TEST_SKEW

Calculates the p-value of the statistical test for the population skew (i.e. 3rd moment).

Syntax

TEST_SKEW(X)

X
is the data sample (a one dimensional array of cells (e.g. rows or columns)).

The data sample may include missing values (e.g. #N/A).
The test hypothesis for the population distribution skewness:

$H_{o}: S=0$

$H_{1}: S\neq 0$

Where:
- $H_{o}$ is the null hypothesisⁱ.
- $H_{1}$ is the alternate hypothesis.
- $S$ is the population skew.
For the case in which the underlying population distribution is normal, the sample skew also has a normal sampling distribution:

$\hat S \sim N(0,\frac{6}{T})$

Where:
- $\hat S$ is the sample skew (i.e. 3rd moment).
- $T$ is the number of non-missing values in the data sample.
- $N(.)$ is the normal (i.e. Gaussian) probability distribution function.
The sample data skew is calculated as:

$\hat S(x)= \frac{\sum_{t=1}^T(x_t-\bar x)^3}{(T-1)\times \hat \sigma^3}$

Where:
- $\hat S$ is the sample skew (i.e. 3rd moment)
- $x_i$ is the i-th non-missing value in the data sample.
- $T$ is the number of non-missing values in the data sample.
- $\hat \sigma$ is the data sample standard deviation.
In the case where the population skew is not zero, the mean is farther out than the median in the long tail.
The underlying distribution is referred to as skewed, unbalanced, or lopsided.
The underlying population distribution is assumed normal (Gaussian).
This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ( $\alpha/2$ ).

Example 1:

	Formula	Description (Result)
	=TEST_SKEW($B$2:$B$17)	p-value of the test when skewness = 0 (0.4025)
	=SKEW($B$3:$B$17)	Sample skewness (-0.1740)