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- https://stats.libretexts.org/Courses/Remixer_University/Username%3A_ckkidder08marianuniversityedu/Applied_Statistics_for_Social_Science_(19-20)/08%3A_The_Chi-Square_Distribution/8.2%3A_Facts_About_the_Chi-Square_Distributionhe chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whe...he chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two populations are the same, (iii) whether two events might be independent, and (iv) whether there is a different variability than expected within a population.
- https://stats.libretexts.org/Courses/Long_Beach_City_College/Book%3A_STAT_227_-_Introductory_Statistics/Text/11%3A_The_Chi-Square_Distribution/11.02%3A_Facts_About_the_Chi-Square_Distributionhe chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whe...he chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two populations are the same, (iii) whether two events might be independent, and (iv) whether there is a different variability than expected within a population.
- https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/11%3A_The_Chi-Square_Distribution/11.02%3A_Facts_About_the_Chi-Square_DistributionFor the \(\chi^2\) distribution, the population mean is \(\mu = df\) and the population standard deviation is \(\sigma=\sqrt{2(d f)}\). The random variable for a chi-square distribution with \(k\) deg...For the \(\chi^2\) distribution, the population mean is \(\mu = df\) and the population standard deviation is \(\sigma=\sqrt{2(d f)}\). The random variable for a chi-square distribution with \(k\) degrees of freedom is the sum of \(k\) independent, squared standard normal variables. For \(\chi \sim \chi_{1,000}^{2}\) the mean, \(\mu = df = 1,000\) and the standard deviation, \(\sigma=\sqrt{2(1,000)}=44.7\). The mean, \(\mu\), is located just to the right of the peak.
- https://stats.libretexts.org/Courses/Fort_Hays_State_University/Elements_of_Statistics/04%3A_Probability_Distributions/4.05%3A_Common_Continuous_Probability_DistributionsIn this section, we name and explore key properties of some of the most commonly used probability density functions in statistical work. We will end by examining how certain regions within our distrib...In this section, we name and explore key properties of some of the most commonly used probability density functions in statistical work. We will end by examining how certain regions within our distributions can directly relate to other regions within our distributions using some basic geometric reasoning.
- https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/11%3A_Chi-Square_and_Analysis_of_Variance_(ANOVA)/11.00%3A_Prelude_to_The_Chi-Square_Distribution/11.0.01%3A_Facts_About_the_Chi-Square_DistributionThe chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) wh...The chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two populations are the same, (iii) whether two events might be independent, and (iv) whether there is a different variability than expected within a population.
- https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/BFE_1201_Statistical_Methods_for_Finance_(Kuter)/07%3A_Hypothesis_Testing/7.14%3A_Facts_About_the_Chi-Square_DistributionFor the \(\chi^2\) distribution, the population mean is \(\mu = df\) and the population standard deviation is \(\sigma=\sqrt{2(d f)}\). The random variable for a chi-square distribution with \(k\) deg...For the \(\chi^2\) distribution, the population mean is \(\mu = df\) and the population standard deviation is \(\sigma=\sqrt{2(d f)}\). The random variable for a chi-square distribution with \(k\) degrees of freedom is the sum of \(k\) independent, squared standard normal variables. For \(\chi \sim \chi_{1,000}^{2}\) the mean, \(\mu = df = 1,000\) and the standard deviation, \(\sigma=\sqrt{2(1,000)}=44.7\). The mean, \(\mu\), is located just to the right of the peak.
- https://stats.libretexts.org/Workbench/PSYC_2200%3A_Elementary_Statistics_for_Behavioral_and_Social_Science_(Oja)_WITHOUT_UNITS/16%3A_Chi-Square/16.02%3A_Introduction_to_Goodness-of-Fit_Chi-Square/16.2.01%3A_Critical_Values_of_Chi-Square_TableFor chi-square, the null hypothesis is that there is no pattern of relationship, but the process of Null Hypothesis Signficance Testing is the same as we've been learning. Illustrated in Figure \(\Pag...For chi-square, the null hypothesis is that there is no pattern of relationship, but the process of Null Hypothesis Signficance Testing is the same as we've been learning. Illustrated in Figure \(\PageIndex{2}\), the value of the chi-square that cuts off a right tail of area \(c\) is denoted \(\chi_c^2\) and is called a critical value (Figure \(\PageIndex{2}\)).
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/14%3A_Apppendices/14.01%3A_B__Mathematical_Phrases_Symbols_and_Formulas/14.1.01%3A_Symbols_and_Their_MeaningsThis page offers a detailed reference table of statistical symbols and their verbal representations, categorized into areas such as Sampling, Descriptive Statistics, Probability, Random Variables, Nor...This page offers a detailed reference table of statistical symbols and their verbal representations, categorized into areas such as Sampling, Descriptive Statistics, Probability, Random Variables, Normal Distribution, Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Chi-Square Distribution, and Linear Regression. Each entry features the symbol, its spoken name, and its statistical meaning.
- https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/Introductory_Statistics_(OpenStax)_With_Multimedia_and_Interactivity/11%3A_The_Chi-Square_Distribution/11.06%3A_Comparison_of_the_Chi-Square_TestsYou have seen the Chi-square test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which Chi-square test is the appropriate one to...You have seen the Chi-square test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which Chi-square test is the appropriate one to use.
- https://stats.libretexts.org/Courses/Marian_University/Applied_Statistics_for_Social_Science_(19-20)/08%3A_The_Chi-Square_Distribution/8.5%3A_Comparison_of_the_Chi-Square_TestsYou have seen the Chi-square test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which Chi-square test is the appropriate one to...You have seen the Chi-square test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which Chi-square test is the appropriate one to use.
- https://stats.libretexts.org/Courses/Concord_University/Elementary_Statistics/11%3A_The_Chi-Square_Distribution/11.02%3A_Facts_About_the_Chi-Square_DistributionThe chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) wh...The chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two populations are the same, (iii) whether two events might be independent, and (iv) whether there is a different variability than expected within a population.
