13.10 Defining Breaks for the Classification of Data

Different methods to classify data have been implemented. These methods are

Break values can be calculated by adding the information reader and executing it. The number of classes can be defined by double clicking on the information reader symbol within the file tree to open the settings dialog. After execution the map applying the classification as specified can be viewed within the right window. Drag and drop the information reader into the right window (see display options and map settings for further details). The original values are not changed within the dataset. If you wish to substitute the original values with the class numbers you have to apply the specific Option File Changer Function.

13.10.1 Equal Breaks

Equal breaks devides all values in classes with equally sized intervals, e.g. 0 to 5, 5 to 10, 10 to 15 etc.

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Figure 41:

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Figure 42: Map displayed with Equal Breaks

The function has the following dependencies:

Equal Breaks Settings Dialog Define the number of classes you want to calculate the breaks for.

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Figure 43: Equal Breaks Settings Dialog

Find more information about the function at the section Equal Breaks.

13.10.2 Quantile Breaks

Quantile breaks devides all values in classes with an equal number of units. There are 9 different mathematical formula implemented to define quantile breaks The default type is No. 8.

The formulas are:

  • Type 1: Inverse of empirical distribution function. γ = 0 if g = 0, and 1 otherwise.
  • Type 2: Similar to type 1 but with averaging at discontinuities. γ = 0.5 if g = 0, and 1 otherwise.
  • Type 3: SAS definition: nearest even order statistic. γ = 0 if g = 0 and j is even, and 1 otherwise.

Continuous sample quantile types 4 through 9

For types 4 through 9, Q[i](p) is a continuous function of p, with gamma = g and m given below. The sample quantiles can be obtained equivalently by linear interpolation between the points (p[k],x[k]) where x[k] is the kth order statistic. Specific expressions for p[k] are given below.

  • Type 4: m = 0. p[k] = k / n. That is, linear interpolation of the empirical cdf.
  • Type 5: m = 1/2. p[k] = (k - 0.5) / n. That is a piecewise linear function where the knots are the values midway through the steps of the empirical cdf. This is popular amongst hydrologists.
  • Type 6: m = p. p[k] = k / (n + 1). Thus p[k] = E[F(x[k])]. This is used by Minitab and by SPSS.
  • Type 7: m = 1-p. p[k] = (k - 1) / (n - 1). In this case, p[k] = mode[F(x[k])]. This is used by S.
  • Type 8: m = (p+1)/3. p[k] = (k - 1/3) / (n + 1/3). Then p[k] =  median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x.
  • Type 9: m = p/4 + 3/8. p[k] = (k - 3/8) / (n + 1/4). The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally distributed.

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Figure 44: Map displayed with Quantile Breaks

The Quantile Breaks function has the following dependencies:

Quantile Breaks Settings Dialog Define the number of classes you want to calculate the breaks for. Select the type of formula you wish to use to calculate the breaks. Find more information about the different types at the section Quantile Breaks

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Figure 45: Quantile Breaks Settings Dialog
13.10.3 Jenks Optimal Breaks

Jenks Optimal Breaks devides all values in classes applying an algorithm minimizing the differences within each class and maximizing the differences between each class.

The Jenks Breaks function has the following dependencies:

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Figure 46: Map displayed with Jenks Breaks

Jenks Optimal Breaks Settings Dialog Define the number of classes you want to calculate the breaks for. Find more information about the different types at the section Jenks Breaks.

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Figure 47: Jenks Breaks Settings Dialog
13.10.4 Variable Breaks

Within the variable breaks function customized break values can be defined to classify all values. The breaks can be defined in the settings dialog by typing the value or by clicking at the the historgram.

The Variable Breaks function has the following dependencies:

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Figure 48: Map displayed with variable breaks

Variable Breaks Settings Dialog Define the number of classes you want to calculate the breaks for by adding or deleting classes through the add button. Define the breaks by clicking at the specific value in the distribution chart or by typing in the value. Find more information about the different types at the section Variable Breaks

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Figure 49: Variable Breaks Settings Dialog