Lamb's Quarters Sampling Report(2)

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BOTANICAL ASSESSMENT Density of Lambs Quarters in Soybean FieldEmily Crouse, Shelby Dean, Alexandre Loureiro, and Wei XiongENVA 3001 - Environmental Sampling and AnalysisSeptember 30th, 20141) Company ReportTo Whom It May Concern,Envirocon Impact Assessment Inc. (EIAI) has performed a blocking, transect sampling method in order to examine and estimate the quantity of Lamb’s Quarters (Chenopodium album) in the field assigned. The density of Lamb’s Quarters estimated in the entire f ield was 10.8 per m², with a precision of 95% confidence interval ± 0.615 (which is 5.3% of the population mean). The circumference of the field is approximately 843.16 meters and the area of the entire field is approximately 29140 m². The method used was dividing the field into two equal halves, running parallel to the river. These two sections were then each divided into five blocks, giving ten equal blocks to sample from in total see figure 1: Division of Field Sampled, below.Figure 1: Division of Field SampledThe reasoning behind dividing the field into two halves with five blocks in each was because our company predicted there may lay heavier concentrations within the blocks closest to the river (blocks 6 through 10). However, once the field was sampled this was not the case at all. In fact, the majority of the Lamb’s Q uarters were present in block 4 (at 5.4 Lamb’s Q uarters per 0.25m²), block 5 (at 4.7 Lamb’s Quarters per 0.25m) and block 10 (at 8.6 L amb’s Quarters per 0.25m²). It was determined that the highest concentrations of Lamb’s Quarters was located c losest to the end of the field where the road was. (See Figure 1: Division of Field Sampled and Table 1).Table 1: Descriptive Statistics per Block* BOLD indicates highest density of Lamb’s QuartersTen samples were selected per block, using a diagonal transect method within each of the ten blocks. 0.25m² quadrats were used in obtaining each sample within the field. After a total of 100 samples were taken from the field, the total density of Lamb’s quarters was calculated using statistical software.There were a couple measures taken in order to achieve an accurate sampling method. The field was divided into equal blocks, in order to obtain samples from every area of the field. There was the same amount of samples examined within every block. This standardized method eliminates some degree of bias. However, there still remains some bias due to the spreading out of quadrats being uneven and unmeasured. There were different interpretations of the amount of Lamb’s quarters present depending on the data collector taking the sample. Lastly, an uncontrollable factor would be the varying clusters of Lambs quarters present within the field.Although the overall mean was discussed above, we also thought it relevant to show the means of each individual block to help understand the distribution of Lamb’s Quarters with in the field (please see Table 2).Table 2: Mean Density of Lamb’s Quarters per Block* BOLD indicates highest density of Lamb’s Quarters2) Standard Operating