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Using the Bootstrap Method for a Statistical Significance Test of Differences between Summary Histograms

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  • 1 NASA Langley Research Center, Hampton, Virginia
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Abstract

A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries–Matusita distance, and the Kuiper distance.

The data used in testing the bootstrap method are satellite measurements of cloud systems called “cloud objects.” Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object, and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.

Corresponding author address: Dr. Kuan-Man Xu, Climate Science Branch, NASA Langley Research Center, Mail Stop 420, Hampton, VA 23681. Email: Kuan-Man.Xu@nasa.gov

Abstract

A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries–Matusita distance, and the Kuiper distance.

The data used in testing the bootstrap method are satellite measurements of cloud systems called “cloud objects.” Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object, and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.

Corresponding author address: Dr. Kuan-Man Xu, Climate Science Branch, NASA Langley Research Center, Mail Stop 420, Hampton, VA 23681. Email: Kuan-Man.Xu@nasa.gov

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