Results from the test for a visual effect

I created this test to see if what I thought I saw was an actual visual effect. I created a poll where you could ‘vote’ your answers, and I’d tally the answers and put up the results. I think there have been as many votes as there are ever going to be.

I went off to meet people at The Mothership™, which is why the blog hasn’t seen anything new written on it over the weekend. Apologies. I had a nice trip. I am now back at work.

I created this test to see if what I thought I saw was an actual visual effect. I created a poll where you could ‘vote’ your answers, and I’d tally the answers and put up the results. I think there have been as many votes as there are ever going to be: 28 people have taken the poll.

First, the answer: The correct choices for the poll are that A and B are wrong, while C is right; all three figures are exactly the same, and both bars are exactly the same height. The effect I saw is that in a histogram, the bar on the right appears to be taller than a bar on the left, even if it actually isn’t. The results from the poll are these.

[results]
[/results]

The poll had numbers suggesting values of height for every figure. Because suggestion is known to be quite powerful, I had to have three figures to correct for any influence of suggestion. On the whole, people seem to have guessed the right answers.

The point is that people seem to think Figure B is ‘wronger’ than Figure A is wrong or Figure C is right. Which was the effect I wanted to see. (That A and C have the exact same number of votes is an accident, if a nice thing.) On the other hand, there have only been 28 votes. Not nearly enough for any great certainty about the results.

In any case, here’s how one would do the analyse the results. As I said, Figure C is only in the test to account for the overarching power of suggestion. But because A and C have the exact same number of votes, the number that matters is how many people think B is worse than A – i.e. the difference between A and B – which here is 4 votes out of 28.

It is possible that somebody who has actually done these tests rigorously will be tearing their hair out at the silliness of trying to infer a visual effect from a 14% positive response over 28 votes. I’m not sure myself that there have been enough votes to be sure that the 14% is statistically significant. Perhaps I should be thinking about the null hypothesis: neither suggestion nor the visual effect I am looking for make any difference to what people think. This would certainly make sense from the results as they are.

Rest assured, I am on the job of learning the maths required to make this judgement. A biologist I know tells me there’s going to be a class on the maths of hypothesis testing sometime this week, at JNC. Maybe I’ll post an update here.

A test: Is there an illusion here?

I thought I saw some effect when I was looking at one of the graphs on the stats page for the blog. I’m not sure if the effect is real, or it was just me. I’ve created a small test to find out.

There are three graphs below, each with two bars of different heights. In each graph are also suggestive values for the heights of the bars. You have to say if you think the suggested values are right or wrong. There’s a poll at the end where you can enter your answers. Pick one option for each of the figures. I’ve hidden the results to prevent any biasing. I’ll put up the results when there have been enough votes.

[Figure A]

[Figure B]

[Figure C]

[/Figures]

[Poll]

[/Poll]

[End. Fini. Kaputshi. Illusion!]

Tell a story – 2 – With a graph

There are geeks and nerds and there are geeks and nerds. The thing about geeks and nerds is that most of us tend to be socially awkward. Perhaps this will help you understand better: some of us are the Leonard Hofstadter kind of socially awkward – we want to fit in, but don’t know how to. Some of us however, are the Sheldon Cooper kind of socially awkward – we border on the misanthropic.

The thing is, though, that even Sheldon Cooper has a certain bunch of people he is friendly with. Vattam was telling me last night that I tend to be this way. It seems he says, and I agree, that I have a circle of friends with whom I’m positively garrulous, but around everybody else, I go into a shell.

There can be one more dimension to this, it turns out: Sheldon Cooper, as a rule, never has more than four friends; it’s too hard to maintain more than four friendships, he says. The number of people I’m prepared to let my guard down around isn’t that restricted. I’m just nutty about who it is I let into this ‘circle’. Time spent together seems to have nothing to do with this. Neither does gender. Let’s just say there’s a reason even I call this behaviour of mine ‘nutty’.

And now, since the title of this post says ‘graphs’, here’s a graph that says everything I’ve just said:

[graph]

[/graph]

If you’re somebody this graph applies to, where in this plane do you think you are?

[End. Fini. Kaputski.]

