Prometheus

Outlier detection is as much art as it is science. Can't help with the code but this paper gives the formulas for several types of outlier detection in multivariate regression. But when you say curves you mean you want to use non-linear regression?

Why do you think 0 is incorrect? If you sketch [latex]x^3[/latex] you might be able to get an intuitive feel for the answer.

Thanks, but there was quite a lot to choose from and i was only confusing myself further. Maybe if i give some details someone could help narrow it down. In my text the overlap rule was defined as: [latex]p_i = |\int_{-\infty}^{\infty} \psi_i^*(x) \Psi(x,t) dx|^2[/latex] Where [latex] \psi_i^*(x) [/latex] is the conjugate of the energy eigenfunction, [latex] \Psi(x,t)[/latex] is the wave function of the system and [latex] p_i [/latex] the probability of obtaining the ith energy eigenvalue. No explanation as to how this was derived is given but the text does describe it as being the overlap between the energy eigenfunction and the wave function. This got me wondering whether this has any relation then to the general form of a convolution: [latex]f*g(t)= \int_{-\infty}^{\infty} f(\tau)g(t-\tau) d\tau[/latex] which i understand has a similar interpretation as a sum of the degree of overlap between the function f and g?

I have just come across the overlap rule used to calculate the probability of finding any particular energy eigenvalue, but little about it was explained. Is an overlap integral the same as a convolution of two functions?

Nor would i discretise the electromagnetic spectrum even though there are obvious qualitative bins such as red blue and green. If i absolutely had to i would use these bins with the caveat of stating it is a very poor model - a first approximation perhaps. Let's talk in the abstract to avoid our political biases. You can cut up a continuum any way you like - the labelling of the bins is a question of taxonomy rather than empiricism. However, certain ways of discretising might be more useful than others by having a greater predictive power. We might then say that certain choices of bins are more scientific: the more predictive the more scientific. But then we have agreed a continuous model is more predictive than any discrete model and so by our measure the most scientific. The conclusion is then that the most scientific way to proceed, if available, is to ignore categorisation. A discrete model would be an inferior approximation which may have some utility in lieu of the continuous model.

I have no idea what that genome plot shows - but it looks like it should be easy enough to model as a continuous variable. That is what i would try first, so i wouldn't discretise.

You could but why would you want to? By categorising a continuous variable you would make a less predictive model and have to make an arbitrary decision regarding the demarcations of the categories. Why introduce various types of error into the model?

Hi mikeraj. What have you tried so far? Which bit in particular are you stuck on?

So you are comparing 2 samples with a null hypothesis that they are drawn from the same, non-Gaussian, distribution. You will then be performing a non-parametric test on this hypothesis (barring anything weird or wonderful). Generally, non-parametric tests test differences in medians, so this is what you should report, along with inter-quartile ranges to describe the spread of the data. You should first consider transforming the data (log or root transformations are most common) and if this data is normally distributed perform standard parametric tests. How much of this stuff are you covering on your course? The Apgar problem is quite interesting; there's not a consensus. Some argue ordinal data is qualitative and the mean should never be calculated and some argue that reporting the mean, so long as certain criteria are met, is fine. Unless you know exactly about these criteria, median is the safe bet. It will be interesting to see which school of thought you are taught - let me know.

Once the West put aside mysticism? You can still get homeopathy on the NHS in the UK. Mysticism is but one part of Eastern philosophies, comparable to the Judeo-Christian mysticism still abundant in the West. I believe that the only difference in the West is that we came to tolerate people with other views (notwithstanding the Catholic church), allowing progress to be made. How have you come to this conclusion anyway? It's fair enough to have a Eurocentric view on this as we are European, but to think this view dominates the world seems a stretch. I'm sure if you live in China for a while you'll start to believe Chinese philosophy dominates the world. Also, we're not comparing like for like. Western philosophy is analytic and based on reason while Eastern philosophy blurs the line between religion and social contracts. Eastern philosophy is more akin to 'my philosophy on life is...', rather than analytic philosophy. Btw, i believe Eastern philosophies have many things from which the West could learn, but energies and such isn't one of them. Scientists have that firmly covered.

You might find this interesting.

Evidence based philosophy is called science.

You've basically answered it. I think question 5 is asking whether the analysis took global statistics for the 'active' and 'placebo' group. But if they did this there would be no point implementing a cross-over trial. Elaborating your answer to question 3 should lead you to the answer to five properly: they follow as you already suspect.

