XxY Statistic

Setting

Description

Statistic

Select a convolution statistic to use.

• Mean
• Minimum
• Maximum
• Median
• Percentile
• Standard deviation
• Variance
• Mean absolute deviation
• Coefficient of variation
• Kurtosis

Percentile (%)

Specifies the Nth Percentile (0 to 100%).

Rows (samples)

Specifies the number of rows (X) in the convolution window. The row value is restricted to an odd number, between 1 and 999, and spans sample space.

Columns (pings)

Specifies the number of columns (Y) in the convolution window. The column value is restricted to an odd number, between 1 and 999, and spans ping space.

Input samples per calculation

Displays the number of input samples for each calculation. This number is based on the specified Row and Column settings.

Although you can set Row and Column to any odd number between 1 and 999, this operator's performance decreases as the product of these settings increases. A warning is displayed when the value for the Input samples per calculation is greater than 1000.

Statistic

Value

Mean

The mean of the values in the XxY window. The mean is calculated in the linear domain.

Where:

n is the number of samples within the XxY window.

xj is the jth sample value in the XxY window.

Minimum

Maximum

Median

The Nth percentile score of the values in the XxY window.

yI, J (window) = Wk + (Wk+1 - Wk) (k' - k)

Where:

yI, J (window)	=	the Nth percentile score of the values in the XxY window
Wk	=	the value of sample k in the list W — (defined below)
k	=	ëk'û *
k'	=	N x P/100
N	=	the number of samples in the list W.
P	=	the Percentile entered on the XxY Statistic page of the Variable properties dialog box
W	=	the ordered list of sample values in the window where (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

*Floor function ëxû, gives the largest integer less than or equal to x.

Standard deviation

The standard deviation (s) of the sample values in the XxY window. Standard deviation is calculated in the linear domain. The (n-1) term is used when a subset is taken of a population. Here, the XY window is a subset of the echogram samples.

Where n, xj and are defined as above.

Variance

The variance (s2) of the sample values in the XxY window. The variance is calculated in the linear domain. The (n-1) term is used when a subset is taken of a population. Here, the XxY window is a subset of the echogram samples.

The variance is s2, where s is defined as above.

Mean absolute deviation

The mean absolute deviation (MAD) of the sample values in the XxY window. MAD is calculated in the linear domain.

Where n, xj and are defined as above.

Coefficient of variation

The coefficient of variation (cv) of the sample values in the XxY window. The coefficient of variation is calculated in the linear domain.

Where s and are defined as above.

Kurtosis

The kurtosis of the sample values in the XxY window. The kurtosis is calculated in the linear domain.

Where n, xj, s and are defined as above. For the Kurtosis calculation n > 3 is required to avoid an undefined division. Calculations are carried out in the linear domain and the output kurtosis is a linear value.