Graphical Summary of Data Distribution Statistical View Point Histograms Skewness Kurtosis Other...
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Transcript of Graphical Summary of Data Distribution Statistical View Point Histograms Skewness Kurtosis Other...
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Graphical Summary of Data DistributionStatistical View PointHistogramsSkewnessKurtosisOther Descriptive Summary MeasuresSource: www.unc.edu/courses/2006spring/geog/090/001/www/Lectures/ 2006- Geog090-Week03-Lecture02-SkewsnessKurtosis.ppt
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Measures of Dispersion Coefficient of VariationCoefficient of variation (CV) measures the spread of a set of data as a proportion of its mean. It is the ratio of the sample standard deviation to the sample mean
It is sometimes expressed as a percentageThere is an equivalent definition for the coefficient of variation of a population
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Coefficient of Variation (CV)It is a dimensionless number that can be used to compare the amount of variance between populations with different means
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Histogram: Frequency & DistributionA histogram is one way to depict a frequency distributionFrequency is the number of times a variable takes on a particular value Note that any variable has a frequency distributione.g. roll a pair of dice several times and record the resulting values (constrained to being between and 2 and 12), counting the number of times any given value occurs (the frequency of that value occurring), and take these all together to form a frequency distribution
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Frequency & DistributionFrequencies can be absolute (when the frequency provided is the actual count of the occurrences) or relative (when they are normalized by dividing the absolute frequency by the total number of observations [0, 1])Relative frequencies are particularly useful if you want to compare distributions drawn from two different sources (i.e. while the numbers of observations of each source may be different)
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HistogramsWe may summarize our data by constructing histograms, which are vertical bar graphsA histogram is used to graphically summarize the distribution of a data setA histogram divides the range of values in a data set into intervalsOver each interval is placed a bar whose height represents the frequency of data values in the interval.
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Building a HistogramTo construct a histogram, the data are first grouped into categoriesThe histogram contains one vertical bar for each categoryThe height of the bar represents the number of observations in the category (i.e., frequency)It is common to note the midpoint of the category on the horizontal axis
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Building a Histogram Example1. Develop an ungrouped frequency tableThat is, we build a table that counts the number of occurrences of each variable value from lowest to highest:TMI ValueUngrouped Freq. 4.162 4.174 4.180 13.711We could attempt to construct a bar chart from this table, but it would have too many bars to really be useful
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Building a Histogram Example2. Construct a grouped frequency table Select an appropriate number of classes Percentage
tmi histograms
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 4
tmi histograms
0.4686767693
14.6070926418
33.6197469145
25.4647711295
11.6388064365
5.8897047336
3.171379472
1.9528198719
1.2029370411
1.0935791283
0.624902359
0.2343383846
0.031245118
GLYNDON
Topographic Moisture Index
Percent of cells in catchment
Glyndon TMI Histogram
tmi data
4.0458530007
27.2083614295
47.5724881996
13.7221847606
2.9332434255
1.1126095752
0.5731625084
0.7417397168
1.4497639919
0.6405933918
0
0
0
POND BRANCH
Topographic Moisture Index
Percent of cells in catchment
Pond Branch TMI Histogram
GLYNDONPOND BRANCH4GLYNDONPOND BRANCHTMI
43012050.46867676934.04585300074Sums from 5-8
5935807614.607092641827.2083614295585.330417122391.4362778152
621521411733.619746914547.57248819966
71630407825.464771129513.72218476067
874587911.63880643652.93324342558
937733Labels ->105.88970473361.11260957529
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Building a Histogram Example3. Plot the frequencies of each classAll that remains is to create the bar graphA proxy for Soil Moisture
Chart2
4.0458530007
27.2083614295
47.5724881996
13.7221847606
2.9332434255
1.1126095752
0.5731625084
0.7417397168
1.4497639919
0.6405933918
0
0
0
POND BRANCH
Topographic Moisture Index
Percent of cells in catchment
Pond Branch TMI Histogram
Figure 4
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 4
Figure 4
13.0322102925
31.4821670986
27.878563495
15.9570529434
6.1458718993
2.8878193262
1.3945452302
0.6540787363
0.320868814
0.2097988399
0.0370233247
0
0
0
0
0
0
0
0
0
0
0
GLYNDON
Slope in degrees
Percent of cells in catchment
Glyndon Slope Histogram
Figure 5
0.9313464609
5.3485896754
8.9941458222
13.7307078233
12.666311868
11.2293773284
8.6216072379
7.4507716871
6.2001064396
5.5082490687
4.7099521022
2.6343799894
2.6343799894
1.9425226184
1.4635444385
1.7030335285
1.3038850452
1.0111761575
0.9845662586
0.3991484832
0.2927088877
0.2394890899
POND BRANCH
Slope in degrees
Percent of cells in catchment
Pond Branch Slope Histogram
Figure 7
A
B
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 5
Figure 7
0.4686767693
14.6070926418
33.6197469145
25.4647711295
11.6388064365
5.8897047336
3.171379472
1.9528198719
1.2029370411
1.0935791283
0.624902359
0.2343383846
0.031245118
GLYNDON
Topographic Moisture Index
Percent of cells in catchment
Glyndon TMI Histogram
Figure 10
4.0458530007
27.2083614295
47.5724881996
13.7221847606
2.9332434255
1.1126095752
0.5731625084
0.7417397168
1.4497639919
0.6405933918
0
0
0
POND BRANCH
Topographic Moisture Index
Percent of cells in catchment
Pond Branch TMI Histogram
Figure 11
A
B
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 7
Figure 11
0.453581529137288-0.508
37289372890
37290372900
3729137291-0.254
37292372920
37293372930
3729437294-2.54
0.4296432442372950
37296372960
3729737297-0.762
3729837298-1.016
372990.32514472290
37300373000
37301373010
0.4048605132373020
37303373030
37304373040
37305373050
37306373060
3730737307-0.254
373080.3168748414-0.254
0.3905513808373090
37310373100
37311373110
37312373120
3731337313-2.032
37314373140
373150.31012270060
0.3720305873373160
3731737317-18.288
3731837318-7.874
37319373190
37320373200
37321373210
373220.33385069610
0.4141677978373230
3732437324-2.286
3732537325-3.556
37326373260
3732737327-1.524
3732837328-9.652
37329373290
373300.32719585970
3733137331-0.508
3733237332-3.81
3733337333-9.906
3733437334-1.016
3733537335-23.622
37336373360
37337373370
37338373380
37339373390
37340373400
3734137341-13.97
37342373420
37343373430
0.45003085010.3330019860
37345373450
3734637346-5.08
37347373470
37348373480
3734937349-1.016
0.4391274660.32229244490
37351373510
37352373520
37353373530
37354373540
3735537355-3.556
3735637356-0.254
0.40961860170.3269122820
37358373580
37359373590
3736037360-4.064
3736137361-3.81
37362373620
0.4101304315373630
373640.294772987-13.208
3736537365-7.112
37366373660
3736737367-5.08
3736837368-3.048
37369373690
373700.32653323770
0.436022790437371-3.048
37372373720
3737337373-3.556
3737437374-33.274
37375373750
37376373760
37377373770
3737837378-31.75
373790.354065625-0.254
37380373800
37381373810
37382373820
3738337383-2.032
373840.3130474222-0.254
0.413932493237385-2.794
37386373860
37387373870
3738837388-4.064
3738937389-2.286
373900.30799418540
37391373910
0.3575455722373920
3739337393-5.334
3739437394-22.352
37395373950
373960.3332398710
0.3956857077373970
37398373980
37399373990
37400374000
