How to test normality in STATA?

A leptokurtic distribution accompanied by negative skewness (left-tailed distribution) implies at a greater risk, because of the higher odds of negative outliers. On the other hand, a leptokurtic distribution accompanied by positive skewness (right-tailed distribution) implies at a higher odds of positive outliers. This sort of distribution is something that would suit an aggressive investor. Meanwhile, for return distributions that are platykurtic (short-tailed distribution), the outliers would be smaller than those found even in normal distribution.

In the above table, notice that Tata Motors had the highest standard deviation as well as the highest excess kurtosis. This means that since the start 2021 till the time of writing, compared to the other two stocks, Tata Motors not only had higher dispersion around the mean return but also had longer tails. Furthermore, a moderate level of positive skewness suggests that the returns of Tata Motors are right-skewed. Skewness is the measure of asymmetry in a statistical distribution or a comparative measure of the two tails. Right skewed distributions will have a positive skew while left skewed distributions will have a negative skew.

However, if the distribution is asymmetrical, the mean will be either above or below the median and the mode. If the outliers lie above the mean, the distribution will be positively skewed . In this case, the mean will be greater than the median, which in turn will be greater than the mode. On the other hand, if the outliers lie below the mean, the distribution will be negatively skewed . In this case, the mean will be less than the median, which in turn will be less than the mode.

Skewness

In order to predict the residuals from the regression model, use the below command. Now that we have a way to calculate kurtosis, we can compare the values obtained rather than shapes. The next article discusses the tests for heteroscedasticity. Heteroscedasticity is a violation of an important ordinary least squares assumption that all residuals belong to apopulationthat has a constant variance . In order to perform this test, use the command ‘jb resid’ in the command prompt. Next, use the below command in order to generate the residuals in the data set.

• On the other hand, Kurtosis represents the height and sharpness of the central peak relative to that of a standard bell curve.
• After performing the above procedure, ‘sktest – Skewness and kurtosis test for normality’ box will appear .
• One of the most well known leptokurtic distributions is Student’s t distribution.
• Knowing the probabilistic range of security returns based on mean and standard deviation can help in making assumptions about the expected future returns of a security as well as in gauging potential risks.
• Now that we have a way to calculate kurtosis, we can compare the values obtained rather than shapes.

There are several normality tests such as the Skewness Kurtosis test, the Jarque Bera test, the Shapiro Wilk test, the Kolmogorov-Smirnov test, and the Chen-Shapiro test. This article shows two tests; Skewness Kurtosis and Jarque Bera tests because they are simple and popular. In economics, the skewness measure is often used to study income distributions that are skewed to the right or to the left. We are a team of dedicated analysts that have competent experience in data modelling, statistical tests, hypothesis testing, predictive analysis and interpretation. Given the skewness and Kurtosis we could predict the shape of a probability distribution. One of the most important thing that one would like to infer from a descriptive statistics output for any data is how much does the data distribution comply or deviate from a normal distribution.

In statistics, bell curve is frequently used to illustrate normal distribution, which is a type of statistical distribution that is symmetrical about its mean. Well, put it in layman terms, it implies the distribution is shaped identically on both sides of its mean – that is, one half of the distribution will fall to the left of the mean, while the other half will fall to the right. The chart below depicts how a normal distribution looks like – resembling a bell-shaped curve that is spaced evenly on either side of the mean (µ), which is represented by the vertical line. In a negatively skewed distribution the value of mode is maximum and that of mean least-the median lies in between the two. In the negatively skewed distribution the position is reversed, i.e., the excess tail is on the left-hand side. The figure above shows a bell-shaped distribution of the residuals.

A leptokurtic distribution is one that has kurtosis greater than a mesokurtic distribution. Besides normal distributions, binomial distributions for whichp is close to 1/2 are considered to be mesokurtic. If the p-value is lower than the Chi value then the null hypothesis cannot https://1investing.in/ be rejected. After performing the above procedure, ‘sktest – Skewness and kurtosis test for normality’ box will appear . Select the main variable to test for normality (here it is ‘resid’). Explain Kurtosis relative to a normal distribution with the help of diagrams.

