# Distribution Transformation

**(What is the Box-Cox Power Transformation?)**

**a procedure to identify an appropriate exponent (Lambda = l) to use to transform data into a “normal shape.”****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.**

**IMPORTANT:!! After a transformation (c), we need to measure the normality of the resulting transformation (d) .**

**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!**

**GUARANTEED NORMALITY?**

**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 – but not a guarantee – 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)**

**+ Additionally, the Box-Cox Power transformation only works if all the data is positive and greater than 0.**

**+ achieved easily by adding a constant ‘c’ to all data such that it all becomes positive before it is transformed. The transformation equation is then:**

**Finally: An awesome**

**tutorial (dead),**

**here is a new one**

**in python with**

**code examples**

**, there is also another code example**

**here**

**“Simply pass a 1-D array into the function and it will return the Box-Cox transformed array and the optimal value for lambda. You can also specify a number, alpha, which calculates the confidence interval for that value. (For example, alpha = 0.05 gives the 95% confidence interval).”**

**(**

**what is?**

**) - the Mann–Whitney U test is a**

**nonparametric**

**test**

**of the**

**null hypothesis**

**that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.**

**In other words: This test can be used to determine whether two independent samples were selected from populations having the same distribution.**

**Unlike the**

**t-test**

**it does not require the assumption of**

**normal distributions**

**. It is nearly as efficient as the t-test on normal distributions.**

- 2.
**Analytics vidhya**- 2.
- 3.
- 1.
**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 won’t 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.**