37401374010
3740237402-9.652
3740337403-9.144
3740437404-0.762
0.4589895962374050
374060.33308279790
3740737407-1.016
37408374080
37409374090
37410374100
3741137411-0.762
3741237412-0.762
0.348986752537413-14.224
374140.3081213146-0.508
3741537415-0.254
37416374160
37417374170
37418374180
0.31435491510.23536620750
3742037420-24.384
3742137421-7.874
3742237422-2.032
37423374230
37424374240
37425374250
0.35493156380.2751649934-0.254
37427374270
37428374280
37429374290
37430374300
37431374310
37432374320
374330.21558350180
3743437434-0.508
0.248990273237435-4.064
37436374360
37437374370
37438374380
37439374390
3744037440-1.016
37441374410
37442374420
37443374430
37444374440
37445374450
3744637446-18.796
3744737447-1.016
0.25236035120.19509432320
3744937449-0.762
3745037450-1.27
3745137451-5.588
3745237452-0.254
37453374530
37454374540
37455374550
0.1852237878374560
37457374570
37458374580
37459374590
37460374600
374610.16475377110
37462374620
3746337463-0.254
3746437464-0.762
3746537465-0.254
37466374660
3746737467-0.254
37468374680
0.1674229225374690
37470374700
3747137471-0.508
37472374720
3747337473-0.254
3747437474-0.254
37475374750
37476374760
37477374770
37478374780
37479374790
37480374800
37481374810
37482374820
0.11757869620.11437196540
37484374840
37485374850
37486374860
37487374870
3748837488-2.794
37489374890
0.09348823280.10325055660
Glyndon
Pond Branch
Precipitation
Date
Vol. Soil Moisture (V/V)
Daily Precipitation (mm)
Precipitation and Soil Moisture for Glyndon and Pond Branch
Figure 11 B&W
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 10
Figure 11 B&W
0.1700648773
0.2682576671
0.2354975246
0.255470977
0.1994583674
0.1808739293
0.1651498143
0.266659151
0.3140898906
0.2604796819
0.4212195635
0.1970835764
0.1791690566
0.1830981635
0.3267551206
0.2383627445
0.1091661714
0.2963985361
0.3298895679
0.2414922416
0.2014687732
0.2850605853
0.2732474044
0.4582524657
TI_5M11X11
TMI
Vol. Soil Moisture (V/V)
Glyndon - 6/28/02 - Average
Figure 12
0.2613054641
0.2283643391
0.3568147719
0.3413809061
0.4911210224
0.3508575037
0.3353383832
0.3476247683
0.3254518523
0.4124278769
0.412856096
0.2674577568
0.3268586919
0.3249692209
0.4835668549
0.2805328459
0.2755795367
0.2555248052
0.2505404644
TI11_25MBC
TMI
Vol. Soil Moisture (V/V)
Pond Branch - 5/30/02 - Wet
Figure 12 B&W
0.4789539248
0.5032712206
0.4271053612
0.5225900397
0.3918205813
0.4424781695
0.4058920562
0.4924496114
0.4792959279
0.4273171097
0.5444826573
0.4413049519
4.5178
0.4438069925
0.4712376267
0.443393971
0.3787522018
0.4624769136
0.4265989423
0.3951214084
0.4310236514
0.4728094161
0.4879961759
0.5541911483
TI_5M11X11
TMI
Vol. Soil Moisture (V/V)
Glyndon - 5/29/02 - Wet
Figure 13
0.0843882855
0.1238871448
0.139086052
0.0996634813
0.0399461064
0.0344541099
0.0519015339
0.0988067488
0.0977560295
0.1182629887
0.1221882518
0.0985545889
0.1122413933
0.1005489536
0.1612017266
0.113050399
0.0338656924
0.0724866561
0.1139788757
0.0942433896
0.0825330896
0.0966592389
0.1031153381
0.0713881564
TI_5M11X11
TMI
Vol. Soil Moisture (V/V)
Glyndon - 8/22/02 - Dry
Figure 14
0.0848772375
0.0560429396
0.0961976767
0.1092117647
0.2587091647
0.0822539918
0.0765071308
0.0799957765
0.0931815188
0.1219747975
0.1175129656
0.0656942884
0.0943358051
0.1310419414
0.2499156371
0.0606326485
0.0658768939
0.0622260727
0.0555723249
TI11_25MBC
TMI
Vol. Soil Moisture (V/V)
Pond Branch - 8/22/02 - Dry
Table 3
0.1696285535
0.1333770912
0.208378388
0.2304897197
0.4113935702
0.2151356079
0.1853029955
0.1984734654
0.2083240472
0.2765943892
0.2715640701
0.1409898361
0.1917807318
0.2400992386
0.447427664
0.1757179469
0.148657329
0.124966085
0.1177858058
TI11_25MBC
TMI
Vol. Soil Moisture (V/V)
Pond Branch - 6/26/02 - Average
Table 4
A
C
E
B
D
F
R2=0.80
R2=0.56
R2=0.70
R2=0.32
R2=0.79
R2=0.10
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 11
Table 4
-0.1024379375-0.2160221966-0.0543228069
0.07757012890.04510843970.0093962149
0.23705226620.15886373960.2620404908
0.1439040319-0.05216531650.2472369546
0.1653479620.0439585708-0.1410250658
0.38682689510.41728994960.0531833091
0.44621406140.22555739770.1514155609
0.55786788990.39819764630.2553783694
0.43850450870.26330716520.1824126146
0.31031106550.3813532960.0342729953
0.32738201240.30970766540.0580947426
0.50150666560.40798590490.1204325705
0.28342419440.42356992250.0862434481
0.34654676160.45597859320.0364918205
0.29719810220.43129818710.0949391458
0.46905476560.47521430.231579944
0.36823733030.28516044330.1862537582
0.16426753560.32943434820.2900077292
0.30078930060.35813457260.0046558987
0.37681428660.34267163480.322884948
0.45893398410.33133983720.0836073498
0.22650841830.40300337050.360267807
0.19935926340.13186101610.1542420728
0.36898720470.50391095110.2887440151
0.24588870340.28511296150.3282030343
0.19444556670.33854944730.1421956515
0.17500634010.25021598220.107905892
0.35457808540.4047687480.3652163721
0.34025162090.38750483620.3454964118
0.31067542240.35797731080.3475213247
05/29/02
06/28/02
08/22/02
Cell Size (metres)
Correlation (r)
Glyndon LIDAR Soil Moisture Correlation vs. Cell Size
Glyndon
0.15303328190.01863639890.0040534288
0.02936735950.02450190450.0111707009
0.0700499192-0.0722304896-0.159977168
0.1577176719-0.0019021137-0.1107502887
-0.00923399-0.1707202837-0.2589824219
0.1496041486-0.0550307926-0.1591352969
0.39577301820.37454388750.2744496813
0.60482613520.58014757480.4667000035
0.77554603640.80777917430.7459113002
0.72795970350.77718074090.7747496436
0.76167999410.81495486090.8048385805
0.67741549870.73681428120.760322476
0.79101395470.82870810560.8015121537
0.81676636880.87042780690.8480400679
0.70642659520.76466115840.7763336438
0.69521223290.75039321410.7651085917
0.6312730310.72136162170.7647748595
0.77463922040.78439426010.7661207592
0.74988233510.82412654110.8340093499
0.67741549870.73681428120.760322476
0.78439264710.80585185240.7679393973
0.62919699310.67509597340.6336546609
0.74827868310.78803396330.7577743198
0.67759704650.67919483830.5986783319
0.61872057410.6213870960.6382774024
0.56661935980.61647139720.5748149557
0.68668931940.78099884030.814016656
0.2996667210.43013088660.4090231883
0.66047200570.70747689860.7430788469
0.64891631930.70513374520.6936879796
05/30/02
06/26/02
08/22/02
Cell Size (metres)
Correlation (r)
Pond Branch LIDAR Soil Moisture Correlation vs. Cell Size
Pond Branch
0.12280286650.0256000639-0.0421502605
0.15030492970.0385098044-0.0421844281
0.26759273650.16558009150.070838412
0.40528195020.31265674480.1859216782
0.30148217430.17842179360.0382759582
0.3208649910.19526288160.0401724184
0.4381688260.32331500170.1823647696
0.35529308990.18764694580.0263208671
0.69498112110.64468434490.5748129837
0.64641101610.53722508260.3910439305
0.76210732510.67085638390.6320354855
0.69414128520.70798319080.7066984773
0.77048254810.80057395350.7942315597
0.81166740670.83728193080.8314499049
0.83611328090.88863545760.8914110115
0.79688065210.83880933440.8083249116
0.71355623240.81210847740.8291896077
0.78747038560.83246069670.8166077293
0.69214188890.74441260150.7464967385
0.78705453470.83613259380.8150567969
0.78260794420.8315567480.8190939562
0.67178524920.72882495230.6720341625
0.72651497880.79746446820.7987558448
0.49183739510.53561235510.4732244469
0.46082400750.5218250920.4801683834
0.67009553620.72621276610.7473345536
0.52749599180.59034937570.5791999178
0.80258702620.82422503110.8040278669
0.70125018510.73176065610.7346651911
0.51078538760.55433076020.5009682741
05/30/02
06/26/02
08/22/02
Cell Size (metres)
Correlation (r)
Pond Branch PG Soil Moisture Correlation vs. Cell Size
stddev data
0.39709082190.34407665250.1012227343
0.4535889540.17106740330.0254288542
0.36278942490.26003908620.3687878906
0.26184728230.21396220340.1861053717
0.49401025830.35175827890.1009992125
0.48694983660.33176792950.070354804
0.48322810090.46183196440.1675110938
0.25059933370.42008464510.4630456879
0.19718367570.32672893990.3713272076
0.12615175010.22642445110.1717379243