ProcedureSampling for Lamb’s Q uartersWritten by: Alexandre Loureiro and Wei XiongSeptember 28th, 2014Introduction: (MAYBE FIND LAMB’S QUARTER’S THRESHOLD IN SOYBEAN FIELDS).Lamb’s Quarters is a weed that competes against soy beans for nutrients in a soybean field. To effectively treat the problem with an herbicide, the density of lamb’s quarters must be determined beforehand, for even if the plant is present, it might not be a problem. To give a good estimate of theoverall distribution and density of Lamb’s Quarters, a stratified sampling method needs to be performed. Materials Required:1. Measuring Wheel2. 18 Field Flags or Steaks3. Google Maps Measuring Tool4. ½ m Quadrats (one per person sampling)5. Clip Boards and Data Sheets (sample attached to the standard operating procedures sheet) Procedure:1 Field Measurements1.1 On Google Maps, locate the field in question. Using its measuring tool,determine the boundaries of the field. You can mark there points by right-clicking your mouseand selecting ‘measure distance’. This will allow you to measure the area of the field as well as the circumference.1.2 On paper, or using Google Maps, divide the field into 10 blocks withapproximately equal areas. Using this grid of blocks, you can determine where to place yourflags in the field. A measurement (in meters) will be given for each point on the field edge andyou can simply walk the circumference of the field, placing flags at the measure locations.1.3 Go to the field with the required materials (listed above). With the measuringwheel, go around the perimeter of the field. Since the length of each block was determinedbeforehand, plant flags on the ground at the points where the corners of each block aresupposed to be. Do the outside perimeter of the field first and then do the middle.2 Sampling2.1 With the quadrat in hand, start at one of the corners of the block (any of themwill work). Then, 10 samples must be taken in a diagonal line inside the block. To do that, simply walk from the corner you are on to the one that is diagonally opposite to you. On your waythere, throw the quadrate 10 times in front of you (distance may vary between quadrats but as long as 10 samples are done, it will not affect the results). To achieve a better qualityassessment, the throws must be somewhat equally divided along the diagonal line so thatsamples from both corners as well as the middle sections of the block are collected.2.2 Every time a throw is performed, count the number of visible Lamb’s Quartersinside the quadrat. Make sure to look underneath leaf material of other plants or dead plants,for little/young Lamb’s Quarte rs sometimes are hidden from view. Enter the counted numberinto the respective place in the data sheet. Do that for every throw in the quadrat.