# What is Chi: Definition and 73 Discussions

Tai chi (simplified Chinese: 太极; traditional Chinese: 太極; pinyin: Tàijí), short for T'ai chi ch'üan or Tàijí quán (太極拳), sometimes colloquially known as "Shadowboxing," is an internal Chinese martial art practiced for defense training, health benefits, and meditation.
Developed as a martial art, it is practiced for reasons including competitive wrestling, competitive demonstrations, and health/longevity. Tai chi has practitioners worldwide.
Yang Shaohou, Yang Chengfu, Wu Chien-ch‘üan and Sun Lutang promoted the art for its health benefits beginning in the early 20th century. Its global following often for its benefit to personal health. Medical studies of t‘ai-chi support its effectiveness as an alternative exercise and a form of martial arts therapy.
Many forms are practiced, both traditional and modern. Most modern styles trace their development to the five traditional schools: Chen, Yang, Wu (Hao), Wu, and Sun. All trace their historical origins to Chen Village.

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1. ### What is the correct formula for the reduced Chi square?

Hi all I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD : ...
2. ### A The chi square goodness-of-fit test with no degrees of freedom left

I have an empirical frequency distribution as for example below: ##f_{2} = \, \, \, 21## ##f_{3} = 111## ##f_{4} = \, \, \, 24## The theoretical distribution is determined by two parameters. So for a chi-square goodness-of-fit test there are actually no degrees of freedom left. Yet the...
3. ### I Reduced chi square for few data points

Hello! I need to make a straight line fit to 8 points, with errors on them. The data is like this ##x = [1,2,3,4,5,6,7,8]##, ##y=[377.488 691.191 , 1030.319, 1428.801, 1753.884, 2113.065 , 2398.642, 2797.664]##, ##y_{err}=[97.145, 131.452, 160.492, 188.997, 209.397, 229.840, 244.879...
4. D

### Tai Chi and Math, Douwe Geluk from Apeldoorn

Hello my name is Douwe Geluk I have studied engineering and i have to complete some courses for my job. I think this is a great forum which can teach.me very much. Besides Physics and studying i practise Tai Chi and Chi Kung to Relax my mind at the Scource of Happiness in Apeldoorn city the...
5. ### I Distribution of ratio std Normal and sqrt chi squared

Hi all, I am trying to understand two things from a paper The ratio of a standard normal by the square root of a a chi squared divided by its df ( degrees of freedom) is a t distribution. So 1) What is the dist of square root of Chi squared? I know a normal squared is a chi squared, but a chi...
6. ### I Small Reduced Chi Squared interpretation

Hello everyone, I would be happy if someone explained the small reduced chi squared value to me. I have fitted a set of measured data with an exponential function, which I need for some sw calculations. The fit seams great, the origin sw also provides the reduced chi squared, but it is very...
7. ### Writing: Input Wanted Scientific use of Chi/Qi/not so espiritual energy

Hi, I wanted you guys to tell me whether you like this idea I had and if you have any ideas on the implication of it, and whether it would work as I describe it or not. So, in this world I created, there is a basic understanding of physics by the scholars, but most people don't even understand...
8. ### A Interpreting Chi Squared .... backward

OK, so, I've forgotten more statistics than my students will ever know, and I'm not too proud to ask for help, because I'm just blanking out on this. I would appreciate it if someone could patiently follow along and let me know what I've got right or wrong please. My understanding of the...
9. ### B Understanding Chi Squared p-values

Hi, I am in AP Biology, and I completely understand how to use chi squared to the level the AP exam and class requires, but I do not completely understand why p-values work the way they do. I have done a lot of research, and I think I may have an idea as to how this works. Can you please tell...
10. ### Mathematica Chi square minimisation wrt variables in an integral?

I'm trying to fit a model curve to some data by performing a chi square minimisation wrt three parameters a,b and NN. The trouble I am having is that the variables with which I want to minimise the chi square with respect to appear in an integral. I attach the code I am working with...
11. ### I Inflation: meaning of χ (chi) for time scales?

