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Assumption and Data TransformationPowerPoint Presentation

Assumption and Data Transformation

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Assumption of Anova

- The error terms are randomly, independently, and normally distributed
- The variance of different samples are homogeneous
- Variances and means of different samples are not correlated
- The main effects are additive

Randomly, independently and Normally distribution

- The assumption of normality do not affect the validity of the analysis of variance too seriously
- There are test for normality, but it is rather point pointless to apply them unless the number of samples we are dealing with is fairly large
- Independence implies that there is no relation between the size of the error terms and the experimental grouping to which the belong
- It is important to avoid having all plots receiving a given treatment occupying adjacent positions in the field
- The best insurance against seriously violating the first assumption of the analysis of variance is to carry out the randomization appropriate to the particular design

Normally test

- Shapiro-Wilk test
- Lilliefors-Kolmogorov-Smirnov Test
- Graphical methods based on residual error (Residual Plotts)

Homogeneity of Variance

- Unequal variances can have a marked effect on the level of the test, especially if smaller sample sizes are associated with groups having larger variances
- Unequal variances will lead to bias conclusion

Way to solve the problem of Heterogeneous variances

- We can separate the data into groups such that the variances within each group are homogenous
- We can use an advance statistic tests rather than analysis of variance
- we might be able to transform the data in such a way that they will be homogenous

Homogeneity test of Variance

- Hartley F-max test
- Bartlett’s test
- Residual plot for checking the equal variance assumption

Independence of Means and Variance

- It is a special case and the most common cause of heterogeneity of variance
- A positive correlation between means and variances is often encountered when there is a wide range of sample means
- Data that often show a relation between variances and means are data based on counts and data consisting of proportion or percentages
- Transformation data can frequently solve the problems

The Main effects are additive

- For each design, there is a mathematical model called a linear additive model.
- It means that the value of experimental unit is made up of general mean plus main effects plus an error term
- When the effects are not additive, there are multiplicative treatment effect
- In the case of multiplication treatment effects, there are again transformation that will change the data to fit the additive model

Data Transformation

- There are two ways in which the anova assumptions can be violated:
1. Data may consist of measurement on an ordinal or a nominal scale

2. Data may not satisfy at least one of the four requirements

- Two options are available to analyze data:
1. It is recommended to use non-parametric data analysis

2. It is recommended to transform the data before analysis

Logaritmic Transformation

- It is used when the standard deviation of samples are roughly proportional to the means
- There is an evidence of multiplicative rather than additive
- Data with negative values or zero can not be transformed. It is suggested to add 1 before transformation

Square Root Transformation

- It is used when we are dealing with counts of rare events
- The data tend to follow a Poisson distribution
- If there is account less than 10. It is better to add 0.5 to the value

Arcus sinus or angular Transformation

- It is used when we are dealing with counts expressed as percentages or proportion of the total sample
- Such data generally have a binomial distribution
- Such data normally show typical characteristics in which the variances are related to the means

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