they get these complex sums and why they don't use simple ones.
I eventually intent to implement but am looking for more academic knowledge at the moment.
Not knowing Final fantasy at all, here are some thoughts.
Attack/Defence could either be a 'chance to hit/block' or 'damage done/mitigated' (or, possibly, a blend of both). If you decide to go for 'damage done/mitigated', you'll probably want to do one of:
Generate a random number in a suitable range, added/subtracted from the base attack/defence value.
Generate a number in the range 0-1, multiplied by the attack/defence
Generate a number (with a Gaussian or Poisson distribution and a suitable standard deviation) in the range 0-2 (or so, to account for the occasional crit), multiplied by the attack/defence
For attack timers, decide what "double speed" and "triple speed" should do for the number of attacks in a given time. That should give you a decent lead for how to implement it. I can, off-hand, think of three methods.
Use N/speed as a base for the timer (that means double/triple speed gives 2/3 times the number of attacks in a given interval).
Use Basetime - Speed as the timer (requires a cap on speed, may not be an issue, most probably has an unintuitive relation between speed stat and timer, not much difference at low levels, a lot of difference at high levels).
Use Basetime - Sqrt(Speed) as the timer.
I doubt you'll find academic work on this. Determining formulae for damage, say, is heuristic. People just make stuff up based on their experience with various functions and then tweak the result based on gameplay.
It's important to have a good feel for what the function looks like when plotted on a graph. The best advice I can give for this is to study a course on sketching graphs of functions. A Google search on "sketching functions" will get you started.
Take a look at printed role playing games like Dungeons & Dragons and how they handle these issues. They are the inspiration for computer RPGs. I don't know of academic work
Some thoughts: you don't have to have an actual "formula". It can be rules like "roll a 20 sided die, weapon does 2 points of damage if the roll is <12 and 3 points of damage if the roll is >=12".
You might want to simplify continuous variables down to small ranges of integers for testing. That way you can calculate out tables with all the possible permutations and see if the results look reasonable. Once you have something good, you can interpolate the formulas for continuous inputs.
Another key issue is play balance. There aren't necessarily formulas for telling you whether your game mechanics are balanced, you have to test.