This is another question related to an undergrad video lecture on inflation by Guth. In the course, he derives the inflationary expansion rate : a(t) ~ eχt, with χ = sqrt(8πGρf/3), and ρf being the mass density of the false vacuum energy. Later in the lecture, around 51:35, Guth gives sample...
12. ### I Online sourses to learn chi square test of homogeneity

I want to study chi square test of homogeneity from any authentic source- book / website especially problems where samples are compared for more than one attribute. What are some relevant sources? Relevant background: I was studying examples from random online sources before I saw this book...
13. ### MHB Chi-Square Test: Solving Doubt w/ Kepler

Good afternoon, I'm glad I've joined this forum. Here's my doubt: I have a serie of values in a table like this: Case 1 34 55 Case 2 23 10 Case 3 55 40 etc... the 34 means the observed value, and the 55 the control group, and so on. It's easy to do the test of course if... The problem is: if...
14. ### Reduced chi square test in physics

Homework Statement Hi everybody! Our experiments teacher asked us to perform a reduced chi square test in order to estimate how good a model fits to our measured data. The experiment was the melde's experiment (vibration of a string) and we measured the frequency ##f_n## for ##n=1## to ##9##...
15. ### A Chi squared test for data with error

Hi everyone. I am totally new to statistics so my question may or may not be simple! I know that for the data fitting we can do a chi squared test like: $$\chi^2 = \Sigma \frac{(f_{data}-f_{model})^2}{(error_{data})^2}$$ So I have been doing this for a while, but now...
16. ### Goodness of fit, Residual STD, chi square

Homework Statement Hello, I am using CasaXPS to model synthetic peak models for X-ray photoelectron spectroscopy data. I am fitting. The software has a lot of manuals online but they do not explain how they yield a Residual Standard Deviation, after each fit iteration. Most software use...
17. ### What is a Chi-Squared Test Against Weighted Mean?

Hi all, I was reading a paper and I wasn't sure how they performed their statistic analysis. What do they mean by a chi-square test against the weighted mean? Is it a chi-square test between the actual data points and the weighted mean? If so, why do they us the function P(X^2,v)? I...
18. ### Chi Square Distribution Problem

Homework Statement Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2. The Attempt at a Solution I honestly have no idea where to begin with this problem. Any ideas?
19. ### Error bars, Chi square distribution

Hi, I'm doing a fit using Chi-square distribution. I have a data set and their errors, I found the best estimate minimizing Chi square, as usual, and I like to found the error bars of my best estimates but I don't know how to do that. Which is the standard form to do it?
20. ### Prove Chi Square is Stochastically Increasing

Homework Statement Prove that the X^2 distribution is stochastically increasing in its degrees of freedom; that is if p>q, then for any a, P(X^2_{p} > a) \geq P(X^2_{q} > a), with strict inequality for some a. Homework Equations 1.(n-1)S^2/\sigma^2 \sim X^2_{n-1} 2.The Chi squared(p) pdf is...
21. ### Showing Chi squared is independent with another variable

So I have X1 and X2 are iid standard normal. Then I have Y=X1^2+ X2^2 and Z=X1/(X1^2+x2^2) I'm supposed to find the distribution of Y and Z and then determine if they are independent. Clearly Y is chi squared with degrees of freedom 2. But I have no idea how to find the distribution of Z...
22. ### CHI square independent test (small expected frequency)

Homework Statement the expected frequency for the age of (21-30, 31-36, more than or equal to 37) for operation is less than 5 , so combination of these numbers are required for the expected frequency to be more than or equal to 5 . my question is which numbers should i combine? would my ans...
23. ### CHI square test - finding degree of freedom

Homework Statement i have problem of finding the degree f freedom for this question. the ans for v is 3 , but my ans is v=n-1 , where n = 6 , so my v=5... Homework EquationsThe Attempt at a Solution
24. ### Is the Dart Throwing Data a Gaussian Distribution?

