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Variance - Covariance Exercise In class we covered the meaning and basic mathematical description of the basic statistical measures of mean, standard deviation, variance, covariance, and correlation coefficient. They are also discussed in Jensen, Chapter 4. The purpose of these measures is to describe the data under examination and, for our purposes, describe the similarity or difference between data sets (e.g. different wavelength bands of satellite data). One use of these measures is to identify duplicate information content in the different bands of satellite data. If two bands vary identically, that is, when one band increases the other band increases by the same magnitude and when one decreases the other decreases by the same, then both bands express the same information. We would want to eliminate one of the bands in our subsequent analysis to reduce our effort. Determining which bands are the important ones to examine is an important step in the preprocessing stage of satellite imagery. To see how this works. use the same imagery we used in the laboratory exercise for Howe Hill, pages 209-211 in the Idrisi tutorial manual. For TM bands 1 - 4 (How87TM1, How87TM2, How87TM3, How87TM4) recreate tables 4.2, 4.4, and 4.6 on pages 83-84 in Jensen. Choose a fairly random selection of 30 pixels. Of course you will need to link all four images and query them according to the "collection editor" and "feature properties" procedures outlined in the IDRISI tutorial. Make all your own calculations of mean, standard deviation, variance, covariance and correlation coefficient. Do not use the automatic formulas in EXCEL. Discuss your results. Are any of the bands very similar to each other? Are any bands different? What are the minimum number of bands you would use to describe the Howe Hill scene and why? Discuss your results in comparison to Jensen's results for Charleston, SC (just for bands 1-4). Don't forget that you are imaging different regions. Please turn in
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