- published: 10 Nov 2010
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In probability theory and statistics, the chi distribution is a continuous probability distribution. It is the distribution of the square root of the sum of squares of independent random variables having a standard normal distribution. The most familiar examples are the Rayleigh distribution with chi distribution with 2 degrees of freedom, and the Maxwell distribution of (normalized) molecular speeds which is a chi distribution with 3 degrees of freedom (one for each spatial coordinate). If are k independent, normally distributed random variables with means and standard deviations , then the statistic
is distributed according to the chi distribution. Accordingly, dividing by the mean of the chi distribution (scaled by the square root of n − 1) yields the correction factor in the unbiased estimation of the standard deviation of the normal distribution. The chi distribution has one parameter: which specifies the number of degrees of freedom (i.e. the number of ).
Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.
The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.
In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.
In probability theory and statistics, the chi-squared distribution (also chi-square or χ²-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e.g., in hypothesis testing or in construction of confidence intervals. When it is being distinguished from the more general noncentral chi-squared distribution, this distribution is sometimes called the central chi-squared distribution.
The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, like Friedman's analysis of variance by ranks.
Probability and statistics are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.
An Introduction to ..... is a 1994 compilation album by Roy Harper.
The album features 13 Harper songs from a 25 year period and is "...a collection of various styles and periods...purely intended for people who may not know where to start (with Harpers music)." Roy Harper
All tracks credited to Roy Harper
Chi-Square Distribution Introduction Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/pearson-s-chi-square-test-goodness-of-fit?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing-two-samples/v/hypothesis-test-comparing-population-proportions?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predict...
I have an updated and improved version of this video available at http://youtu.be/hcDb12fsbBU. A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape.
A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape.
When you want to estimate the population variance and standard deviation you use a chi squared distribution. At 3:24 I make a mistake in my work. I forget to subtract 1 while finding the sample variance, but luckily I type it into my calculator correctly and so the answer turns our correct. The process is correct, I just wrote down an incorrect number.
An explanation of how to compute the chi-squared statistic for independent measures of nominal data. For an explanation of significance testing in general, see http://evc-cit.info/psych018/hyptest/index.html There is also a chi-squared calculator at http://evc-cit.info/psych018/chisquared/index.html
Paul Andersen shows you how to calculate the ch-squared value to test your null hypothesis. He explains the importance of the critical value and defines the degrees of freedom. He also leaves you with a problem related to the animal behavior lab. This analysis is required in the AP Biology classroom. Intro Music Atribution Title: I4dsong_loop_main.wav Artist: CosmicD Link to sound: http://www.freesound.org/people/CosmicD/sounds/72556/ Creative Commons Atribution License
I work through an example of testing the null hypothesis that the data comes from a binomial distribution. I do this for two tests, one in which the probability of success is specified in the null hypothesis, and one where it is estimated from the data. Data reference The Larry Bird free throw data based on information in: Wardrop, R.L. (1995). Simpson's paradox and the hot hand in basketball. The American Statistician, 49 (1), 24-28.
Learn how to perform a Chi Square Test with this easy to follow statistics video. I also provided the links for my other statistics videos as well. Chi Square Test - with contingency table https://www.youtube.com/watch?v=misMgRRV3jQ Hypothesis testing - two tailed test https://www.youtube.com/watch?v=0XXT3bIY_pw Hypothesis testing - one tailed test https://www.youtube.com/watch?v=lNoxKsuJ6Xc Confidence Intervals - with 't' value https://www.youtube.com/watch?v=UmAJJtEo6cQ Practice Quiz - z-test and t-test https://www.youtube.com/watch?v=o_QGaqYAqjo YouTube Channel: http://Youtube.com/MathMeeting Website: http://MathMeeting.com
Pearson's Chi Square Test (Goodness of Fit) Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/contingency-table-chi-square-test?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/chi-square-distribution-introduction?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our...
Chi-Square Distribution Introduction Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/pearson-s-chi-square-test-goodness-of-fit?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing-two-samples/v/hypothesis-test-comparing-population-proportions?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predict...
I have an updated and improved version of this video available at http://youtu.be/hcDb12fsbBU. A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape.
A brief introduction to the chi-square distribution. I discuss how the chi-square distribution arises, its pdf, mean, variance, and shape.
When you want to estimate the population variance and standard deviation you use a chi squared distribution. At 3:24 I make a mistake in my work. I forget to subtract 1 while finding the sample variance, but luckily I type it into my calculator correctly and so the answer turns our correct. The process is correct, I just wrote down an incorrect number.
An explanation of how to compute the chi-squared statistic for independent measures of nominal data. For an explanation of significance testing in general, see http://evc-cit.info/psych018/hyptest/index.html There is also a chi-squared calculator at http://evc-cit.info/psych018/chisquared/index.html
Paul Andersen shows you how to calculate the ch-squared value to test your null hypothesis. He explains the importance of the critical value and defines the degrees of freedom. He also leaves you with a problem related to the animal behavior lab. This analysis is required in the AP Biology classroom. Intro Music Atribution Title: I4dsong_loop_main.wav Artist: CosmicD Link to sound: http://www.freesound.org/people/CosmicD/sounds/72556/ Creative Commons Atribution License
I work through an example of testing the null hypothesis that the data comes from a binomial distribution. I do this for two tests, one in which the probability of success is specified in the null hypothesis, and one where it is estimated from the data. Data reference The Larry Bird free throw data based on information in: Wardrop, R.L. (1995). Simpson's paradox and the hot hand in basketball. The American Statistician, 49 (1), 24-28.
Learn how to perform a Chi Square Test with this easy to follow statistics video. I also provided the links for my other statistics videos as well. Chi Square Test - with contingency table https://www.youtube.com/watch?v=misMgRRV3jQ Hypothesis testing - two tailed test https://www.youtube.com/watch?v=0XXT3bIY_pw Hypothesis testing - one tailed test https://www.youtube.com/watch?v=lNoxKsuJ6Xc Confidence Intervals - with 't' value https://www.youtube.com/watch?v=UmAJJtEo6cQ Practice Quiz - z-test and t-test https://www.youtube.com/watch?v=o_QGaqYAqjo YouTube Channel: http://Youtube.com/MathMeeting Website: http://MathMeeting.com
Pearson's Chi Square Test (Goodness of Fit) Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/contingency-table-chi-square-test?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/chi-square-distribution-introduction?utm_source=YT&utm;_medium=Desc&utm;_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our...
Sampling distribution: chi-squared distribution: goodness-of-fit and independence of attributes tests (BSE) Subject : Business Economics Paper : Applied business statistics
Subject: Business Economics Paper: Applied Business Statistics
Math/Stat 341: Probability: Lecture 23: October 31, 2016: Chi-Square Distributions, Markov's Inequality, Chebyshev' Inequality
Statistics Lecture 7.5: Finding Confidence Intervals Involving Variance and Standard Deviation. Using the Chi-Squared Distribution.