skewness and kurtosis

Descriptive Statistics

Check for errors and outliers • Describe & summarise • Spread of the data • Ensure appropriate analysis • Data parametric or non‐parametric

negatively skewed <0

Negative Skewness is when the tail of the left side of the distribution is longer or fatter than the tail on the right side. The mean and median will be less than the mode. right skewness <0

Measure of Dispersion

Variation, Range, Standard Deviation

normal distribution

skewness 0

ordinal scales

the order of the values is significant but the differences between each one is not really known. typically measures of non-numeric concepts like satisfaction

nominal variables

used for labelling variables, without any quantitative value.

positively skewed

Positive Skewness means when the tail on the right side of the distribution is longer or fatter. The mean and median will be greater than the mode. left skewness >0

Skewness

Skewness is the degree of distortion from the symmetrical bell curve or the normal distribution. It measures the lack of symmetry in data distribution. It differentiates extreme values in one versus the other tail. A symmetrical distribution will have a skewness of 0. There are two types of Skewness: Positive and Negative

How to interpret skewness values

So, when is the skewness too much? The rule of thumb seems to be: If the skewness is between -0.5 and 0.5, the data are fairly symmetrical. If the skewness is between -1 and -0.5(negatively skewed) or between 0.5 and 1(positively skewed), the data are moderately skewed. If the skewness is less than -1(negatively skewed) or greater than 1(positively skewed), the data are highly skewed.

why use non parametric test

area of study is better represented by the median When distribution skewed enough, the mean strongly affected by changes far out in the distribution's tail whereas the median continues to more closely reflect the centre of the distribution. small sample size

Measure of Central Tendency

measure of Central Tendency • Mean, Median, Mode

kurtosis

measures the degree of tailedness in the distribution

Interval scale

numeric scales in which we know the order and also the exact differences between the values.

why use parametric

perform well with skewed and non-normal distributions usually have more statistical power than nonparametric tests. Thus, you are more likely to detect a significant effect when one truly exists.