I am collecting data from a Geiger-Muller radiation detector, which generates clicks that correspond to particles entering the detector. These clicks come in purely at random, so the number of clicks in a given time interval are governed by the Poisson distribution. My job is to find the average...
When subtracting measurements that each have a certain level of uncertainty, we can end up with huge levels of error if the two measurements are roughly equal in value. However, this problem doesn't appear when adding numbers.
Question: Is there a name for this type of error? Does anyone...
Okay, so you state that "As ##N## gets larger, this peak gets taller and narrower." That makes sense and what I always thought. Would this not mean that ##\sigma## drops as N increases? I would normally think that a tall, narrow probability distribution would correspond to a small ##\sigma##.
Okay, let's go back to the equation:
$$\sigma = \sqrt{ \frac{\sum_{i=1}^N (x_i-\langle x\rangle)^2}{N-1} }$$
Let's not even use the term "standard deviation." Here, N is the number of samples selected from a population. The average in the equation refers to the sample mean. The x_i's are...
I used the NORMINV[] function in Excel to generate random numbers that are distributed normally about a mean. The distribution is continuous, unlike coin flips. As more and more numbers are generated, the standard deviation doesn't drop. Most say that as I increase the sample size, that the...
As for Jensen's inequality and such, I'm not saying that the variance and standard deviations would rise by the same amount as N increases, only that if one increases the other must do as well and that if one stays constant, the other does as well.
Sure, here is the standard deviation:
$$\sigma = \sqrt{ \frac{\sum_{i=1}^N (x_i-\langle x\rangle)^2}{N-1} }$$
where $N$ is the sample size, $x_i$ is an individual measurement, and $\langle x\rangle$ is the mean of all measurements.
As for your first question, I am referring to the standard deviation of N measurements of (say) the mass of an object, with an underlying normal probability distribution understood.
As for the variance, why would it behave any different than the standard deviation? I mean, if the variance...
But isn't the only difference between the two the fact that you divide √N in one case and √(N-1) in the other? That means for large N they pretty much behave the same. Or am I misunderstanding your point?
In high school, I was taught that the standard deviation drops as you increase the sample size. For this reason, larger sample sizes produce less fluctuation. At the time, I didn't question this because it made sense.
Then, I was taught that the standard deviation does not drop as you increase...
I was thinking about this a bit more. Could this sensitivity error simply be a crude alternative to performing a large number of trials and finding the standard deviation? For example, suppose the nature of an experiment doesn't allow for a large number of trials, or even multiple trials. Could...
The force table, where you have three pulleys hanging by strings, with each string tied to a small loop centered over the table. Theoretically, there is one combination of masses and angles that should work. But you can change the angle slightly with no effect on the position of the loop. .
Yes, because of bearing friction a little mass can be added or subtracted without affecting the apparatus. Why? Because friction can take on any value (up to a maximum) to keep the system from accelerating.
It may be that other uncertainties, such as the standard deviation, already take this...
It appears I missed this:
"The term bias has been in use for statistical matters for a very long time, but because it caused certain philosophical objections among members of some professions (such as medical and legal practitioners), the positive aspect has been emphasized by the invention of...
I understand the distinction between accuracy and precision. However, the terms trueness and bias seem almost interchangeable and I am hoping someone can clarify the difference.
In scientific experiment, we often have a physical property that can change but have no detectable impact on the measurement.
For example, suppose I have a mass of (say) 30 grams attached to a string passing over a pulley. I can add up to another 2 grams and the system doesn't budge.
In our...
It appears that there is an assumption made in this thread (and seemingly everywhere else on the Internet) that digital instruments round their values before displaying. But I don't think that is correct.
For example, if I measure the time it takes for a ball to roll down a ramp with a timer...
Looks like someone took a sloppy representation of the first excited state of a particle in a well and elevated it above the well. I certainly wouldn't put any stock in this image.
The interference is caused by the restrictions on the possible paths that light can take when going from the source to the screen. Essentially, the light "samples" all possible paths it can take to reach a certain point on the screen. How these paths interfere with each other determines the...
I'm not sure it's that simple. First, let's consider the location where blue light appears on the screen. Let's call this point A. Then consider a point slightly above it, where "above" is defined as the vertical direction toward the apex of the triangular prism. Let's call this point B...
Both the red and blue light enter the prism at the same point. Because of their differences in frequency, they end up at different points once they exit the prism. So far, so good. But the problem is that it appears the blue light takes a path where it spends more time in the prism and less...
That much I realize. The problem is that Snell's law is derived by placing the detector inside the glass. As I pointed out, that is not where the detector is actually located. So why does Snell's Law work at the interface between the air and glass?
I realize that blue light travels a different...
I have a conundrum of sorts that has made me feel like an idiot and I am hoping someone can point out my mistake.
Suppose a light source is placed to the left of a prism and a detector is placed on the opposite side. I have seen plenty of pictures of this sort, and they all appear to show the...
In simple terms, promoting an electron from one bound level to another bound level is not the same as ejecting the electron. When promoting an electron from one bound level to another, the energy of the photon must match the difference in energy levels of the two orbitals. When ejecting an...
The term "total internal reflection" is a bit misleading. If I place a light source under the water, its light rays will refract up into the air no matter the light source is placed. All you have to is stand directly over the the light source and you will see it.
Consider a giant arc...
Aaty, thanks for the suggestions. I think Carroll's work would make for great supplementary reading. How well I can get across the concept of the wave function remains to be seen. I have what I think is a clear way of presenting it, but we'll see. The book Sneaking a Look at God's Cards appears...
Thanks for the suggestion. I had forgotten all about that book. I will see if it will serve my students' needs.
I want to keep the math at the arithmetic level. I can do this in many cases by not asking them to solve for anything, but simply use arithmetic to verify the results of an...
It appears that I will be assigned to teach a modern physics course centered on quantum mechanics for those with almost no math background and I am searching for a suitable book. Essentially, this would be the modern physics equivalent of Paul Hewitt's Conceptual Physics book.
I thought of...