The normal distribution is found to have a kurtosis of three. A distribution with kurtosis greater than three is leptokurtic and a distribution with kurtosis less than three is platykurtic. When skewness is negative, it means that the data is left skewed.

Explain Kurtosis relative to a normal distribution with the help of diagrams.

Skewness and Kurtosis are measures that quantify such deviation, often referred to as measures for ’shape‘ related parameters. These measures will be particularly useful while comparing 2 distributions, and decide on the extent of normality – For eg. The delivery time for a product when compared between two delivery outlets.

Skewness is a measure of the asymmetry of the probability distribution of a random variable about its mean. On the other hand, Kurtosis represents the height and sharpness of the central peak relative to that of a standard bell curve. The figure below shows the results obtained after performing the Skewness and Kurtosis test for normality in STATA. You might have heard of the term ‘bell curve’, a curve that resembles the shape of a bell when plotted on a chart.

Some are asymmetric and skewed to the left or to the right. Another feature to consider when talking about a distribution is the shape of the tails of the distribution on the far left and the far right. Kurtosis is the measure of the thickness or heaviness of the tails of a distribution.

Concept of Kurtosis

0; a negative kurtosis, known as Platykurtic will have β2–3 More sharing options… An application oriented question on the topic along with responses can be seen below. The best answer was provided by Vishwadeepak Choudhary on 27th August 2018.

Here median, mode and mean are at the same point and the skewness is zero. Kurtosis is typically measured with respect to the normal distribution. A distribution that has tails shaped in roughly the same way as any normal distribution, not just the standard normal distribution, is said to be mesokurtic. The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. Distributions of data and probability distributions are not all the same shape.

There are two other comparable characteristics called skewness and kurtosis that help us to understand a distribution. In addition to this the discrete probability distribution from a single flip of a coin is platykurtic. One of the most well known leptokurtic distributions is Student’s t distribution. Leptokurtic distributions are sometimes identified by peaks that are thin and tall. The tails of these distributions, to both the right and the left, are thick and heavy. Leptokurtic distributions are named by the prefix „lepto“ meaning „skinny.“

In short, a positively skewed distribution will have a tail that stretches to the right, while a negatively skewed distribution will have a tail that stretches to the left. The image below shows distributions that exhibit positive skewness, zero skewness, and negative skewness. Earlier in this chapter, we spoke about skewness and kurtosis, which are the third and the fourth central moment, respectively, in statistics . When observations in the data set are normally distributed about the mean, one can use standard deviation as an effective measure of risk. That said, keep in mind that standard deviation assumes a distribution that is normal.

Chapter: 11th Statistics : Chapter 6 : Measures of Dispersion

We would talk about the usage of these two parameters now. As explained above, these definitely help us to know about the shapes of the distribution; more importantly whether we are working with normal distribution or not. In the next chapter, we will continue our discussion of statistical measures of risk by talking about covariance and correlation. Based on the above table, let us now calculate the possible range of log returns within which Nifty could trade over the next one month. We can find how much the frequency curve is flatter than the normal curve using measure of kurtosis.

Conducting a normality test in STATA

Kurtosis is a measure of sharpness of the peak of a distribution. It also gives us a measure of the combined weight of the tails as compared to the weight of the remaining part of the distribution. If the weight of tails is large, it means the curve will look flatter while if the weight is less, the curve will look like a sharp peak. In a similar manner, one could calculate the potential range of returns discuss the concept of kurtosis. for Nifty for any other period, such as for the next 1 session, next 1 week, next 1 quarter, next 1 year etc. Knowing the probabilistic range of security returns based on mean and standard deviation can help in making assumptions about the expected future returns of a security as well as in gauging potential risks. Based on one’s risk tolerance, it can also help in stock screening and selection.

In the real word however, the distribution of security returns is not always normal. In fact, there is a tendency for security returns to get asymmetric and exhibit skewness and kurtosis. In such a case, skewness and kurtosis would better represent risk.