# Relationship between skewness and type of data transformation

The most frequent reason that researchers transform their data is to make the distribution A transformation is needed when the data is excessively skewed positively or negatively. The figure below suggests that type of transformation that can. Most people find it difficult to accept the idea of transforming data. transformed variables can occasionally reverse the difference of means of the lower end, it may also have the effect of making positively skewed distributions more nearly. When the dose-response relationship is plotted it is curvilinear. In a nutshell, transformation can be carried out to make the data follow normal to the mean, the distribution is positively skewed and logarithmic transformation is the ideal one.

Apart from these simple methods, normality can be verified by statistical tests like Kolmogorov - Smirnov test.

Once skewness is identified, every attempt should be made to convert it into a normal distribution, so that the robust parametric tests can be applied for analysis. This can be accomplished by transformation. Transformations can also be done for the ease of comparison and interpretation. The classical example of a variable which is always reported after logarithmic transformation is the hydrogen ion concentration pH.

- Data transformation

Another example where transformation helps in the comparison of data is the logarithmic transformation of dose-response curve. When the dose-response relationship is plotted it is curvilinear. When the same response is plotted against log dose log dose-response plot it gives an elongated S-shaped curve. The middle portion of this curve is a straight line and comparing two straight lines by measuring their slope is easier than comparing two curves.

Hence transformation can assist in the comparison of data. Many a times, the transformation which makes the distribution normal also makes the variance equal.

### Data transformation (statistics) - Wikipedia

Even though there are many transformations like logarithm, square root, reciprocal, cube root, square, the initial three are more commonly used. The following are the guidelines for the selection of a method of transformation.

**Stata Tutorial 3: Data Transformation Basics**

If the variance is proportional to the mean, square root transformation is preferred. This happens more in case of variables which are measured as counts e.

If the standard deviation is proportional to the mean squared, a reciprocal transformation can be performed. Reciprocal transformation is carried out for highly variable quantities such as serum creatinine. Among these three transformations, logarithmic transformation is commonly used as it is meaningful on back transformation antilog.

They are assured that transformation is a statistically approved method and it is universally valid. This is called the rank transform[ citation needed ], and creates data with a perfect fit to a uniform distribution. This approach has a population analogue.

### Data transformation

From a uniform distribution, we can transform to any distribution with an invertible cumulative distribution function. Variance stabilizing transformations[ edit ] Main article: Variance-stabilizing transformation Many types of statistical data exhibit a " variance -on-mean relationship", meaning that the variability is different for data values with different expected values.

As an example, in comparing different populations in the world, the variance of income tends to increase with mean income. If we consider a number of small area units e. A variance-stabilizing transformation aims to remove a variance-on-mean relationship, so that the variance becomes constant relative to the mean.

## Data transformation (statistics)

Examples of variance-stabilizing transformations are the Fisher transformation for the sample correlation coefficient, the square root transformation or Anscombe transform for Poisson data count datathe Box—Cox transformation for regression analysis and the arcsine square root transformation or angular transformation for proportions binomial data.

While commonly used for statistical analysis of proportional data, the arcsine square root transformation is not recommended because logistic regression or a logit transformation are more appropriate for binomial or non-binomial proportions, respectively, especially due to decreased type-II error. It is also possible to modify some attributes of a multivariate distribution using an appropriately constructed transformation.

For example, when working with time series and other types of sequential data, it is common to difference the data to improve stationarity.