A test statistic that is calculated as the sum of the squares of observed values minus expected values divided by the expected values
A statistic that helps determine whether the pattern of frequencies found in data assigned to categories is likely due to chance or is atypical Also used to compare data with a model to determine whether the data's fit is within the typical range of sampling and chance error Also, used to combined the results of independently conducted studies to determine overall statistical significance
Rather than measuring the value of each of a set of items, a calculated value of chi-square compares the frequencies of various kinds (or categories) of items in a random sample to the frequencies that are expected if the population frequencies are as hypothesized by the investigator Chi-square is often used to assess the "goodness of fit" between an obtained set of frequencies in a random sample and what is expected under a given statistical hypothesis For example, chi-square can be used to determine if there is reason to reject the statistical hypothesis that the frequencies in a random sample are as expected when the items are from a normal distribution
Represented by the symbol χ2; statistical test used to determine if differences among nominal, or categorical, level data are statistically significant; examines the observed frequencies in comparison to the expected frequencies to determine if the categorical differences that occurred are the same as would occur by chance
A test that uses the chi-square statistic to test the fit between a theoretical frequency distribution and a frequency distribution of observed data for which each observation may fall into one of several classes
A test that uses the chi-square statistic to test the fit between a theoretical frequency distribution and a frequency distribution of observed data for which each observation may fall into one of several classes
A statistic calculated in the Crosstabulation and Contingency Table statlets It ranges from -1 to +1 and is based on the number of concordant and discordant pairs of observations A concordant pair is one is which the two variables (row and column) have the same relative ranking (greater than or less than) A discordant pair is one in which the two variables have the opposite ranking Both variables must be ordinal No correction is made for ties
A statistical significance test based on frequency of occurrence; it is applicable both to qualitative attributes and quantitative variables Among its many uses, the most common are test of hypothesized probabilities or probability distributions (goodness of fit), statistical dependence or independence (association), and common population (homogeneity)
A statistical measure of goodness of fit, independence, or homogeneity of a population The Chi-square test can be used to determine whether a sample of data was drawn from a normally distributed population by comparing the sample's frequency distribution with the normal distribution It can also be used to determine whether two variables are independent by comparing their observed joint occurrence with their expected joint occurrence, assuming independence Finally, it can be used to determine whether or not categories of a single variable are represented in the same proportions in two or more populations
A statistical test for comparing the frequency distributions observed in a sample of observations with what would be expected under the null hypothesis This test is often used for 2x2 tables for evaluating the association of the two variables
A test performed on a two-way frequency table to test whether two variables can be considered statistically independent It is calculated in the Crosstabulation and Contingency Table Statlets In calculating the chi-square test, the observed frequency in each cell is compared to the frequency which would be expected if the row and column classifications were independent If the calculated statistic is large (i e , if its P value is less than a predetermined significance level such as 05), then the null hypothesis of independence must be rejected The chi-square test is valid only if the expected frequency in each cell is relatively large If any frequency is less than 5, a warning is displayed If the two-way table contains exactly 2 rows and 2 columns and the total count in the table does not exceed 100, Fisher's exact test is also performed
The chi-square test is performed on a two-way frequency table to test whether two variables can be considered statistically independent It is calculated in the Crosstabulation and Contingency Table statlets In calculating the chi-square test, the observed frequency in each cell is compared to the frequency which would be expected if the row and column classifications were independent If the calculated statistic is large (i e , if its P value is less than a predetermined significance level such as 05), then the null hypothesis of independence must be rejected The chi-square test is valid only if the expected frequency in each cell is relatively large If any frequency is less than 5, a warning is displayed If the two-way table contains exactly 2 rows and 2 columns and the total count in the table does not exceed 100, Fisher's exact test is also performed
A test that uses the chi-square statistic to test the fit between a theoretical frequency distribution and a frequency distribution of observed data, measuring correlation