Homework Statement We threw a bunch of darts at a dart board to find the statistics of the positions. They ranged from -20 to 20 and the data is right here. ( each column corresponds to the dart number, it is just a syntax thing) The frequencies are below. Dart 1 Dart 2 Dart 3 Dart 4...
25. ### How to do a chi squared test on a linear fit

I'm getting a bit confused with the stats of a chi squared test, everyone in physics labs seems to use this as a test but I don't know why it's appropriate? My main question is how would I take a linear equation in say excel which has been fitted to a series of (x,y) data points (I do have...
26. ### Analyzing Enrollment Campaigns with Chi-Square: Is It the Right Approach?

Homework Statement I'm trying to test a hypothesis that sending people both an email announcement and direct mail announcement produces significantly more enrollments in a free webinar than email or direct mail alone. I'd like to do an analysis on these groups created from 400 people...
27. ### Interpreting a very small reduced chi squared value

So I have been analyzing data a took in an experiment recently and have been using a chi squared as a "goodness of fit" test to against a linear model. I am using excel and used the LINEST function (least square fitting method) to get an idea for a theoretical gradient and intercept for my...
28. ### Statistics Chi Square test of normally distributed data

Homework Statement The following data is hypothesized to possesses a normal distribution, is that hypothesis sustained by a Chi-square test at .05 significance: <66...4 67-68...24 68-70...35 70-72...15 72-74...8 >74...4 The Attempt at a Solution 1. I know that I should...
29. ### Is Today the Chi Meson's Birthday?

Hapy Birthday Chi meson !1111 Wishing you a very Happy Bithday!
30. ### How do you use a chi square table?

For example, if the moment generating function is (1-2t)^(-6), then the degree of freedom r=3, right? The question is asking me to find P(X< 5.23)...I want to use the chi-square table, but I'm not sure how... This is what the question states: If (1-2t)^{-6}, t<1/2, is the mgf of the...
31. ### Convolution of iid non central Chi square and normal distribution

Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.
32. ### Inverse Chi Square: Rejecting Null Hypothesis at α=5%, 9DF

How can I determine what the smallest value of a χ2 statistic must be to reject the null hypothesis at α = 5%, for a distribution with 9 degrees of freedom? Thanks in advance.
33. ### Deciding Bins for Chi Square Tests

Homework Statement I know that for a Chi Square test to adequately describe a distribution, you need each bin to have an estimated frequency > 5. As a rule of thumb though, do I want to pool the bins with less than 5 estimated frequency so as to maximize the number of bins or minimize them? For...
34. ### Standard normal limiting function chi squared

Hi, I have a question If X1,X2,...,Xn are independent random variables having chi-square distribution witn v=1 and Yn=X1+X2+...+Xn, then the limiting distribution of (Yn/n) - 1 Z= --------------- as n->infinity is the standard normal distribution. sqrt(2/n) I know that Yn has...
35. ### Chi Meson's Home Solar System Success Story

The panels are up. 7kW system will be 110% of our electrical needs. Grid intertie, no batteries, no pile of money up front: \$109/month for the next 15 years. Plus dig the new deck I built last summer. --Chi "Happy Homeowner" Meson
36. ### Minimum chi squared estimation

hi i have some data (star counts) and i have a model and i want to perform min chi squared so if i call my data di, and my model mi with std dev = \sigmai = 1 then \chi^2 = \sum \frac{(di - mi)^2}{\sigma i^2} no my model is this mi = bi - Fo where bi is the background which has been...
37. ### Distribution of Difference of 2 2nd Degree Non-Central Chi Squared RVs

Distribution of difference of two second degree non central chi squared random variables. This problem can be cast as an indefinite quadratic form for which there are a number of general numerical techniques to determine the CDF. Alternatively, it may be written as a linear combination of...
38. ### What Distribution Does Z Follow When Both Means and Variances Differ?

