Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies

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M G Vangel1, A L Rukhin

  • 1Statistical Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-0001, USA. vangel@cam.nist.gov

Biometrics
|April 25, 2001
PubMed

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One-Way ANOVA01:18

One-Way ANOVA

One-way ANOVA analyzes more than three samples categorized by one factor. For example, it can compare the average mileage of sports bikes. Here, the data is categorized by one factor - the company. However, one-way ANOVA cannot be used to simultaneously compare the sample mean of three or more samples categorized by two factors. An example of two factors would be sports bikes from different companies driven in different terrains, such as a desert or snowy landscape. Here, two-way ANOVA is used...
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
Two-Way ANOVA01:17

Two-Way ANOVA

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 means for...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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What is an ANOVA?

The Analysis of Variance or ANOVA is a statistical test developed by Ronald Fisher in 1918. It is performed on three or more samples to check for equality between their means.
Before performing ANOVA, one must ensure that the samples used for this analysis have three crucial characteristics or statistical assumptions. The first assumption states that the samples should be drawn from normally distributed samples, while the second requires that all the drawn samples should be randomly and...
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Statistical Methods to Analyze Parametric Data: ANOVA

Analysis of Variance, or ANOVA, is a powerful statistical technique used to analyze parametric data, primarily in research and experimental studies. It's designed to compare the means of two or more groups, assisting researchers in identifying any significant differences between these group means. There are two main types of ANOVA based on the complexity of the analysis: one-way and two-way.
One-way ANOVA is applied when a single independent variable or factor is scrutinized. It compares the...