Skewness, Kurtosis, and Correlation Flashcards
Skewness or skew, refers to
the extent to which a distribution is not symmetrical
Outliers are
observations extraordinarily far from the mean, either above or below a Positively Skewed Distribution or a Negatively Skewed Distribution
The effect of Symmetrical, Positive (Right), and Negative (Left) Skewness on Mean, Median, and Mode
Symmetrical Skew: Mean = Median = Mode
Positive Skew: Mean > Median > Mode
Negative Skew: Mode > Median > Mean
Sample Skewness is equal to
the sum of the Cubed Deviations from the Mean divided by the Cubed Standard Deviation and by the Number of Observations
Used for larger samples
Kurtosis is a measure of
the degree to which a distribution is more or less peaked than a normal distribution
Leptokurtic describes
a distribution that is more peaked than a normal distribution.
Platykurtic describes
a distribution that is less peaked, or flatter than a normal one
A distribution is Mesokurtic if it has
the same kurtosis as a normal distribution
A distribution is said to exhibit Excess Kurtosis if it has
either more or less Kurtosis than the normal distribution
Greater excess Kurtosis and more negative skew in returns distributions indicate
increased risk
Sample Kurtosis for large samples is approximated by
using deviations raised to the forth power
Scatter Plots are a method for
displaying the relationship between two variables.
A key advantage of using Scatter Plots is that
they can reveal nonlinear relationships that are not correlation coefficient and linear relationships that are highly correlation coefficient
Covariance is a measure of
how two variables move together.
A standardized measure of the linear relationship between two variables is called the
Correlation Coefficient, or simply Correlation
(Property of correlation)
Correlation measures the
strength of the linear relationship between two random variables
(Property of Correlation)
Correlation has how many units?
Zero
(Property of Correlation)
Correlation ranges from
-1 to +1
That is, -1 less than or equal to Pxy less than or equal to +1
(Property of Correlation)
If Pxy =1.0, the random variables have
perfect positive correlation. Meaning, the one movement of one random variable results in a proportional positive movement from the other relative to its mean
(Property of Correlation)
If Pxy =-1.0, the random variables have
perfect negative correlation. Meaning, the movement of one random variable results in an exact opposite proportional movement from the other relative to its mean
(Property of Correlation)
If Pxy = 0, the random variables have
No linear relationship and therefore predicting the movement of Y cannot be made on the basis of X using linear methods
Spurious Correlation refers to correlation that is
either the result if chance or present due to changes in both variables over time that is caused by their association with a third variable that the causation for why the correlation is not present.
Ex: the age of each years Miss America and the number of films that Nicolas Cage appeared in that year is 87% - random
Kurtosis deals with the
overall shape of a distribution, not it’s skewness
A distribution of returns that has a greater percentage of small deviations from the mean and a greater percentage of extremely large deviations from the mean compared with a normal deviation will be
Leptokurtic and will exhibit excess (positive) Kurtosis. The distribution will be more peaked and have fatter tails than a normal distribution
a Correlation of +0.25 indicates a
Positive linear relationship between the two variables (although not a strong one). When one variable is above its mean, the other variable tends to be above its mean as well.
Remember, correlation does not imply causation (same reason for movement)