0.29202232030.43244102770.28340716
0.23329188440.40113229610.28618954
0.28755382010.28529639280.2814087832
0.15585399650.39483273830.2507498503
0.34385150060.31945401160.2100610532
0.29171104620.47401370480.5650532243
0.50697987760.19847848830.2496879062
0.21188933380.35588300240.1542779164
0.41550438560.37216130920.5002139878
0.31084601450.47088663310.3883234783
0.28881809790.35665409630.5311163703
0.30853415280.3494515050.3316548049
0.2900754370.3706484090.5636261014
0.31221043460.4447498670.3456178454
0.35998832990.35032336810.5740371023
0.23530758460.14827266070.4187977223
0.32160108230.42366426760.4524246872
0.07128553790.35878081850.3046309103
0.29288231440.25770634540.4737547215
0.26386987360.21522489490.4565309965
05/29/02
06/28/02
08/22/02
Cell Size (metres)
Correlation (r)
Glyndon PG Soil Moisture Correlation vs. Cell Size
plot data
A
B
C
D
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 11
plot data
-0.1024379375-0.2160221966-0.0543228069
0.07757012890.04510843970.0093962149
0.23705226620.15886373960.2620404908
0.1439040319-0.05216531650.2472369546
0.1653479620.0439585708-0.1410250658
0.38682689510.41728994960.0531833091
0.44621406140.22555739770.1514155609
0.55786788990.39819764630.2553783694
0.43850450870.26330716520.1824126146
0.31031106550.3813532960.0342729953
0.32738201240.30970766540.0580947426
0.50150666560.40798590490.1204325705
0.28342419440.42356992250.0862434481
0.34654676160.45597859320.0364918205
0.29719810220.43129818710.0949391458
0.46905476560.47521430.231579944
0.36823733030.28516044330.1862537582
0.16426753560.32943434820.2900077292
0.30078930060.35813457260.0046558987
0.37681428660.34267163480.322884948
0.45893398410.33133983720.0836073498
0.22650841830.40300337050.360267807
0.19935926340.13186101610.1542420728
0.36898720470.50391095110.2887440151
0.24588870340.28511296150.3282030343
0.19444556670.33854944730.1421956515
0.17500634010.25021598220.107905892
0.35457808540.4047687480.3652163721
0.34025162090.38750483620.3454964118
0.31067542240.35797731080.3475213247
05/29/02
06/28/02
08/22/02
Cell Size (metres)
Correlation (r)
Glyndon LIDAR Soil Moisture Correlation vs. Cell Size
gl 0.5x11 LI
0.15303328190.01863639890.0040534288
0.02936735950.02450190450.0111707009
0.0700499192-0.0722304896-0.159977168
0.1577176719-0.0019021137-0.1107502887
-0.00923399-0.1707202837-0.2589824219
0.1496041486-0.0550307926-0.1591352969
0.39577301820.37454388750.2744496813
0.60482613520.58014757480.4667000035
0.77554603640.80777917430.7459113002
0.72795970350.77718074090.7747496436
0.76167999410.81495486090.8048385805
0.67741549870.73681428120.760322476
0.79101395470.82870810560.8015121537
0.81676636880.87042780690.8480400679
0.70642659520.76466115840.7763336438
0.69521223290.75039321410.7651085917
0.6312730310.72136162170.7647748595
0.77463922040.78439426010.7661207592
0.74988233510.82412654110.8340093499
0.67741549870.73681428120.760322476
0.78439264710.80585185240.7679393973
0.62919699310.67509597340.6336546609
0.74827868310.78803396330.7577743198
0.67759704650.67919483830.5986783319
0.61872057410.6213870960.6382774024
0.56661935980.61647139720.5748149557
0.68668931940.78099884030.814016656
0.2996667210.43013088660.4090231883
0.66047200570.70747689860.7430788469
0.64891631930.70513374520.6936879796
05/30/02
06/26/02
08/22/02
Cell Size (metres)
Correlation (r)
Pond Branch LIDAR Soil Moisture Correlation vs. Cell Size
pb 11.25 PG
0.12280286650.0256000639-0.0421502605
0.15030492970.0385098044-0.0421844281
0.26759273650.16558009150.070838412
0.40528195020.31265674480.1859216782
0.30148217430.17842179360.0382759582
0.3208649910.19526288160.0401724184
0.4381688260.32331500170.1823647696
0.35529308990.18764694580.0263208671
0.69498112110.64468434490.5748129837
0.64641101610.53722508260.3910439305
0.76210732510.67085638390.6320354855
0.69414128520.70798319080.7066984773
0.77048254810.80057395350.7942315597
0.81166740670.83728193080.8314499049
0.83611328090.88863545760.8914110115
0.79688065210.83880933440.8083249116
0.71355623240.81210847740.8291896077
0.78747038560.83246069670.8166077293
0.69214188890.74441260150.7464967385
0.78705453470.83613259380.8150567969
0.78260794420.8315567480.8190939562
0.67178524920.72882495230.6720341625
0.72651497880.79746446820.7987558448
0.49183739510.53561235510.4732244469
0.46082400750.5218250920.4801683834
0.67009553620.72621276610.7473345536
0.52749599180.59034937570.5791999178
0.80258702620.82422503110.8040278669
0.70125018510.73176065610.7346651911
0.51078538760.55433076020.5009682741
05/30/02
06/26/02
08/22/02
Cell Size (metres)
Correlation (r)
Pond Branch PG Soil Moisture Correlation vs. Cell Size
wet
0.39709082190.34407665250.1012227343
0.4535889540.17106740330.0254288542
0.36278942490.26003908620.3687878906
0.26184728230.21396220340.1861053717
0.49401025830.35175827890.1009992125
0.48694983660.33176792950.070354804
0.48322810090.46183196440.1675110938
0.25059933370.42008464510.4630456879
0.19718367570.32672893990.3713272076
0.12615175010.22642445110.1717379243
0.29202232030.43244102770.28340716
0.23329188440.40113229610.28618954
0.28755382010.28529639280.2814087832
0.15585399650.39483273830.2507498503
0.34385150060.31945401160.2100610532
0.29171104620.47401370480.5650532243
0.50697987760.19847848830.2496879062
0.21188933380.35588300240.1542779164
0.41550438560.37216130920.5002139878
0.31084601450.47088663310.3883234783
0.28881809790.35665409630.5311163703
0.30853415280.3494515050.3316548049
0.2900754370.3706484090.5636261014
0.31221043460.4447498670.3456178454
0.35998832990.35032336810.5740371023
0.23530758460.14827266070.4187977223
0.32160108230.42366426760.4524246872
0.07128553790.35878081850.3046309103
0.29288231440.25770634540.4737547215
0.26386987360.21522489490.4565309965
05/29/02
06/28/02
08/22/02
Cell Size (metres)
Correlation (r)
Glyndon PG TMI-Soil Moisture Correlation vs. Cell Size
avg
A
B
C
D
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 12
avg
-0.1024379375-0.2160221966-0.0543228069
0.0338397515-0.05850078080.319923907
0.43692196290.29548054320.4154837123
0.52596215680.34068674580.2737285493
0.5983532740.374628190.2551553211
0.74670017720.56968389330.3238456809
0.75060121880.52906665430.281300497
0.73015777190.47085631230.1772287592
0.68540820030.40524442870.1062366012
0.65923356890.37109198010.0841178066
0.62565186310.33542334650.0859838822
0.61981229020.31555316470.0967391499
0.64075350530.33375191490.1073207311
0.68425264010.38868034110.1589812855
0.70016253010.41141729020.1831203203
0.69550347990.3982364340.1932290598
0.68116656260.39721228720.2076995394
0.64454318970.37069825280.1932199563
0.65014487760.36892722290.2205284349
0.630511180.36731969390.2137869094
0.61107472030.36018290460.2007474377
05/29/02
06/28/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Glyndon 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size
dry
0.15303328190.01863639890.0040534288
-0.0965837793-0.2050147854-0.2182026987
-0.1532202509-0.2321189388-0.2153695699
-0.1815675472-0.2322967953-0.2078278531
-0.2665210579-0.326869259-0.316524123
-0.2823789106-0.3691327028-0.3711084241
-0.2708117901-0.3733514484-0.3882179648
-0.2453946662-0.3520972494-0.3829730683
-0.2269786135-0.3382085716-0.3838637478
-0.2133463045-0.3300768347-0.3891987144
-0.2101504093-0.3279808647-0.3909324714
-0.1944041063-0.3034338274-0.3606472212
-0.1914021328-0.3027103713-0.3567281456
-0.1951607647-0.3051783585-0.3552818813
-0.2138851495-0.3286063632-0.3787489433
-0.2153365257-0.3312964789-0.3810092781
-0.2043957306-0.3259897295-0.3734538384
-0.195480557-0.3212342677-0.3623079767
-0.1814397097-0.3085447109-0.3450053207
-0.1632199963-0.2908219336-0.3246253028
-0.1609507981-0.2880864537-0.3197856783
05/30/02
06/26/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Pond Branch 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size
cell data
0.45538263050.29940646540.0775390196
0.46908013240.32513847160.0910106979
