Question

(a) What does it mean to have a skewed distribution? (2) What causes a skew in statistical terms? (3) And how does one deal with skewed data when conducting research? (4)Are there specific types of research questions and types of data where one would expect the data to be skewed? Give specific examples.

Answer 1

Answer to the question)

Answer to 1.

Definition of skewed distribution: it is dataset in which the mean and the medain do not match. If the mean and median are equal then the dataset is said to have normal distribution. But if the mean is either greater than the median or smaller than the median , then we do not get a symmetrical bellshaped curve for this dataset. The curve is either inclined towards the left axis or towards the right axis. this implies the curve is skewed. This type of dataset is said to have skewed distribution.

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Answer to 2)

Reasons: If in a dataset there are a few set of values that are either extremely large or extremely small as compared to the rest of the datapoints, this causes the mean to be pulled towards them. Thus this makes the mean different from the median. In statistical terms we can state , that is there is any outlier in the dataset , the distribution of such a dataset is bound to be skewed.

Suppose we have a dataset as follows:

0,1,2 , 6 , 6, 6 ,7 , 7 , 7 ,7 ,8 ,8 ,8 , 9 , 9 10

If we plot the same on graph we get:

8 6 4 0 5453525150

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We find the normal curve, stretches towards the left , this is because there are few extreme values to the left. Such a dataset is called Negatively skewed.

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Similarly if the stretch on the curve is towards the right side, this implies there are few extremely large values in the dataset , and the distribution is called Positively skewed.

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The following graphs show the different types of skewness

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Positively Skewed Negatively Skewed

Answer to 3)

There are various methods to deal with skewed data.

1. Median: Instead of mean , median can be used to represent the data as the best measure of central tendency for skewed data

2. Outlier: we can prefer to remove outliers from the data. For this first of all the outliers are to be identified from the dataset. and then the data must be considered after removing the outliers. This helps to reduce the skewness of the data.

3. Trimmed mean method: There is a method to trim the data : like 5% trim or 10% trim. This method also helps to eliminte the extreme values and focus on the more consistent values for the research purpose.

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Answer to 4)

Yes, there are research questions and types of data which are skewed. Research relate to many rare topics, and fileds which are not always normally distributed, and it is quite natural to have a skewed distribution for them. It may depend on the dataset and the factors related to it , that decide whether it is a positive skew or negative skew.

For example:

First example: in any developed country where there is Zero percent poverty , if we collect the data of income of the households, we will get majority people with average income , adn very few people who have extreme high income levels. This leads the data to be positively skewed.

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Second example: Now if the research question is related to some rare disease. The data is bound to be skewed, because it is a rare disease, and it is not any normal parameter of the population. Thus clinical research are genrally related to skewed data.

Thus we can say that there are various research questions and datasets that are based on a skewed data.