Statistics Properties


The Statistics Properties dialog configures parameters for Statistics Measurements in Image Windows and Plot Windows. Mira keeps two sets of parameters, one for image windows and the other for plot windows. The Statistics Properties dialog makes a distinction between these two sets when opened from either type of window. For example, if both Image Windows and Plot Windows are visible on the Mira desktop, then the parameter set opened and saved corresponds to the Image Window or Plot Window that has the focus (the "top-most" window with the active title bar).

Sample value estimators like Mean, Median,MTM Sigma Clipped Mean, etc., automatically calculate the standard deviation. Non-value estimators, like Minimum, Skewness, etc., do not. The standard deviation and standard error estimators duplicate the estimator as the standard deviation.

Most of the statistical estimators are also available for combining and normalizing images. See Statistical Estimators for Image Combining.

The Statistics Properties dialog is opened from several locations:

Several of the estimators have Parameters that control their calculation. The specific parameters are enabled when their Estimator bullet is selected.

Properties of the Statistics Properties dialog

Mean

Calculates the simple average with no weighting or rejection of bad values.

Mean - Geometric

Calculates the geometric mean, which is a mean value weighted by the reciprocal of the individual values.

Mean - Contra Harmonic

Calculates the weighted harmonic mean value in which each weight involves the value raised to the p power.

Mean - Yp Power

Calculates the weighted mean value in which the weight is given by the exponent "p", which is the value raised to the p power.

Mean - Alpha Clipped

Calculates a clipped mean in which a specified number N(high) and N(low) values are excluded from the sample.

Mean - Rank Clipped

Calculates a clipped mean in which the specified percentiles %(high) and %(low) of values are excluded from the sample.

Mean - Sigma Clipped

Calculates a clipped mean in which values are rejected if more deviant than ß(high) and ß(low) above and below the sample distribution mean. Refinement of the calculated mean value is repeated up to specified maximum number of cycles. Use this method when calculating the mean value in the presence of deviant values that are outliers from a Normal distribution.

Mean - MTM Sigma Clipped

Calculates a clipped mean in which values are rejected if more deviant than ß(high) and ß(low) above and below the sample distribution estimator. This computation includes both the mean and median values of the sample distribution. Refinement of the calculated mean value is repeated up to specified maximum number of cycles. Use this method when calculating the mean value in the presence of deviant values that are outliers from a Normal distribution.

Mid Point

Calculates the midpoint between the sample minimum and maximum values.

Median

Calculates the sample median (50th percentile).

Minimum

Calculates the minimum values of the sample.

Maximum

Calculates the maximum values of the sample.

Rank Percentile

Calculates the ranked percentile value based on the %Rank parameter. For example, if %rank = 50, then the 50th percentile, or median, value is returned.

Standard Deviation

Calculates the Standard Deviation about the mean value. To calculate the standard deviation about a specified value, check the Reference Mean box and enter the target value. Otherwise, the ordinary standard deviation is calculated.

Standard Deviation - Clipped

Calculates the Standard Deviation in which values are rejected if more deviant than ß(high) and ß(low) above and below the sample distribution mean. Refinement of the calculated mean value is repeated up to specified maximum number of cycles. Use this method when calculating the standard deviation in the presence of deviant values that are outliers from a Normal distribution.

Std Err of the Mean

Calculates the Standard Error of the Mean. This is the standard deviation divided by the square root of the number of points in the sample, also known as the "error of the mean." This statistic is used when comparing the mean values for two different populations, such as the mean value of one image to the mean value of another image. Comparatively, the standard deviation measures the variation (or "scatter") of the sample values (e.g., pixels) with respect to their own mean.

Std Err of the Mean - Clipped

Calculates the Standard Error of the Mean in which values are rejected if more deviant than ß(high) and ß(low) above and below the sample distribution mean. Refinement of the calculated mean value is repeated up to specified maximum number of cycles. Use this method when calculating the standard deviation in the presence of deviant values that are outliers from a Normal distribution. This is the standard deviation divided by the square root of the number of points in the sample, also known as the "error of the mean." This statistic is used when comparing the mean values for two different populations, such as the mean value of one image to the mean value of another image. Comparatively, the standard deviation measures the variation (or "scatter") of the sample values (e.g., pixels) with respect to their own mean.

Skewness

Calculates the statistical skewness to characterize the asymmetry of the sample distribution. Skewness greater than 0 indicates a positive bias and skewness less than 0 indicates a negative bias.

Kurtosis

Calculates the relative weight of central values to tail values in the sample distribution. The value is adjusted to a reference value of 0 for the Normal ("Gaussian") distribution. A kurtosis value greater than 0 indicates that the distribution is taller than a Normal distribution (too narrow, or "leptokurtic"). Conversely, a kurtosis value less than 0 indicates the distribution is flatter than a Normal distribution (too flat, or "platykurtic"). By definition, the Normal distribution has the reference ratio of central area to tail area adjusted to 0, and is called "mesokurtic".

 Save Statistics to Header

Check this box to save the statistics measurements as FITS keywords in the image header. This feature is available when the dialog is opened for an Image Window but not for a Plot Window. See "Saving Statistics to the FITS Header," below.

[OK]

Saves the changed parameters and closes the dialog.

[Cancel]

Closes the dialog without saving the changed parameters.

Saving Statistics to the FITS Header

The computed statistics can be saved to the FITS image header for documentation purposes or for further analysis. For example, you might need to assess how the CCD dark current varies with CCD temperature across a series of dark frames. An example is given in the tutorial Using FITS Keywords to Analyze Image Data.

The table below lists the FITS keyword names used for representing statistics measurements in the image header. This keyword is a coded version of the estimator name, a consequence of the 8 character maximum length of FITS header keywords. For example, the Mean - Sigma Clipped estimator is abbreviated to make the keyword name S_SCMEAN. If the estimator also uses parameters, as does Mean - Sigma Clipped which has ß(high), ß(low), and Cycles parameters, then these parameters are saved in the Comment field of the keyword. Note that the S_REGION keyword is always saved to the header as it contains the column and row region over which the most recent estimator was calculated.

Additional Details:

The FITS keyword abbreviations below follow a few mnemonic rules. First, all begin with "S_". In addition, clipped estimators use the letters "CL" or "C", depending on the total number of characters in the name.

FITS Keywords for Statistical Estimators

FITS Keyword

Statistic (see table above)

S_REGION

Specifies the column and row limits of the region, for example, [150:351,128:762]

S_MEAN

Mean

S_GOMEAN

Mean - Geometric

S_CHMEAN

Mean - Contra Harmonic

S_YPMEAN

Mean - Yp Power

S_ACMEAN

Mean - Alpha Clipped

S_RCMEAN

Mean - Rank Clipped

S_SCMEAN

Mean - Sigma Clipped

S_MTMEAN

Mean - MTM Sigma Clipped

S_MIDPT

Mid Point

S_MEDIAN

Median

S_MIN

Minimum

S_MAX

Maximum

S_RANK

Rank Percentile

S_SDEV

Standard Deviation

S_CLSDEV

Standard Deviation - Clipped

S_SERR

Std Err of the Mean

S_CLSERR

Std Err of the Mean - Clipped

S_SKEW

Skewness

S_KURT

Kurtosis

Related Topics

Statistics Measurements

List Statistics Keywords

Remove Statistics Keywords

Report Windows

Measurement Panes

Grid Controls

Measuring Images


Mira Pro x64 User's Guide, Copyright Ⓒ 2023 Mirametrics, Inc. All Rights Reserved.