0.47211684940.34845700150.0514353184
0.48845918780.36955391730.0495688035
0.47256826130.36440043350.0219560432
0.47341585130.36498885510.0179630401
0.4667123690.35191048940.0076011949
0.46777219310.34669451040.0050178962
0.46878080760.33950483610.013069383
0.46646240990.32887582330.0061908858
0.46799826170.326856663-0.0038254923
0.48488334010.3416513036-0.0071789082
0.4950741140.3440935549-0.0096191056
0.5038462740.3456192671-0.0135616413
0.50932844730.3473335119-0.022181752
0.51184668820.3468934012-0.0324663067
0.51281692710.3459100843-0.0421904349
0.5143664420.3487428925-0.048350148
0.51660427460.3525015936-0.0557416852
0.51474810220.3565538181-0.0599981061
0.51844394090.3596777103-0.0578695131
05/29/02
06/28/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Glyndon 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size
kernel data
0.12280286650.0256000639-0.0421502605
0.1351085680.0319896557-0.0419767203
0.15842509140.0464872485-0.0361184013
0.18722893640.0667423795-0.0255512852
0.21648363540.0898850721-0.0123252387
0.27030068510.13753744870.0280686388
0.33205697120.19601926910.0839381493
0.38343185020.24793782030.1356344582
0.42810255020.29378210020.1807041203
0.45910931250.32647293610.2107002761
0.46213584620.33064605030.2071411506
0.46926279250.33940953820.2103217556
0.47930129930.35093581010.2178636308
0.49832109880.37138241920.2361727583
0.51594718820.39047815480.2535398048
0.53277576250.40887324930.2708362119
0.55083417230.42916653970.2906202614
0.57110895010.45461268170.316711861
0.58836310710.47991430070.3437822993
0.60808882520.50418318750.3676406201
0.62594004710.52399154840.3864090095
05/30/02
06/26/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Pond Branch 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size
avgtheta data
A
B
C
D
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 12
avgtheta data
-0.1024379375-0.2160221966-0.0543228069
0.0338397515-0.05850078080.319923907
0.43692196290.29548054320.4154837123
0.52596215680.34068674580.2737285493
0.5983532740.374628190.2551553211
0.74670017720.56968389330.3238456809
0.75060121880.52906665430.281300497
0.73015777190.47085631230.1772287592
0.68540820030.40524442870.1062366012
0.65923356890.37109198010.0841178066
0.62565186310.33542334650.0859838822
0.61981229020.31555316470.0967391499
0.64075350530.33375191490.1073207311
0.68425264010.38868034110.1589812855
0.70016253010.41141729020.1831203203
0.69550347990.3982364340.1932290598
0.68116656260.39721228720.2076995394
0.64454318970.37069825280.1932199563
0.65014487760.36892722290.2205284349
0.630511180.36731969390.2137869094
0.61107472030.36018290460.2007474377
05/29/02
06/28/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Glyndon 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size
slope data
0.15303328190.01863639890.0040534288
-0.0965837793-0.2050147854-0.2182026987
-0.1532202509-0.2321189388-0.2153695699
-0.1815675472-0.2322967953-0.2078278531
-0.2665210579-0.326869259-0.316524123
-0.2823789106-0.3691327028-0.3711084241
-0.2708117901-0.3733514484-0.3882179648
-0.2453946662-0.3520972494-0.3829730683
-0.2269786135-0.3382085716-0.3838637478
-0.2133463045-0.3300768347-0.3891987144
-0.2101504093-0.3279808647-0.3909324714
-0.1944041063-0.3034338274-0.3606472212
-0.1914021328-0.3027103713-0.3567281456
-0.1951607647-0.3051783585-0.3552818813
-0.2138851495-0.3286063632-0.3787489433
-0.2153365257-0.3312964789-0.3810092781
-0.2043957306-0.3259897295-0.3734538384
-0.195480557-0.3212342677-0.3623079767
-0.1814397097-0.3085447109-0.3450053207
-0.1632199963-0.2908219336-0.3246253028
-0.1609507981-0.2880864537-0.3197856783
05/30/02
06/26/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Pond Branch 0.5m LIDAR TMI-Soil Moisture Correlation vs. Kernel Size
tmi data
0.45538263050.29940646540.0775390196
0.46908013240.32513847160.0910106979
0.47211684940.34845700150.0514353184
0.48845918780.36955391730.0495688035
0.47256826130.36440043350.0219560432
0.47341585130.36498885510.0179630401
0.4667123690.35191048940.0076011949
0.46777219310.34669451040.0050178962
0.46878080760.33950483610.013069383
0.46646240990.32887582330.0061908858
0.46799826170.326856663-0.0038254923
0.48488334010.3416513036-0.0071789082
0.4950741140.3440935549-0.0096191056
0.5038462740.3456192671-0.0135616413
0.50932844730.3473335119-0.022181752
0.51184668820.3468934012-0.0324663067
0.51281692710.3459100843-0.0421904349
0.5143664420.3487428925-0.048350148
0.51660427460.3525015936-0.0557416852
0.51474810220.3565538181-0.0599981061
0.51844394090.3596777103-0.0578695131
05/29/02
06/28/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Glyndon 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size
0.12280286650.0256000639-0.0421502605
0.1351085680.0319896557-0.0419767203
0.15842509140.0464872485-0.0361184013
0.18722893640.0667423795-0.0255512852
0.21648363540.0898850721-0.0123252387
0.27030068510.13753744870.0280686388
0.33205697120.19601926910.0839381493
0.38343185020.24793782030.1356344582
0.42810255020.29378210020.1807041203
0.45910931250.32647293610.2107002761
0.46213584620.33064605030.2071411506
0.46926279250.33940953820.2103217556
0.47930129930.35093581010.2178636308
0.49832109880.37138241920.2361727583
0.51594718820.39047815480.2535398048
0.53277576250.40887324930.2708362119
0.55083417230.42916653970.2906202614
0.57110895010.45461268170.316711861
0.58836310710.47991430070.3437822993
0.60808882520.50418318750.3676406201
0.62594004710.52399154840.3864090095
05/30/02
06/26/02
08/22/02
Kernel Size (Cells)
Correlation (r)
Pond Branch 0.5m PG TMI-Soil Moisture Correlation vs. Kernel Size
A
B
C
D
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 13
1
1.9322521739
2.1180173913
2.0543086957
2.0322782609
2.1807826087
2.2163565217
2.1955652174
2.1744565217
2.1543608696
2.1440086957
2.1320652174
2.1377391304
2.1195173913
2.1011913043
2.0944217391
2.0898217391
2.0875913043
2.0844391304
2.0828043478
2.0803130435
Kernel Size (Cells)
Standard Deviation
Glyndon 0.5m LIDAR TMI Standard Deviation vs. Kernel Size
1
1.3228684211
1.5641631579
1.7131052632
1.8493473684
1.9248210526
1.9403789474
1.9437421053
1.9456
1.9498894737
1.9486157895
1.9710368421
1.9757421053
1.9829105263
1.9906473684
2.0032947368
2.0136368421
2.0313473684
2.0400736842
2.0605947368
2.0637578947
Kernel Size (Cells)
Standard Deviation
Pond Branch 0.5m LIDAR TMI Standard Deviation vs. Kernel Size
1
0.3719291667
0.7546458333
1.0493833333
1.1689375
1.2235375
1.3186583333
1.3491333333
1.4271791667
1.4426208333
1.4424916667
1.485575
1.4920291667
1.5097125
1.533375
1.548275
1.55745
1.5737583333
1.5906541667
1.6123208333
1.6187333333
Kernel Size (Cells)
Standard Deviation
Glyndon 0.5m PG TMI Standard Deviation vs. Kernel Size
1
0.1313052632
0.2036263158
0.2656473684
0.3632
0.5132368421
0.6201210526
0.6898315789
0.7465684211
0.7907210526
0.8258263158
0.8633421053
0.8918105263
0.9094578947
0.9230315789
0.9354842105
0.9505
0.9790526316
1.0258210526
1.0489526316
1.0664263158
Kernel Size (Cells)
Standard Deviation
Pond Branch 0.5m PG TMI Standard Deviation vs. Kernel Size
A
B
C
D
&L&"Times New Roman,Regular"&12D.E. TenenbaumFigure 14
0.60339546
0.7021852693
0.7285011829
0.6481694061
0.5550706732
0.6571506574
0.7499584573
0.7106245095
0.6802068873
0.6905600069
0.6753971465
0.687752858
0.5755608767
0.5701249137
0.7467001772
0.5621786709
0.5242210489
0.4409197429
0.5696838933
0.3499347867
0.3270030327
0.3903975193
0.2723545608
0.3238456809
TMI-Theta Corr.
Average Volumetric Soil Moisture (V/V)
Correlation (r)
Glyndon Average Soil Moisture vs. Soil Moisture-TMI Correlation (derived from Soil Moisture vs. TMI from 0.5m LIDAR, 11x11 Kernel)
Date
2/1/020.36
2/8/020.49
2/15/020.53
2/22/020.42
3/1/020.31
3/8/020.43
3/29/020.56
4/4/020.50
4/11/020.46
4/17/020.48
4/25/020.46
5/9/020.47
5/16/020.33
5/21/020.33
5/29/020.56
6/6/020.32
6/12/020.27
6/19/020.19
6/28/020.32
7/11/020.12
7/19/020.11
8/1/020.15
8/15/020.07
8/22/020.10
R2=0.83
TMI-Theta Corr.