Plan of Action – The grad-student-who’s-a-compulsive-blogger Version

I, like most people, don’t start working on something I’m supposed to be doing until atleast the halfway mark. Perhaps later. Never sooner. I still do expect (maybe ‘hope’ is a better word to use here) to finish my work on time. Somewhat like this:

I write a lot, and about a laundry-list of things, these days. So much so that I’ve started, to be accurate, telling people that I’m a blogger, and I do some fluid mechanics in my spare time. The blog is a source of great enjoyment, of course… What with all the ‘Dude’s that prop up in the comments, say something stupid, and get mothered by people. And unlike the ‘Dude’ post which was written in twenty minutes, quite a bit of what I write takes (much) more time:

What I cannot do if my life depended on it

So it turns out I decided it was finally time I shaved my own beard. Now, being quite the theorist, I knew what the process entailed and what I needed for successful completion of said process. Off I went to the local supermarket to get the necessary implements.

The parameters of the experiment were these: Could I, given that this is fairly mundane activity for most men, and that I had put some thought into this, give myself a shave without doing lasting damage?

There comes a time in a man’s life when he has to accept that he isn’t meant to do some things… Halfway through the preposterously tedious exercise, I noticed that the razor had a certain spring-loaded button. I shall say nothing here of what I did, or the time I spent trying to get the damn blade back onto the razor. It shall suffice to say that half an hour into the effort, I’d cut myself twice, wasted quite a bit of shaving gel, and probably ruined the razor (and was really quite late to catch the frikkin’ bus).

So there. I am hopeless at this. Now, in the spirit of engineering, or something, here’s all the above in graphical form.

The first Venn diagram here is something I discovered when I found people in the Aerospace dept. staring at me in the DCF. It turns out I had a habit of singing out loud when I had earphones on. (No, I no longer do.)

The second Venn diagram comes from my general history of social awkwardness bordering on misanthropy, and My Experiments with Truth a Razor.

Murphy’s Law – Probability Distributions at the Bus Stop

I live currently on the IISc campus, and travel everyday to and from JNC using the buses run by the centre. These buses are quite on time, especially relatively, but there’s still a nonzero spread of the probability.

I’ve trained myself to get up early enough in the morning to get the bus that leaves for JNC, but the probability of my getting to the bus stop has a nonzero support (function support. Go wiki.) as well.

Combine these two facts, and I always end up having to sprint from my room to the bus stop, about a km, every morning.

Let’s say that the probability of my getting to the bus stop at a time ‘t1’ is roughly uniform from -0.5 to 0.5 time units (this can always be scaled back to the five minutes that this represents). Let’s say as well that the probability that the bus gets to the bus stop also has a distribution similar to the one just used. They’re both identical (in this model, if you want) and are:

Probability Distribution for me/bus. Horizontal is time. Vertical is Prob. Dist.

Now, the probability distribution for the time difference between my arriving at the bus stop and the bus leaving the bus stop is the convolution of the two probability distributions above. (Do you know how to get this?) Which means that the probability distribution for (t1 – t2) is this:

Convolution of the above probability with itself. Horizontal is time. Vertical is Prob. Dist.

What that should say to you is this:

a) The probability that I will get to the bus stop before the bus leaves is about the same as that the bus will leave before I get to the bus stop. (This, of course, doesn’t happen because I can always run a bit faster to get to the bus stop before the bus leaves. I am effectively skewing the probability distributions by doing that.)

b) However, the probability that I’ll get to the bus stop exactly when the bus gets to the bus stop is still the highest single probability in the distribution.

This, incidentally, is a baby step towards the central limit theorem of statistics: Any probability distribution that is convolved with itself many times will tend to the Gaussian.

If you’ve understood all that (I love you! And…), on to Murphy’s law. Instead of looking like the triangle of height 1 (1. NOT 2)and base 2, the probability distribution for me, in practice looks something like this:

Probability normalised after Srinivas pointed out that I was only going to catch one bus a day.

Which means that I’m either ready so early that I can walk peacefully to the bus stop to wait there for five minutes (or whatever 1 unit represents), or I have to run panting to the bus stop in half the time it usually takes me to avoid missing the bus.

I can now state the probability distribution at the bus stop version of Murphy’s law: If you want to catch a bus, even the central limit theorem of statistics is inverted. You WILL run. Period.