*Note: Keep in mind that the work can be divided among people, so the more people there are, the quicker the assessment can be done.3 Calculations3.1 After all the data is collected, calculate a mean for each of the blocks as wellas the overall mean of the field (see sample calculations).3.2 Calculate the standard deviation of each block as well as the standarddeviation of the whole field (see sample calculations).3.3 Calculate the standard error for a stratified random sampling method (seesample calculations).3.4 Calculate the confidence interval with 95% certainty and make sure the D valuethat was f ound is within 20% of the field’s mean (see sample calculations).3) JustificationWe used three sampling methods in order to determine which was the most accurate and/or efficient. The three methods used were; Whole-Field Transect, Blocked-Random and Blocked-Transect.Table 3: Comparison of People-Hours per MethodWe chose the Blocked-Transect Method as it seems to be the most accurate. Statistically, the Blocked-Random method is the most precise (smallest StDev) and the Whole-Field Transect is the most efficient for time.Whole-Field TransectFor this method the blocks were not used and the field was sampled as a whole. A total of 25 samples were taken along one transect line across the entire field. The data was collected using a ½ m quadrat. (For results please see Figure 2 and Table 4)Table 4: Descriptive Statistics for Whole-Field Transect MethodFigure 2: Whole-Field Transect MethodBlocked-RandomFor this method the field was divided up into 10 blocks of equal size and the random sampling took place within each block. 3 quadrats were thrown in each block for a total of 30 samples. The data was collected using a ½ m quadrat. (For results please see Figure 3 and Table 5)Table 5: Descriptive Statistics for Blocked-Random MethodFigure 3: Blocked-Random MethodBlocked-Transect (chosen method)For this method the field was divide up into 10 block of equal size and transect sampling was conducted within each block. 10 quadrats were thrown in each block for a total of 100 samples. The data was collected using a ½ meter quadrat. (For results please see Figure 4 and Table 6)Table 6: Descriptive Statistics for Blocked-Transect Method (chosen method)Figure 4: Blocked-Transect Method (chosen method)ReferencesKrebs, Charles J. 1998. Ecological methodology-2nd .ed:265-278 [2] Crabb, A. C., J. J. Marois, and T. P. Salmon. 1994. Evaluation of field sampling techniques for estimation of bird damage in pistachio orchards. Proc. 16th Vertebrate. Pest Conference, W.S. Halverson& A.C. Crabb, Eds. University of California, Davis..2 45126CalculationsBlock 1x1̅̅̅ = 0+0+1+0+1+1+0+2+0+010= 0.5Sd1 = √∑( x1̅̅̅̅− x i )2n−1= √(0−0.5)2+(0−0.5)2+(1−0.5)2+(0−0.5)2+(1−0.5)2+(1−0.5)2+(0−0.5)2+(2−0.5)2+(0−0.5)2+(0−0.5)210−1=0.707S12 = ∑( x1̅̅̅̅− x i )2n−1= (0−0.5)2+(0−0.5)2+(1−0.5)2+(0−0.5)2+(1−0.5)2+(1−0.5)2+(0−0.5)2+(2−0.5)2+(0−0.5)2+(0−0.5)210−1= 0.500Block 2x2̅̅̅ = 3+4+3+3+5+2+2+1+2+010= 2.5Sd2 = √∑( x2̅̅̅̅− x i )2n−1= √(3−2.5)2+(4−2.5)2+(3−2.5)2+(3−2.5)2+(5−2.5)2+(2−2.5)2+(2−2.5)2+(1−2.5)2+(2−2.5)2+(0−2.5)210−1= 1.434S22 = ∑( x2̅̅̅̅− x i )2n−1= (3−2.5)2+(4−2.5)2+(3−2.5)2+(3−2.5)2+(5−2.5)2+(2−2.5)2+(2−2.5)2+(1−2.5)2+(2−2.5)2+(0−2.5)210−1= 2.056Block 3x3̅̅̅ = 2+7+4+2+1+0+0+15+0+410= 3.5Sd3 = √∑( x3̅̅̅̅− x i )2n−1= √(2−3.5)2+(7−3.5)2+(4−3.5)2+(2−3.5)2+(1−3.5)2+(0−3.5)2+(0−3.5)2+(15−3.5)2+(0−3.5)2+(4+3.5)210−1= 4.62S32 = ∑( x3̅̅̅̅− x i )2n−1= (2−3.5)2+(7−3.5)2+(4−3.5)2+(2−3.5)2+(1−3.5)2+(0−3.5)2+(0−3.5)2+(15−3.5)2+(0−3.5)2+(4+3.5)210−1= 