Characteristic Statistical Values in DIAdem

Characteristic Statistical Values in DIAdem

The descriptive statistics functions characterize the properties of data series, for example, of measured values. You use characteristic statistical values to compress data series, which makes the data series easier to compare to other data series.

DIAdem calculates the characteristic statistical values either channel or line oriented. You can execute the channel oriented calculation over the entire channel or over a specified line section. DIAdem saves the results as custom properties of the input channels. You can also limit the line oriented calculation over several channels to a specified line area. Because line oriented characteristic values are not saved at the input channels, you should enable the result storage in channels.

For the dispersion measurements and for form measurements you can choose whether the data series displays the population or a sample. The specified formulas have the index P for population or S for sample.

Mean values

The mean values are moments of a data series. DIAdem calculates the following mean values:

Arithmetic mean

The arithmetic mean is the most commonly used type of mean and is also called the average.

Root mean square

The root mean square, also called the quadratic mean, is used to calculate the RMS level of a signal.

Geometric mean

The geometric mean is useful for the description of data series of which the product is required, for example, for growth rates of bacterial cultures or in the calculation of interest rates. DIAdem calculates the geometric mean when all the measured values are greater than zero.

Harmonic mean

The harmonic mean is used, for example, to calculate the average speed from partial speeds given for partial distances. DIAdem calculates the harmonic mean when all the measured values are greater than zero.

Normal distribution

Many statistical studies are based on the assumption that data series are normal distributions. With the Anderson-Darling test you can check this assumption.

Anderson-Darling test

The Anderson-Darling test calculates whether the values of a data series are normally distributed. To do so, DIAdem determines the p-value. If the p-value is greater than 0.05, it is a normal distribution.

Quantiles

Quantiles and the mean values are moments. Quantiles are usually less subject to outliers than the mean values. DIAdem requires at least four values to calculate quantiles. DIAdem calculates the following quantiles:

0.25 quantile (lower quartile)

If the measured values are sorted according to size, the 0.25 quantile is the measured value that is undershot by 25% of the measured values. The 0.25 quantile is also called the lower quartile.

0.50 quantile (median)

If the measured values are sorted according to size, the 0.50 quantile is the measured value of which an equal number of values are less than and greater than the value. The 0.50 quantile is also called the median.

0.75 quantile (upper quartile)

If the measured values are sorted according to size, the 0.75 quantile is the measured value that is undershot by 75% of the measured values. The 0.75 quantile is also called the upper quartile.

Dispersion

The dispersion values describe the dispersion of data series. For the dispersion measurements, standard deviation, standard error, variance, variation coefficient, and relative variation coefficient you can select whether the data series displays the population or a sample. The specified formulas have the index P for population or S for sample. DIAdem calculates the following dispersion values:

Range

The range is the difference between the highest and the lowest measured value.

Quartile distance

The quartile distance is the difference between the upper quartile (the 0.75 quantile) and the lower quartile (the 0.25 quantile). This means that 50% of the measured values are inside the quartile distance.

Standard deviation

The standard deviation is the square root of the variance of the data series.

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Standard error

The standard error is the quotient of the standard deviation of the data series and the root of the number of measured values.

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Variance

The variance is the average squared deviation of the data series from its arithmetic mean.

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Variation coefficient

The variation coefficient is the quotient from the standard deviation and the arithmetic mean of the data series.

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Relative variation coefficient

The relative variation coefficient is the quotient from the variation coefficient and its theoretically possible maximum. DIAdem specifies the relative variation coefficient as a percentage.

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Average Absolute Deviation

Average absolute deviations are especially useful when the variance of a data series is almost infinite. DIAdem calculates the average absolute deviations from the mean and from the median:

Average absolute deviation from mean

MAD_μ specifies the average absolute deviation from the mean value.

Average absolute deviation from median

MAD_x˜specifies the average absolute deviation from the median (the 0.50 quantile).

Form

The forms are also called central moments and describe the deviation of the distribution of the measured values from a normal distribution. For the form measurements you can choose whether the data series displays the population or a sample. The specified formulas have the index P for population or S for sample:

Skewness

The skewness is the third order central moment and characterizes the degree of asymmetry to the right (positive skewness) or to the left (negative skewness) of a distribution around its mean. Normal distribution has zero skewness.

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Kurtosis

The kurtosis is the fourth order central moment and describes the peakedness of a distribution of measured values. Normal distribution has kurtosis 3. If the kurtosis is greater than 3, the distribution is more peaked than a normal distribution. If the kurtosis is less than 3, the distribution is flatter.

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Excess

The excess kurtosis describes the difference of the kurtosis of a random value to the kurtosis of the normal distribution. Because the normal distribution has the kurtosis 3, the value 3 is subtracted from the calculated kurtosis.

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