Calculates the p-value of the statistical test for the population excess kurtosis (4th moment).
Syntax
TEST_XKURT(X, Return_type, Alpha)
- X
- is the input data sample (one/two dimensional array of cells (e.g. rows or columns)).
- Return_type
- is a switch to select the return output (1 = P-Value (default), 2 = Test Stats, 3 = Critical Value.
Method Description 1 P-Value 2 Test Statistics (e.g. Z-score) 3 Critical Value - Alpha
- is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
Remarks
- The data sample may include missing values (e.g. #N/A).
- The test hypothesis for the population excess kurtosis:
$$H_{o}: K=0$$
$$H_{1}: K\neq 0$$
Where:
- $H_{o}$ is the null hypothesis.
- $H_{1}$ is the alternate hypothesis.
- For the case in which the underlying population distribution is normal, the sample excess kurtosis also has a normal sampling distribution:
$$\hat K \sim N(0,\frac{24}{T}) $$
Where:
- $\hat k$ is the sample excess kurtosis (i.e. 4th moment).
- $T$ is the number of non-missing values in the data sample.
- $N(.)$ is the normal (i.e. gaussian) probability distribution function.
- Using a given data sample, the sample excess kurtosis is calculated as:
$$\hat K (x)= \frac{\sum_{t=1}^T(x_t-\bar x)^4}{(T-1)\hat \sigma^4}-3$$
Where:
- $\hat K(x) $ is the sample excess kurtosis.
- $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 sample standard deviation.
- 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 ($\frac{\alpha}{2}$).
Examples
Example 1:
|
|
Formula | Description (Result) |
---|---|
=KURT($B$2:$B$20) | Sample excess kurtosis (-1.0517) |
=TEST_XKURT($B$2:$B$20) | p-value of the test when excess kurtosis = 0 (0.171) |
Comments
Article is closed for comments.