Average Volumetric Soil Moisture (V/V)
Correlation (r)
Pond Branch Average Soil Moisture vs Soil Moisture-TMI Correlation (derived from Soil Moisture vs. TMI from 11.25m Photogrammetric)
0.3251447229
0.3168748414
0.3101227006
0.3338506961
0.3271958597
0.333001986
0.3222924449
0.326912282
0.294772987
0.3265332377
0.354065625
0.3130474222
0.3079941854
0.333239871
0.3330827979
0.3081213146
0.2353662075
0.2751649934
0.2155835018
0.1950943232
0.1647537711
0.1143719654
0.1032505566
0.8662238591
0.8437180938
0.8514558261
0.9327887143
0.7712995775
0.8626652593
0.8703667662
0.8854485582
0.8728218142
0.8479346718
0.6522067235
0.8801345494
0.7811441848
0.8417075744
0.8361132809
0.8164506496
0.8407099111
0.8612792532
0.8886354576
0.8644705299
0.8935161775
0.9105822734
0.8914110115
R2=0.18
A
B
&L&"Times New Roman,Regular"&12D.E. TenenbaumTable 2
Date
2/12/020.75
2/21/020.71
2/28/020.72
3/7/020.87
3/15/020.59
3/29/020.74
4/4/020.76
4/11/020.78
4/18/020.76
4/24/020.72
5/3/020.43
5/8/020.77
5/14/020.61
5/20/020.71
5/30/020.70
6/7/020.67
6/12/020.71
6/19/020.74
6/26/020.79
7/11/020.75
7/24/020.80
8/15/020.83
8/22/020.79
&L&"Times New Roman,Regular"&12D.E. TenenbaumTable 3
13.0322102925
31.4821670986
27.878563495
15.9570529434
6.1458718993
2.8878193262
1.3945452302
0.6540787363
0.320868814
0.2097988399
0.0370233247
0
0
0
0
0
0
0
0
0
0
0
GLYNDON
Slope in degrees
Percentage of all grid cells in catchment
Glyndon Slope Histogram
0.9313464609
5.3485896754
8.9941458222
13.7307078233
12.666311868
11.2293773284
8.6216072379
7.4507716871
6.2001064396
5.5082490687
4.7099521022
2.6343799894
2.6343799894
1.9425226184
1.4635444385
1.7030335285
1.3038850452
1.0111761575
0.9845662586
0.3991484832
0.2927088877
0.2394890899
POND BRANCH
Slope in degrees
Percentage of all grid cells in catchment
Pond Branch Slope Histogram
GLLIPBLIGLPGPBPG
Kernel Size (cells)
1
31.93225217391.32286842110.37192916670.1313052632
52.11801739131.56416315790.75464583330.2036263158
72.05430869571.71310526321.04938333330.2656473684
92.03227826091.84934736841.16893750.3632
112.18078260871.92482105261.22353750.5132368421
132.21635652171.94037894741.31865833330.6201210526
152.19556521741.94374210531.34913333330.6898315789
172.17445652171.94561.42717916670.7465684211
192.15436086961.94988947371.44262083330.7907210526
212.14400869571.94861578951.44249166670.8258263158
232.13206521741.97103684211.4855750.8633421053
252.13773913041.97574210531.49202916670.8918105263
272.11951739131.98291052631.50971250.9094578947
292.10119130431.99064736841.5333750.9230315789
312.09442173912.00329473681.5482750.9354842105
332.08982173912.01363684211.557450.9505
352.08759130432.03134736841.57375833330.9790526316
372.08443913042.04007368421.59065416671.0258210526
392.08280434782.06059473681.61232083331.0489526316
412.08031304352.06375789471.61873333331.0664263158
DateGlThetaPbThetaPrecip (mm)Precip (mm)Precip (inches)GlThetaPbTheta
2/1/020.4535815291-0.508-0.508-0.020.453582
2/2/020000.450162
2/3/020000.446742
2/4/02-0.254-0.254-0.010.443322
2/5/020000.439902
2/6/020000.436482
2/7/02-2.54-2.54-0.10.433063
2/8/020.42964324420000.429643
2/9/020000.426103
2/10/02-0.762-0.762-0.030.422563
2/11/02-1.016-1.016-0.040.419023
2/12/020.32514472290000.4154820.325145
2/13/020000.4119420.324226
2/14/020000.4084010.323307
2/15/020.40486051320000.4048610.322388
2/16/020000.4028170.321469
2/17/020000.4007730.32055
2/18/020000.3987290.319631
2/19/020000.3966850.318712
2/20/02-0.254-0.254-0.010.394640.317794
2/21/020.3168748414-0.254-0.254-0.010.3925950.316875
2/22/020.39055138080000.3905510.31591
2/23/020000.3879050.314945
2/24/020000.3852590.313981
2/25/020000.3826130.313017
2/26/02-2.032-2.032-0.080.3799680.312052
2/27/020000.3773220.311087
2/28/020.31012270060000.3746760.310123
3/1/020.37203058730000.3720310.313513
3/2/02-18.288-18.288-0.720.3780510.316903
3/3/02-7.874-7.874-0.310.3840710.320293
3/4/020000.390090.323682
3/5/020000.396110.327072
3/6/020000.4021290.330461
3/7/020.33385069610000.4081490.333851
3/8/020.41416779780000.4141680.333019
3/9/02-2.286-2.286-0.090.4158760.332187
3/10/02-3.556-3.556-0.140.4175840.331355
3/11/020000.4192920.330523
3/12/02-1.524-1.524-0.060.4210.329691
3/13/02-9.652-9.652-0.380.4227080.328859
3/14/020000.4244160.328028
3/15/020.32719585970000.4261240.327196
3/16/02-0.508-0.508-0.020.4278320.327611
3/17/02-3.81-3.81-0.150.429540.328026
3/18/02-9.906-9.906-0.390.4312480.328441
3/19/02-1.016-1.016-0.040.4329560.328856
3/20/02-23.622-23.622-0.930.4346630.329271
3/21/020000.4363710.329686
3/22/020000.4380790.3301
3/23/020000.4397860.330515
3/24/020000.4414930.330929
3/25/020000.4432010.331344
3/26/02-13.97-13.97-0.550.4449090.331759
3/27/020000.4466160.332173
3/28/020000.4483230.332588
3/29/020.45003085010.3330019860000.4500310.333002
3/30/020000.4482140.331217
3/31/02-5.08-5.08-0.20.4463970.329432
4/1/020000.444580.327647
4/2/020000.4427620.325862
4/3/02-1.016-1.016-0.040.4409440.324077
4/4/020.4391274660.32229244490000.4391270.322292
4/5/020000.4349120.322952
4/6/020000.4306970.323612
4/7/020000.4264810.324272
4/8/020000.4222660.324932
4/9/02-3.556-3.556-0.140.418050.325592
4/10/02-0.254-0.254-0.010.4138340.326252
4/11/020.40961860170.3269122820000.4096190.326912
4/12/020000.4097040.322321
4/13/020000.4097890.31773
4/14/02-4.064-4.064-0.160.4098740.313139
4/15/02-3.81-3.81-0.150.4099590.308547
4/16/020000.4100450.303956
4/17/020.41013043150000.410130.299365
4/18/020.294772987-13.208-13.208-0.520.4133670.294773
4/19/02-7.112-7.112-0.280.4166040.300066
4/20/020000.419840.305359
4/21/02-5.08-5.08-0.20.4230770.310653
4/22/02-3.048-3.048-0.120.4263140.315946
4/23/020000.429550.32124
4/24/020.32653323770000.4327860.326533
4/25/020.4360227904-3.048-3.048-0.120.4360230.329592
4/26/020000.4344450.332651
4/27/02-3.556-3.556-0.140.4328670.33571
4/28/02-33.274-33.274-1.310.4312890.338769
4/29/020000.4297110.341828
4/30/020000.4281330.344888
5/1/020000.4265550.347947
5/2/02-31.75-31.75-1.250.4249770.351007
5/3/020.354065625-0.254-0.254-0.010.4233990.354066
5/4/020000.4218210.345862
5/5/020000.4202430.337658
5/6/020000.4186650.329454
5/7/02-2.032-2.032-0.080.4170870.32125
5/8/020.3130474222-0.254-0.254-0.010.4155090.313047
5/9/020.4139324932-2.794-2.794-0.110.4139320.312205
5/10/020000.4058770.311363
5/11/020000.3978220.310521
5/12/02-4.064-4.064-0.160.3897670.309679
5/13/02-2.286-2.286-0.090.3817120.308836
5/14/020.30799418540000.3736570.307994
5/15/020000.3656020.312202
5/16/020.35754557220000.3575460.31641
5/17/02-5.334-5.334-0.210.3651740.320618
5/18/02-22.352-22.352-0.880.3728020.324825
5/19/020000.380430.329032
5/20/020.3332398710000.3880580.33324
5/21/020.39568570770000.3956860.333224
5/22/020000.4035990.333208
5/23/020000.4115120.333192
5/24/020000.4194250.333176
5/25/020000.4273380.333161
5/26/02-9.652-9.652-0.380.4352510.333145
5/27/02-9.144-9.144-0.360.4431640.33313
5/28/02-0.762-0.762-0.030.4510770.333114
5/29/020.45898959620000.458990.333099
5/30/020.33308279790000.445240.333083
5/31/02-1.016-1.016-0.040.431490.329963
6/1/020000.4177390.326843
6/2/020000.4039890.323723
6/3/020000.3902380.320603
6/4/02-0.762-0.762-0.030.3764880.317483
