Note that, although the primary distribution that we took sample from is a continuous distribution (x ~ Gamma(10,3)) by using the histogram we convert it to the discrete samples.
In other words, it compares multiple observed proportions to expected probabilities.

3 Finding \(\chi^2_{left} \text{ and } \chi^2_{right}\). 4. Chi-square test when our expectations are based on predetermined results. Because the chi square distribution isn’t symmetric both left and right densities must be found. The p-value of the test is 0.9037, which is greater than the significance level alpha = 0.05. In this R tutorial you’ll learn how to apply the chi square functions. The following tables summarizes the result:Reference Distribution Chi square test Kolmogorov–Smirnov test Cramér–von Mises criterion Gamma(11,3) 5e-4 2e-10 0.019 N(30, 90) 4e-5 2.2e-16 3e-3 Gamme(10, 3) .2 .22 .45 Clearly, Gamma(10,3) is a good fit for the sample dataset, which is consistent with the primary distribution. Uses of Chi-Square Test: 1. The chi-square test statistic is 4.47, which is less than the critical value of CHIINV (.05,7) = 14.07, and so we can conclude that there is a good fit.
The chi-square test (Snedecor and Cochran, 1989) is used to test if a sample of data came from a population with a specific distribution.

Chi-Square test is a statistical method to determine if two categorical variables have a significant correlation between them. Chi Square Distribution in R (4 Examples) | dchisq, pchisq, qchisq & rchisq Functions . The chi-square distribution is used in the common chi-square 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. Chi-Square test in R is a statistical method which used to determine if two categorical variables have a significant correlation between them. You are basically producing a 100x100 contingency table consisting of mostly zeros and some ones. We can conclude that the observed proportions are not significantly different from the expected proportions. Correction for discontinuity or Yates’ correction in calculating χ 2. 5.

Then Pearson's chi-squared test is performed of the null hypothesis that the joint distribution of the cell counts in a 2-dimensional contingency table is the product of the row and column marginals. Chi-squared test for given probabilities data: tulip X-squared = 0.20253, df = 2, p-value = 0.9037. The chi-square goodness of fit test is used to compare the observed distribution to an expected distribution, in a situation where we have two or more categories in a discrete data. What test in R I should use for this purpose? Both those variables should be from same population and they should be categorical like − Yes/No, Male/Female, Red/Green etc. Chi-square test of independence in contingency tables. The two variables are selected from the same population. 3. 3.0 Model choice The first step in fitting distributions consists in choosing the mathematical model or function to represent data in the better way. Chi-square test when expectations are based on normal distribution. 5] where x.wei is the vector of empirical data, while x.teo are quantiles from theorical model.