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Related Concept Videos

Goodness-of-Fit Test01:16

Goodness-of-Fit Test

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The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...
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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test01:09

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In parametric statistics, two fundamental tests stand out for their utility and wide application: the Student's t-test and goodness-of-fit tests. These tests provide researchers with a robust method for drawing insights from data, testing hypotheses, and making informed decisions based on their findings.
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with...
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Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Test for Homogeneity01:23

Test for Homogeneity

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The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
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Two-Way ANOVA01:17

Two-Way ANOVA

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The two-way ANOVA is an extension of the one-way ANOVA. It is a statistical test performed on three or more samples categorized by two factors - a row factor and a column factor. Ronald Fischer mentioned it in 1925 in his book 'Statistical Methods for Researchers.'
The two-way ANOVA analysis initially begins by stating the null hypothesis that there is an interaction effect between the two factors of a dataset. This effect can be visualized using line segments formed by joining the...
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Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
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Power Analysis in Covariance Structure Modeling Using GFI and AGFI.

R C MacCallum, S Hong

    Multivariate Behavioral Research
    |January 21, 2016
    PubMed
    Summary

    Power analysis for covariance structure models reveals counter-intuitive results for GFI and AGFI fit indexes. The RMSEA index is recommended for more reliable power analysis and model evaluation.

    Area of Science:

    • Statistics
    • Psychometrics
    • Structural Equation Modeling

    Background:

    • Extends previous research on power analysis for covariance structure models.
    • Focuses on tests of overall model fit using GFI and AGFI fit indexes.

    Purpose of the Study:

    • To develop procedures for power analysis when null and alternative model fit levels are specified using GFI or AGFI.
    • To evaluate the behavior of power as a function of degrees of freedom for these indexes.

    Main Methods:

    • Conducting power analyses for covariance structure models.
    • Specifying null and alternative model fit levels using GFI (Goodness of Fit Index) and AGFI (Adjusted Goodness of Fit Index).

    Main Results:

    • For GFI, power decreases as degrees of freedom increase, a counter-intuitive finding.

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  • For AGFI, power increases as degrees of freedom increase.
  • Establishing appropriate null and alternative hypothesis values for GFI and AGFI is problematic.

    • Conclusions:

    • The behavior of GFI and AGFI in power analyses presents challenges for model evaluation.
    • The RMSEA (Root Mean Square Error of Approximation) index is recommended as a preferable basis for power analysis and model evaluation.