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A (max) heap is a tree-based data structure which satisfies the heap property: for any given node C, if P is a parent node of C, then the key (the value) of P is greater than or equal to the key of C. In addition to the operations of an abstract priority queue, the following table lists the complexity of two additional logical operations:
A parametric test for equal variance can be visualized by indexing the data by some variable, removing data points in the center and comparing the mean deviations of the left and right side. In statistics, the Goldfeld–Quandt test checks for heteroscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups ...
The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other. Multiple-comparison testing is conducted using needed data in already completed F-test, if F-test leads to rejection of null hypothesis and the factor under study has an impact on the dependent variable. [1]
In statistics, one-way analysis of variance (or one-way ANOVA) is a technique to compare whether two or more samples' means are significantly different (using the F distribution). This analysis of variance technique requires a numeric response variable "Y" and a single explanatory variable "X", hence "one-way".
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation between the group means to the amount of variation within each group.
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
The F statistics of the omnibus test is: = = (¯ ¯) = = (¯) Where, ¯ is the overall sample mean, ¯ is the group j sample mean, k is the number of groups and n j is sample size of group j. The F statistic is distributed F (k-1,n-k),(α) under assumption of null hypothesis and normality assumption.
[28] [29] Bartlett's test for heteroscedasticity between grouped data, used most commonly in the univariate case, has also been extended for the multivariate case, but a tractable solution only exists for 2 groups. [30] Approximations exist for more than two groups, and they are both called Box's M test.