If you have the time and inclination i'd recommend learning R for your stats. Its far more versatile and gives you a toe into computational medicine which is a fast developing field.

Yes, report something like OR (95% CI) = 4.28 (2.36, 5.94). The OR is the ratio of the odds . If the OR = 1, then there is no difference between the odds as would be expected under the null. If you then had an OR (95% CI) = 4.28 (0.92, 12.22) you would say that the OR is not statistically significant (at alpha = 0.05), as the interval between 0.92 and 12.22 includes 1.

In a publication you could expect to find both: the frequencies maybe buried in a table somewhere and a ratio of the proportions explicitly (OR or RR). Generally the difference in proportions is not discussed. Consider, the difference between 0.01 and 0.001 is more noteworthy than the difference between 0.41 and 0.401 even though the difference in proportions is 0.009 in both cases. Thus the OR (with confidence intervals!) is more informative and is more easily comparable across different models too (e.g. logistic regression).

Is it not just stonewalling?

There is no except. If the flips are independent then they do not influence each other at all - the sequence does not try to 'correct' itself to conform to the expectation. That is the gamblers fallacy. I think you are confusing this for the law of large numbers (a very common thing, it's not really intuitive).

The Han court was influenced by the eunuchs by the time of Rome's height and was declining towards the 3 states period of turmoil, and i can't think of any other states that could match Rome (certainly at its height). But imagine if Hannibal had taken Rome - he came so close - or if the Mongols had not invaded the Arab world allowing the Caliphates extra resources to invade most of Europe as they nearly did a couple of times (siege of Vienna x 2). Or if the Chinese Emperor hadn't burned their powerful fleets just as Europe started to explore the seas, or... Then we would have someone asking the biological reason why 'white' people have never had a dominant civilisation or advanced as much as other races.

For about 1000 years, not in 1000AD. That was a very rough estimate based on Roman regional dominance for about 500 years then European colonial dominance for about 500 years. So at a very generous stretch we could say 'white' civilisations were dominant for 1000 of the 6000 years of recorded human history. That doesn't fit with the idea that white races are more advanced for biological reasons. Edit: Ah, you thought i meant 1000 years starting from 1000AD. But that's kind of my point anyway, this is a historical discussion, not a biological one.

Seems to be a simple confusion about whether we are just using a real life example to visualise a purely mathematical consideration (which was how i read the OP), or whether we are trying to actually model reality. Both interesting problems, but quite different.

Surely it's a false premise: in 6000 years of recorded history 'white' civilisations have dominated for about 1000 years (white is in tags because the Roman Empire was multi-cultural, it's inclusion of other peoples was one of the contributing factors to the Empire's success). I think a history forum, rather than a biology forum, would be better equipped to explore why 'white' races came to dominate at the times they did. How are we defining advanced? The ancient Greeks were perhaps a little more technologically advanced than a lot of surrounding powers, but arguably far more culturally advanced.

Be careful with terminology when speaking about probability; expectation has a very precise definition and is not just what one would personally 'expect'. It depends on what you're counting. Consider flipping a fair coin 3 times; these are all the possible outcomes: HHH HHT HTH HTT THH THT TTH TTT Each particular outcome is equally likely at p = 1/8.Intuitively we think that HHH or TTT is more unlikely, but we see it's just as likely as HTH or any other sequence. But if you're counting the number outcomes with exactly 2 heads, say, then that outcome has p = 3/8 of happening (and 1-p = 5/8 of not happening). If we are counting the number of runs of 3 heads then there is only one outcome with p = 1/8.

These skills all overlap to a degree: teaching is a different skill to maths say, but while learning to teach you will also be going over your knowledge in maths, filling in blanks. I've found teaching to be a great way to learn. In your scientific writing you can also focus on the science you know best, again allowing you to mull over what you think you already know while developing the skills to write.

The expectation of the number of attempts before achieving n consecutive successes (or misses in this case), is given by: [math]\frac{1-p^{-n}}{p-1}[/math] Derived here. Assuming an average hit rate of 70% then you'd expect 2.7 x 10^52 attempts to get 100 consecutive misses. Some-one more clever than me could then probably then use a zero-one law to prove the chance of this occurring in infinitely many attempts is 1.