6/5/02-0.762-0.762-0.030.3627370.314362
6/6/020.3489867525-14.224-14.224-0.560.3489870.311241
6/7/020.3081213146-0.508-0.508-0.020.3432150.308121
6/8/02-0.254-0.254-0.010.3374430.29357
6/9/020000.3316710.279019
6/10/020000.3258990.264468
6/11/020000.3201270.249917
6/12/020.31435491510.23536620750000.3143550.235366
6/13/02-24.384-24.384-0.960.3201520.241052
6/14/02-7.874-7.874-0.310.3259490.246738
6/15/02-2.032-2.032-0.080.3317460.252423
6/16/020000.3375420.258109
6/17/020000.3433390.263794
6/18/020000.3491360.269479
6/19/020.35493156380.2751649934-0.254-0.254-0.010.3549320.275165
6/20/020000.3431610.266653
6/21/020000.331390.258141
6/22/020000.3196190.24963
6/23/020000.3078480.241118
6/24/020000.2960760.232607
6/25/020000.2843050.224096
6/26/020.21558350180000.2725330.215584
6/27/02-0.508-0.508-0.020.2607610.214218
6/28/020.2489902732-4.064-4.064-0.160.248990.212852
6/29/020000.2492490.211486
6/30/020000.2495080.21012
7/1/020000.2497670.208754
7/2/020000.2500260.207388
7/3/02-1.016-1.016-0.040.2502850.206022
7/4/020000.2505440.204656
7/5/020000.2508030.20329
7/6/020000.2510620.201924
7/7/020000.2513220.200558
7/8/020000.2515820.199192
7/9/02-18.796-18.796-0.740.2518410.197826
7/10/02-1.016-1.016-0.040.25210.19646
7/11/020.25236035120.19509432320000.252360.195094
7/12/02-0.762-0.762-0.030.2439680.19276
7/13/02-1.27-1.27-0.050.2355760.190426
7/14/02-5.588-5.588-0.220.2271840.188092
7/15/02-0.254-0.254-0.010.2187920.185758
7/16/020000.21040.183424
7/17/020000.2020080.18109
7/18/020000.1936160.178756
7/19/020.18522378780000.1852240.176422
7/20/020000.1838550.174088
7/21/020000.1824860.171755
7/22/020000.1811170.169421
7/23/020000.1797480.167088
7/24/020.16475377110000.1783790.164754
7/25/020000.177010.162464
7/26/02-0.254-0.254-0.010.175640.160174
7/27/02-0.762-0.762-0.030.174270.157884
7/28/02-0.254-0.254-0.010.1729010.155594
7/29/020000.1715320.153304
7/30/02-0.254-0.254-0.010.1701620.151014
7/31/020000.1687930.148724
8/1/020.16742292250000.1674230.146434
8/2/020000.1638630.144144
8/3/02-0.508-0.508-0.020.1603030.141854
8/4/020000.1567430.139564
8/5/02-0.254-0.254-0.010.1531830.137274
8/6/02-0.254-0.254-0.010.1496230.134984
8/7/020000.1460630.132694
8/8/020000.1425030.130404
8/9/020000.1389420.128114
8/10/020000.1353820.125824
8/11/020000.1318210.123534
8/12/020000.1282610.121244
8/13/020000.12470.118953
8/14/020000.121140.116663
8/15/020.11757869620.11437196540000.1175790.114372
8/16/020000.1141370.112783
8/17/020000.1106960.111194
8/18/020000.1072540.109605
8/19/020000.1038130.108016
8/20/02-2.794-2.794-0.110.1003710.106428
8/21/020000.096930.10484
8/22/020.09348823280.10325055660000.0934880.103251
ID3/1/023/29/024/17/025/21/025/29/026/28/028/15/028/22/02TI_5M11X11
GG10.34689707760.48409167680.44104720060.31676950010.47895392480.17006487730.09259817450.08438828553.9067
GG20.39410912990.51504385170.45496432330.43374121040.50327122060.26825766710.16267356460.12388714483.8481
GG30.29128392340.35848792490.32911257150.49370266940.42710536120.23549752460.19437860770.1390860523.5198
GG40.42546416820.53493342550.43622336830.34552505610.52259003970.2554709770.13038094680.09966348134.0261
NW10.36605455130.40031552310.39265268450.36032252160.39182058130.19945836740.05873256790.03994610643.2731
NW20.34337961830.42335755080.35017535240.35449630020.44247816950.18087392930.04975737860.03445410994.0838
NW30.34379665850.38618393090.32949605730.32150172370.40589205620.16514981430.06109171270.05190153393.1037
NW40.41329714950.49072657230.4433977410.4325234070.49244961140.2666591510.11332521330.09880674883.4311
NW50.36133473660.47825503950.42140113560.40863462980.47929592790.31408989060.10200107690.09775602953.8990
NW60.38934373260.46349093910.42335593850.39016383440.42731710970.26047968190.10379052010.11826298874.4938
NW70.46919455530.57990131530.55427510140.56850710510.54448265730.42121956350.1390943840.12218825184.9584
SF10.29631584810.44987951220.33953484450.36768425410.44130495190.19708357640.08744369760.09855458893.4674
SF20.31638655510.43597423880.37777913660.34864933340.17916905660.09322543420.11224139334.5178
SH10.35667334650.48515341880.45880955760.37089480090.44380699250.18309816350.11454617310.10054895363.5992
SH20.41549423780.46932332660.4359602290.42259566930.47123762670.32675512060.18231523710.16120172663.9363
SH30.36733421980.40528032630.35725152490.3527352840.4433939710.23836274450.13671900220.1130503993.1557
SH40.31696817730.3786635980.310840030.31305653150.37875220180.10916617140.03336603280.03386569243.0045
SH50.345644030.41130246070.42366602720.43970087170.46247691360.29639853610.09305959330.07248665613.6470
SH60.39862423540.4262894630.40143169460.41003566830.42659894230.32988956790.14321437660.11397887575.3968
SH70.29145292490.34444015920.29300249590.31034527720.39512140840.24149224160.08838938890.09424338962.8013
WW10.38476399630.3787373140.40335077050.36388864220.43102365140.20146877320.15505319770.08253308963.0697
WW20.40308903010.44509851930.45648309440.4137798980.47280941610.28506058530.17739663680.09665923893.4947
WW30.39540817590.46495636550.45084360240.41492140590.48799617590.27324740440.17306659520.10311533814.3454
WW40.52301766430.56711256210.54937713740.55663135050.55419114830.45825246570.16190487670.07138815644.5633
TI_5M11X11
3/1/020.5235793939AVG
3/29/020.5994606813WET
4/17/020.5769030349AVG
5/21/020.5093752948AVG
5/29/020.5424530654WET
6/28/020.5831598129AVG
8/15/020.2919076052DRY
8/22/020.3428597019DRY
ID2/28/023/29/024/18/025/20/025/30/026/26/028/15/028/22/02TI11_25MBC
LP10.2347822130.23137611450.22294357790.26837906760.26130546410.16962855350.07858541920.08487723755.9118
LP20.2177531660.23842750150.21407065990.26260925380.22836433910.13337709120.06953043640.05604293965.2601
S10.31582127140.32237354220.31915329770.35408081860.35681477190.2083783880.10120302030.09619767676.3204
S20.3267729610.34669102440.2755656920.36169248220.34138090610.23048971970.09370066670.10921176475.6571
S30.4891056210.52706876990.43771131780.46171629730.49112102240.41139357020.30133131890.258709164712.3070
U10.31590856690.31833227870.30535286440.30688476340.35085750370.21513560790.0842500040.08225399186.5774
U20.29047725650.33503619280.26350902920.31350215520.33533838320.18530299550.08726369810.07650713086.9281
U30.31694184910.33632339980.27754685510.31527430420.34762476830.19847346540.09455433490.07999577656.6413
U40.31945617720.31466057150.28885666880.31686313080.32545185230.20832404720.10171768480.09318151888.4846
U50.37564064410.40475796460.32363439050.36659451720.41242787690.27659438920.14187448510.12197479759.6434
U60.37029919920.40008640140.32203469720.37678444680.4128560960.27156407010.12793117390.11751296567.9888
UP10.2611313850.27876047490.23412838580.28103902710.26745775680.14098983610.07078592820.06569428846.1589
UP20.32445485520.33792641090.2904521480.30618173480.32685869190.19178073180.0987077590.09433580516.6176
UP30.29933222090.33901175480.31376008020.33876412210.32496922090.24009923860.14190191550.13104194149.4935
UP40.51284800770.51639865340.46461419610.50653767730.48356685490.4474276640.28010451460.249915637111.6750
