Machine & Deep Learning Compendium

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Distribution Transformation

**a procedure to identify an appropriate exponent (Lambda = l) to use to transform data into a βnormal shape.β****The Lambda value indicates the power to which all data should be raised.**

**Many statistical tests and intervals are based on the assumption of normality.****The assumption of normality often leads to tests that are simple, mathematically tractable, and powerful compared to tests that do not make the normality assumption.****Unfortunately, many real data sets are in fact not approximately normal.****However, an appropriate transformation of a data set can often yield a data set that does follow approximately a normal distribution.****This increases the applicability and usefulness of statistical techniques based on the normality assumption.**β

**The correlation is computed between the vertical and horizontal axis variables of the probability plot and is a convenient measure of the linearity of the probability plot****In other words: the more linear the probability plot, the better a normal distribution fits the data!**

**NO!****This is because it actually does not really check for normality;****the method checks for the smallest standard deviation.****The assumption is that among all transformations with Lambda values between -5 and +5, transformed data has the highest likelihood β but not a guarantee β to be normally distributed when standard deviation is the smallest.****it is absolutely necessary to always check the transformed data for normality using a probability plot. (d)**

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**Analytics vidhya**- 1.
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**if the means of two or more groups are significantly different from each other. ANOVA checks the impact of one or more factors by comparing the means of different samples.** - 2.
**A one-way ANOVA tells us that at least two groups are different from each other. But it wonβt tell us which groups are different.** - 3.
**For such cases, when the outcome or dependent variable (in our case the test scores) is affected by two independent variables/factors we use a slightly modified technique called two-way ANOVA.**

- 3.
**multivariate case and the technique we will use to solve it is known as MANOVA.**

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