Statistical differences between histograms

CALL HDIFF (ID1,ID2,PROB*,CHOPT)

Action: Statistical test of compatibility in shape between two histograms using the Kolmogorov test. The histograms are compared and the probability that they could come from the same parent distribution is calculated.

The comparison may be done between two 1-dimensional histograms or between two 2-dimensional histograms.   For further details on the method, see below.

Input parameters:

ID1

Identifier of first histogram to be compared.

ID2

Identifier of second histogram to be compared.

CHOPT

A character string specifying the options desired.

'D'

Debug printout, produces a blank line and two lines of information at each call, including the identifier numbers ID, the number of events in each histogram, the value of PROB, and the maximum Kolmogorov distance between the two histograms. For 2-dimensional histograms, there are two Kolmogorov distances (see below). If option 'N' is specified, there is a third line of output giving the probalility PROB for shape and normalization alone separately.

'F1'

Histogram ID1 has no errors (it is a function).

'F2'

Histogram ID2 has no errors (it is a function).

'N'

Include a comparison of the relative normalization of the two histograms, in addition to comparing the shapes. The output parameter PROB is then a combined confidence level taking into account absolute contents.

'O'

Overflow, requests that overflow bins be taken into account (also valid for 2-dim).

'U'

Underflow, requests that underflow bins be taken into account (also valid for 2-dim).

For 2-dimensional histograms only

'L'

Left, include X-underflows in the calculation.

'R'

Right, include X-overflows in the calculation.

'B'

Bottom, include Y-underflows in the calculation.

'T'

Top, include Y-overflows in the calculation.

Output Parameter:

PROB

The probability of compatibility between the two histograms.

Remark:

• Options 'O' and 'U' can also refer to 2-dimensional histograms, so that, for example the string 'UT' means that underflows in X and Y and overflows in Y should be included in the calculation.
• The histograms ID1 and ID2 must exist and already have been filled before the call to HDIFF. They must also have identical binning (lower and upper limits as well as number of bins).
• The probability PROB is returned as a number between zero and one. A values close to one indicates very similar histograms, and a value near zero means that it is very unlikely that the two arose from the same parent distribution.
• By default (no options selected with CHOPT) the comparison is done only on the shape of the two histograms, without consideration of the difference in number of events, and ignoring all underflow and overflow bins.

• Weights and Saturation
• Statistical Considerations