PE10.25345181820.26524311230.28821240370.33076158760.28053284590.17571794690.08060726080.06063264855.7995
PE20.2314879820.26801042780.2665791720.32069643590.27557953670.1486573290.08019341580.06587689397.8622
PE30.22124480310.27171595770.25111220330.2660683990.25552480520.1249660850.07016093680.06222607275.3588
PE40.21542131380.27483718060.24144911240.27712732850.25054046440.11778580580.06866337020.05557232494.8671
TI11_25MBCTI_5M11X11
5/30/020.8361132809WET5/29/020.5424530654
6/26/020.8886354576AVG6/28/020.5831598129
8/22/020.8914110115DRY8/22/020.3428597019
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 3/29/02 Wet
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 3/29/02 Wet
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 5/29/02 Wet
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 5/30/02 Wet
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 3/1/02 Average
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 2/28/02 Average
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 5/21/02 Average
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 5/20/02 Average
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 6/28/02 Average
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 6/26/02 Average
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 4/17/02 Average
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 4/18/02 Average
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 8/15/02 Dry
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 8/15/02
3.9067
3.8481
3.5198
4.0261
3.2731
4.0838
3.1037
3.4311
3.899
4.4938
4.9584
3.4674
4.5178
3.5992
3.9363
3.1557
3.0045
3.647
5.3968
2.8013
3.0697
3.4947
4.3454
4.5633
TI_5M11X11
Theta
TMI
Glyndon 8/22/02 Dry
5.9118
5.2601
6.3204
5.6571
12.307
6.5774
6.9281
6.6413
8.4846
9.6434
7.9888
6.1589
6.6176
9.4935
11.675
5.7995
7.8622
5.3588
4.8671
TI11_25MBC
Theta
TMI
Pond Branch 8/22/02 Dry
Glyndon LIDARPond Branch LIDARGlyndon PhotogrammetricPond Branch Photogrammetric
Cell Size (metres)05/29/0206/28/0208/22/0205/30/0206/26/0208/22/0205/29/0206/28/0208/22/0205/30/0206/26/0208/22/02
0.5-0.10-0.22-0.050.150.020.000.400.340.100.120.03-0.04
1.00.080.050.010.030.020.010.450.170.030.150.04-0.04
1.50.240.160.260.07-0.07-0.160.360.260.370.270.170.07
2.00.14-0.050.250.16-0.00-0.110.260.210.190.410.310.19
2.50.170.04-0.14-0.01-0.17-0.260.490.350.100.300.180.04
3.00.390.420.050.15-0.06-0.160.490.330.070.320.200.04
3.50.450.230.150.400.370.270.480.460.170.440.320.18
4.00.560.400.260.600.580.470.250.420.460.360.190.03
4.50.440.260.180.780.810.750.200.330.370.690.640.57
5.00.310.380.030.730.780.770.130.230.170.650.540.39
6.30.330.310.060.760.810.800.290.430.280.760.670.63
7.50.500.410.120.680.740.760.230.400.290.690.710.71
8.80.280.420.090.790.830.800.290.290.280.770.800.79
10.00.350.460.040.820.870.850.160.390.250.810.840.83
11.30.300.430.090.710.760.780.340.320.210.840.890.89
12.50.470.480.230.700.750.770.290.470.570.800.840.81
13.80.370.290.190.630.720.760.510.200.250.710.810.83
15.00.160.330.290.770.780.770.210.360.150.790.830.82
16.30.300.360.000.750.820.830.420.370.500.690.740.75
17.50.380.340.320.680.740.760.310.470.390.790.840.82
18.80.460.330.080.780.810.770.290.360.530.780.830.82
20.00.230.400.360.630.680.630.310.350.330.670.730.67
21.30.200.130.150.750.790.760.290.370.560.730.800.80
22.50.370.500.290.680.680.600.310.440.350.490.540.47
23.80.250.290.330.620.620.640.360.350.570.460.520.48
25.00.190.340.140.570.620.570.240.150.420.670.730.75
26.30.180.250.110.690.780.810.320.420.450.530.590.58
27.50.350.400.370.300.430.410.070.360.300.800.820.80
28.80.340.390.350.660.710.740.290.260.470.700.730.73
30.00.310.360.350.650.710.690.260.220.460.510.550.50
Glyndon LIDARPond Branch LIDARGlyndon PhotogrammetricPond Branch Photogrammetric
Kernel Size (metres)05/29/0206/28/0208/22/0205/30/0206/26/0208/22/0205/29/0206/28/0208/22/0205/30/0206/26/0208/22/02
1-0.1024379375-0.2160221966-0.05432280690.15303328190.01863639890.00405342880.45538263050.29940646540.07753901960.12280286650.0256000639-0.0421502605
30.0338397515-0.05850078080.319923907-0.0965837793-0.2050147854-0.21820269870.46908013240.32513847160.09101069790.1351085680.0319896557-0.0419767203
50.43692196290.29548054320.4154837123-0.1532202509-0.2321189388-0.21536956990.47211684940.34845700150.05143531840.15842509140.0464872485-0.0361184013
70.52596215680.34068674580.2737285493-0.1815675472-0.2322967953-0.20782785310.48845918780.36955391730.04956880350.18722893640.0667423795-0.0255512852
90.5983532740.374628190.2551553211-0.2665210579-0.326869259-0.3165241230.47256826130.36440043350.02195604320.21648363540.0898850721-0.0123252387
110.74670017720.56968389330.3238456809-0.2823789106-0.3691327028-0.37110842410.47341585130.36498885510.01796304010.27030068510.13753744870.0280686388
130.75060121880.52906665430.281300497-0.2708117901-0.3733514484-0.38821796480.4667123690.35191048940.00760119490.33205697120.19601926910.0839381493
150.73015777190.47085631230.1772287592-0.2453946662-0.3520972494-0.38297306830.46777219310.34669451040.00501789620.38343185020.24793782030.1356344582
170.68540820030.40524442870.1062366012-0.2269786135-0.3382085716-0.38386374780.46878080760.33950483610.0130693830.42810255020.29378210020.1807041203
190.65923356890.37109198010.0841178066-0.2133463045-0.3300768347-0.38919871440.46646240990.32887582330.00619088580.45910931250.32647293610.2107002761
210.62565186310.33542334650.0859838822-0.2101504093-0.3279808647-0.39093247140.46799826170.326856663-0.00382549230.46213584620.33064605030.2071411506
230.61981229020.31555316470.0967391499-0.1944041063-0.3034338274-0.36064722120.48488334010.3416513036-0.00717890820.46926279250.33940953820.2103217556
250.64075350530.33375191490.1073207311-0.1914021328-0.3027103713-0.35672814560.4950741140.3440935549-0.00961910560.47930129930.35093581010.2178636308
270.68425264010.38868034110.1589812855-0.1951607647-0.3051783585-0.35528188130.5038462740.3456192671-0.01356164130.49832109880.37138241920.2361727583
290.70016253010.41141729020.1831203203-0.2138851495-0.3286063632-0.37874894330.50932844730.3473335119-0.0221817520.51594718820.39047815480.2535398048
310.69550347990.3982364340.1932290598-0.2153365257-0.3312964789-0.38100927810.51184668820.3468934012-0.03246630670.53277576250.40887324930.2708362119
330.68116656260.39721228720.2076995394-0.2043957306-0.3259897295-0.37345383840.51281692710.3459100843-0.04219043490.55083417230.42916653970.2906202614
350.64454318970.37069825280.1932199563-0.195480557-0.3212342677-0.36230797670.5143664420.3487428925-0.0483501480.57110895010.45461268170.316711861
370.65014487760.36892722290.2205284349-0.1814397097-0.3085447109-0.34500532070.51660427460.3525015936-0.05574168520.58836310710.47991430070.3437822993
390.630511180.36731969390.2137869094-0.1632199963-0.2908219336-0.32462530280.51474810220.3565538181-0.05999810610.60808882520.50418318750.3676406201
410.61107472030.36018290460.2007474377-0.1609507981-0.2880864537-0.31978567830.51844394090.3596777103-0.05786951310.62594004710.52399154840.3864090095
GlyndonPond Branch
AvgthetaTMI-Theta Corr.AvgthetaTMI-Theta Corr.
