One Way ANOVA

 

Summary of Analysis Technique.

ANOVA is used for examining the differences in the mean values of the dependent variable associated with the effect of the controlled independent variables, after taking into account the influence of the uncontrolled independent variables.

ANOVA must have a dependent variable which should be metric (measured using an interval or ratio scale). 

ANOVA must also have one or more independent variables, which should be categorical in nature. 

In ANOVA, categorical independent variables are called factors. A particular combination of factor levels, or categories, is called a treatment.

https://www.statisticssolutions.com/anova-in-spss/

To test if the means are different, an ANOVA test compares the explained variance (caused by the input factor) to the unexplained variance (caused by the error source). 

If the ratio of explained variance to unexplained variance is high, the means are statistically different.

https://www.ibm.com/docs/en/cognos-analytics/11.1.0?topic=tests-analysis-variance-anova

The One-Way ANOVA procedure produces a one-way analysis of variance for a quantitative dependent variable by a single factor (independent) variable and estimates the effect size in one-way ANOVA. 

Analysis of variance is used to test the hypothesis that several means are equal. This technique is an extension of the two-sample t test.

https://www.ibm.com/docs/en/spss-statistics/27.0.0?topic=features-one-way-anova

ANOVA with only factors, can be referred as Factorial ANOVA.

Standard set of ANONA analysis, also provides parameter estimates and significance testing of parameter estimates based on t-test. 

Standard error of estimate is used for significance testing of parameter estimates.

Assumptions for using OLS model fit (Standard or usual analysis) is group/each factor level is normal distributed, with equivalent variance. Each observations/ experiments are independent.

ANOVA is robust to normality assumption in general, and robust to equivalent variance when sample size is same (balanced design). One may consider to used Repeated measure ANOVA when measurements are repeated or observations are independent.

After fitting ANOVA model, unexplained differences in observed and predicted results is residual and expected to be homoscedastic. 

You can use ANOVA in two different ways, as a completely randomized design or as randomized block design.

https://www.ibm.com/docs/en/ias?topic=anova-background




ANOVA explanation and plots using R.

https://www.youtube.com/watch?v=UpsPDRXTJWc
https://www.youtube.com/watch?v=BxsCdxLhKww



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