Hello all, I've been working on error analysis of the system, and I finally faced a big problem. Let X~N(mu1, sigma1^2) and Y~N(mu2, sigma2^2), and Z=sqrt( X^2 + Y^2 ) For Z to be a Chi, mu's should be zero and sigma's should be 1, to be a Rayleigh, mu's should be zero and two...
39. ### Non central chi square distribution

I read this article about non central chi square distribution http://en.wikipedia.org/wiki/Noncentral_chi-square_distribution in practice, if I have a sum of X_i^2, where X_i is gaussian with mean \mu_i and std \sigma_i what would be the pdf of the sum? In the article the assume you have...
40. ### Chi Squared and Gaussian Population Question

The following data represent a frequency distribution of 200 variables drawn from a parent Gaussian population with mean=26.00 and standard deviation=5.00. the bins are 2 units wide and the lower edge of the first bin is at x=14. 4;8;11;20;26;31;29;22;26;13;5;2;3 a. plot a histogram of these...
41. ### Evo and Chi Meson: Blue Canary in the Outlet

How nifty is this? https://www.amazon.com/dp/B002SLGNJG/?tag=pfamazon01-20 Blue canary in the outlet by the light switch Who watches over you Make a little birdhouse in your soul Not to put too fine a point on it Say I'm the only bee in your bonnet Make a little birdhouse in your soul
42. ### Help with chi square distribution

How do i show that the a [X1 has a chi square distribution with n degrees of freedom] + [X2 has a chi square distribution with m degrees of freedom] is a [X1+X2 has a chi square distribution with n+m degrees of freedom]? How can i use moment generating functions to do this?
43. ### Finding Uncertainty in a coefficient with a Chi Squared Test

Hello, I have done a chi squared test on the measurements from a neutron flux experiment to get the best parameters for a function of the form Ysim=Acos(B*X). I used Solver in Excel to find the minimum parameters. The test takes the form chi^2 / dof = SUM(Ysim-Yi)^2/(sigma i)^2 Where...
44. ### Central Limit Theorem Variation for Chi Square distribution?

Central Limit Theorem Variation for Chi Square distribution? If this question fits into Homework Help, please move it over there. I'm not too sure. I encountered the following problem: Now, this problem seems fairly similar to a simple proof the central limit theorem. I am damn sure...
45. ### Interpreting Chi Squared Test Results for Lab Report

for a lab report i have to perform a chi squared test... i have no idea how to interprete my results from that chi squared test I got c^2= .26 and its way under the 3.84 cap... does that mean i accept the hypothesis or reject it... I get confused about this... i got 32 and 28 for my two...
46. ### Help with Chi-Squared Test: Probability Link to \chi^2 Value

Chi- squared test--please help Posted this on 12.04.10 but haven't gotten a response. Is my data unclear? Can someone explain how to link the probability to the \chi^2 value please. 1. Homework Statement In a cross between two types of pea plants, one heterozygous for the round yellow...
47. ### Chi-Squared Test for Pea Plant Crosses: Calculate, Interpret, and Analyze

Homework Statement In a cross between two types of pea plants, one heterozygous for the round yellow seed condition, and the other, pure breeding with wrinkled green seeds, the following offsprings were recorded; Round yellow peas-- 108 Round green peas-- 102 Wrinkled yellow peas--105...
48. ### Chi Square Analysis of Phenotype Problem

Parental Pheotypes Long x ShortF1 All LongF2 Phenotypes 787 long, 277 short1. What is the expected value for the recessive phentotype of the cross Long versus Short 787+277= 1064 I did 787/1064= .739 Rounded up to .74 For Long 277/1064= .26 for Short .74x1064= 787.36 Is the Expected...
49. ### Chi square Dominant phenotype problem

What is the ChiSquare value for the dominant phentotype of the cross Purple versus White. Shouldn't the answer be 696 or 696.75?? Parental Phenotypes Purple X WhiteF1 Phenotype All PurpleF2 Phenotype 705 purple, 224 whiteI must be missing something: Observed Purple=705 Observed White= 224...
50. ### How are degrees of freedom determined in a Chi-square test for genetics?

In the Chi-square test, my textbook says that degrees of freedom are the number of independent variables minus one ,df = n - 1 does this mean that that n is equal to the number of observed values from the equation aka the number of times I've added or the number of terms? sum [(O-E)^2]/E Is...