2/1/020.45407212430.603395462/12/020.32514472290.87
2/8/020.43033268070.70218526932/21/020.31687484140.84
2/15/020.40492817570.72850118292/28/020.31012270060.85
2/22/020.39178401510.64816940613/7/020.33385069610.93
3/1/020.37313865590.55507067323/15/020.32719585970.77
3/8/020.41385719880.65715065743/29/020.3330019860.86
3/29/020.44904162560.74995845734/4/020.32229244490.87
4/4/020.4378330770.71062450954/11/020.3269122820.89
4/11/020.40862515120.68020688734/18/020.2947729870.87
4/17/020.40976798410.69056000694/24/020.32653323770.85
4/25/020.43610559790.67539714655/3/020.3540656250.65
5/9/020.4139334390.6877528585/8/020.31304742220.88
5/16/020.35870981240.57556087675/14/020.30799418540.78
5/21/020.39628362270.57012491375/20/020.3332398710.84
5/29/020.45758130690.74670017725/30/020.33308279790.84
6/6/020.35046784310.56217867096/7/020.30812131460.82
6/12/020.31630006890.52422104896/12/020.23536620750.84
6/19/020.35669306670.44091974296/19/020.27516499340.86
6/28/020.25236107710.56968389336/26/020.21558350180.89
7/11/020.2546389160.34993478677/11/020.19509432320.86
7/19/020.18905617310.32700303277/24/020.16475377110.89
8/1/020.17098047720.39039751938/15/020.11437196540.91
8/15/020.11864684960.27235456088/22/020.10325055660.89
8/22/020.09434200960.3238456809
AvgthetaTMI-Theta Corr.AvgthetaTMI-Theta Corr.
Avgtheta1Avgtheta1
TMI-Theta Corr.0.90839417551TMI-Theta Corr.-0.42339443841
0GLYNDONPOND BRANCH
113.03221029250.9313464609
231.48216709865.3485896754
327.8785634958.9941458222
415.957052943413.7307078233
56.145871899312.666311868
62.887819326211.2293773284
71.39454523028.6216072379
80.65407873637.4507716871
90.3208688146.2001064396
100.20979883995.5082490687
110.03702332474.7099521022
1202.6343799894
1302.6343799894
1401.9425226184
1501.4635444385
1601.7030335285
1701.3038850452
1801.0111761575
1900.9845662586
2000.3991484832
2100.2927088877
00.2394890899
GLYNDONPOND BRANCH4GLYNDONPOND BRANCH
43012050.46867676934.0458530007
5935807614.607092641827.2083614295
621521411733.619746914547.5724881996
71630407825.464771129513.7221847606
874587911.63880643652.9332434255
937733105.88970473361.1126095752
1020317113.1713794720.5731625084
1112522121.95281987190.7417397168
127743131.20293704111.4497639919
137019141.09357912830.6405933918
14400150.6249023590
15150160.23433838460
1620170.0312451180
64012966
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Further Moments of the DistributionWhile measures of dispersion are useful for helping us describe the width of the distribution, they tell us nothing about the shape of the distribution
-
Further Moments of the DistributionThere are further statistics that describe the shape of the distribution, using formulae that are similar to those of the mean and variance1st moment - Mean (describes central value)2nd moment - Variance (describes dispersion)3rd moment - Skewness (describes asymmetry)4th moment - Kurtosis (describes peakedness)
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Further Moments SkewnessSkewness measures the degree of asymmetry exhibited by the data
S: sample standard deviation If skewness equals zero, the histogram is symmetric about the meanPositive skewness vs negative skewness
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Further Moments SkewnessSource: http://library.thinkquest.org/10030/3smodsas.htm
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Further Moments SkewnessPositive skewnessThere are more observations below the mean than above itWhen the mean is greater than the medianNegative skewnessThere are a small number of low observations and a large number of high onesWhen the median is greater than the mean
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Further Moments KurtosisKurtosis measures how peaked the histogram is
The kurtosis of a normal distribution is 0Kurtosis characterizes the relative peakedness or flatness of a distribution compared to the normal distribution
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Further Moments KurtosisPlatykurtic When the kurtosis < 0, the frequencies throughout the curve are closer to be equal (i.e., the curve is more flat and wide) Thus, negative kurtosis indicates a relatively flat distributionLeptokurtic When the kurtosis > 0, there are high frequencies in only a small part of the curve (i.e, the curve is more peaked)Thus, positive kurtosis indicates a relatively peaked distribution
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Further Moments KurtosisSource: http://www.riskglossary.com/link/kurtosis.htmKurtosis is based on the size of a distribution's tails. Negative kurtosis (platykurtic) distributions with short tailsPositive kurtosis (leptokurtic) distributions with relatively long tailsleptokurticplatykurtic
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Why Do We Need Kurtosis?These two distributions have the same variance, approximately the same skew, but differ markedly in kurtosis.Source: http://davidmlane.com/hyperstat/A53638.html
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How to Graphically Summarize Data?
Histograms
Box plots
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Functions of a HistogramThe function of a histogram is to graphically summarize the distribution of a data set The histogram graphically shows the following: 1. Center (i.e., the location) of the data 2. Spread (i.e., the scale) of the data 3. Skewness of the data 4. Kurtosis of the data4. Presence of outliers 5. Presence of multiple modes in the data.
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Functions of a HistogramThe histogram can be used to answer the following questions: 1. What kind of population distribution do the data come from? 2. Where are the data located? 3. How spread out are the data? 4. Are the data symmetric or skewed? 5. Are there outliers in the data?
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Source: http://www.robertluttman.com/vms/Week5/page9.htm (First three) http://office.geog.uvic.ca/geog226/frLab1.html (Last)
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Box PlotsWe can also use a box plot to graphically summarize a data setA box plot represents a graphical summary of what is sometimes called a five-number summary of the distributionMinimumMaximum25th percentile75th percentileMedianInterquartile Range (IQR)
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Box PlotsExample Consider first 9 Commodore prices ( in $,000) 6.0, 6.7, 3.8, 7.0, 5.8, 9.975, 10.5, 5.99, 20.0 Arrange these in order of magnitude 3.8, 5.8, 5.99, 6.0, 6.7, 7.0, 9.975, 10.5, 20.0The median is Q2 = 6.7 (there are 4 values on either side) Q1 = 5.9 (median of the 4 smallest values) Q3 = 10.2 (median of the 4 largest values) IQR = Q3 Q1 = 10.2 - 5.9 = 4.3
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Example (ranked) 3.8, 5.8, 5.99, 6.0, 6.7, 7.0, 9.975, 10.5, 20.0The median is Q1 = 6.7Q1 = 5.9 Q3 = 10.2 IQR = Q3 Q1 = 10.2 - 5.9 = 4.3
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Box PlotsRanked commuting times:
5, 5, 6, 9, 10, 11, 11, 12, 12, 14, 16, 17, 19, 21, 21, 21, 21, 21, 22, 23, 24, 24, 26, 26, 31, 31, 36, 42, 44, 47Example: Table 1.1 Commuting data (Rogerson, p5)25th percentile is represented by observation (30+1)/4=7.7575th percentile is represented by observation 3(30+1)/4=23.2525th percentile: 11.7575th percentile: 26Interquartile range: 26 11.75 = 14.25
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Example (Ranked commuting times):
5, 5, 6, 9, 10, 11, 11, 12, 12, 14, 16, 17, 19, 21, 21, 21, 21, 21, 22, 23, 24, 24, 26, 26, 31, 31, 36, 42, 44, 47
25th percentile: 11.75 75th percentile: 26Interquartile range: 26 11.75 = 14.25
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Other Descriptive Summary MeasuresDescriptive statistics provide an organization and summary of a datasetA small number of summary measures replaces the entirety of a datasetWell briefly talk about other simple descriptive summary measures
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Other Descriptive Summary MeasuresYou're likely already familiar with some simple descriptive summary measuresRatiosProportionsPercentagesRates of ChangeLocation Quotients
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Other Descriptive Summary MeasuresRatios # of observations in A# of observations in Be.g., A - 6 overcast, B - 24 mostly cloudy daysProportions Relates one part or category of data to the entire set of observations, e.g., a box of marbles that contains 4 yellow, 6 red, 5 blue, and 2 green gives a yellow proportion of 4/17 or colorcount = {yellow, red, blue, green}acount = {4, 6, 5, 2}=
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Other Descriptive Summary MeasuresProportions - Sum of all proportions = 1. These are useful for comparing two sets of data w/different sizes and category counts, e.g., a different box of marbles gives a yellow proportion of 2/23, and in order for this to be a reasonable comparison we need to know the totals for both samplesPercentages - Calculated by proportions x 100, e.g., 2/23 x 100% = 8.696%, use of these should be restricted to larger samples sizes, perhaps 20+ observations
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Other Descriptive Summary MeasuresLocation Quotients - An index of relative concentration in space, a comparison of a region's share of something to the totalExample Suppose we have a region of 1000 Km2 which we subdivide into three smaller areas of 200, 300, and 500 km2 (labeled A, B, & C)The region has an influenza outbreak with 150 cases in A, 100 in B, and 350 in C (a total of 600 flu cases):Proportion of AreaProportion of CasesLocation QuotientA 200/1000=0.2 150/600=0.25 0.25/0.2=1.25B 300/1000=0.3 100/600=0.17 0.17/0.3 = 0.57C 500/1000=0.5 350/600=0.58 0.58/0.5=1.17