21.39Block 4x4̅̅̅ = 8+9+4+4+12+2+4+5+4+210= 5.4Sd4 = √∑( x4̅̅̅̅− x i )2n−1= √(8−5.4)2+(9−5.4)2+(4−5.4)2+(4−5.4)2+(12−5.4)2+(2−5.4)2+(4−5.4)2+(5−5.4)2+(4−5.4)2+(2−5.4)210−1= 3.24S42 = ∑( x4̅̅̅̅− x i )2n−1= (8−5.4)2+(9−5.4)2+(4−5.4)2+(4−5.4)2+(12−5.4)2+(2−5.4)2+(4−5.4)2+(5−5.4)2+(4−5.4)2+(2−5.4)210−1= 10.49Block 5x5̅̅̅ = 4+10+6+7+1+1+0+5+3+1010= 4.7Sd5 = √∑( x5̅̅̅̅− x i )2n−1= √(4−4.7)2+(10−4.7)2+(6−4.7)2+(7−4.7)2+(1−4.7)2+(1−4.7)2+(0−4.7)2+(5−4.7)2+(3−4.7)2+(10−4.7)210−1= 3.59S52 = ∑( x5̅̅̅̅− x i )2n−1= (4−4.7)2+(10−4.7)2+(6−4.7)2+(7−4.7)2+(1−4.7)2+(1−4.7)2+(0−4.7)2+(5−4.7)2+(3−4.7)2+(10−4.7)210−1= 12.9Block 6x6̅̅̅ = 0+0+0+0+0+0+0+0+0+010= 0Sd6 = √∑( x6̅̅̅̅− x i )2n−1= √(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2(0−0)210−1= 0S62 = ∑( x6̅̅̅̅− x i )2n−1= (0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2+(0−0)2(0−0)210−1= 0Block 7x7̅̅̅ = 0+1+1+0+2+0+0+1+2+010= 0.7Sd7 = √∑( x7̅̅̅̅− x i )2n−1= √(0−0.7)2+(1−0.7)2+(1−0.7)2+(0−0.7)2+(2−0.7)2+(0−.7)2+(0−0.7)2+(1−0.7)2+(2−0.7)2+(0−0.7)210−1= 0.823S72 = ∑( x7̅̅̅̅− x i )2n−1= (0−0.7)2+(1−0.7)2+(1−0.7)2+(0−0.7)2+(2−0.7)2+(0−.7)2+(0−0.7)2+(1−0.7)2+(2−0.7)2+(0−0.7)210−1= 0.678Block 8x8̅̅̅ = 1+0+0+3+0+1+0+0+0+010= 0.5Sd8 = √∑( x8̅̅̅̅− x i )2n−1= √(1−0.5)2+(0−0.5)2+(0−0.5)2+(3−0.5)2+(0−0.5)2+(1−0.5)2+(0−0.5)2+(0−0.5)2+(0−0.5)2+(0−0.5)210−1= 0.972S82 = ∑( x8̅̅̅̅− x i )2n−1= (1−0.5)2+(0−0.5)2+(0−0.5)2+(3−0.5)2+(0−0.5)2+(1−0.5)2+(0−0.5)2+(0−0.5)2+(0−0.5)2+(0−0.5)210−1= 0.944 Block 9 x 9̅̅̅ =1+0+1+0+0+1+1+2+0+010= 0.6 Sd 9 = √∑( x 9̅̅̅̅− x i )2n−1= √(1−0.6)2+(0−0.6)2+(1−0.6)2+(0−0.0)2+(0−0.6)2+(1−0.6)2+(1−0.6)2+(2−0.6)2+(0−0.6)2+(0−0.6)210−1=0.699 S 12=∑( x 1̅̅̅̅− x i )2n−1= (1−0.6)2+(0−0.6)2+(1−0.6)2+(0−0.0)2+(0−0.6)2+(1−0.6)2+(1−0.6)2+(2−0.6)2+(0−0.6)2+(0−0.6)210−1= 0.489 Block 10 x 10̅̅̅̅ =17+7+3+12+5+19+6+3+3+1110= 8.6 Sd 10 = √∑( x 10̅̅̅̅̅− x i )2n−1= √(17−8.6)2+(7−8.6)2+(3−8.6)2+(12−8.6)2+(5−8.6)2+(19−8.6)2+(6−8.6)2+(3−8.6)2+(3−8.6)2+(11−8.6)210−1= 5.89 S 102 = ∑( x 10̅̅̅̅̅− x i )2n−1=(17−8.6)2+(7−8.6)2+(3−8.6)2+(12−8.6)2+(5−8.6)2+(19−8.6)2+(6−8.6)2+(3−8.6)2+(3−8.6)2+(11−8.6)210−1= 34.71x ST ̅̅̅̅ = ∑x i ̅∗block size total area=0.5∗2914+2.5∗2914+3.5∗2914+5.4∗2914+4.7∗2914+0∗2914+0.7∗2914+0.5∗2914+0.6∗2914+8.6∗291429140= 2.7 lamb ’s quarters per 0.25 square meters =10.8 lamb ’s quarters per square metersX ST ̂ = N*x ST ̅̅̅̅ = 29140*10.8= 314712 lamb ’s quartersVariance of ( x ST ̅̅̅̅ ) = ∑[w i 2s i 2n i(1−f i )]=(110)2(0.5+2.056+21.39+10.49+12.90+0.678+0.944+0.489+34.71)10*(1 - 102914)= 0.084157Standard error of ( x ST ̅̅̅̅ ) = √Variance of ( x ST ̅̅̅̅ ) = 0.29Variance of (X ST ̂) = (N)2 * Variance of ( x ST ̅̅̅̅) = 291402 * 0.084157 = 71461041Standard error of ( X ST ̂ ) = √Variance of ( X ST ̂ )= √71461041 = 8453 95%Ci = 1.96SeFor the population mean, the 95% confidence limits are 10.8 ± 1.96(0.084157) = 10.8 ± 0.1651.96Sex ST̅̅̅̅̅ *100% =1.5% < 20% ∴ From 10.6 to 11 lamb ’s quarters per square meters For the population total, the 95% confidence limits are 314712 ± 1.96(8453) = 314712 ± 165681.96SeX ST̂ = 5.3% < 20% ∴ From 298144 to 331280 lamb ’s quarters per square meter.Data Collection Sheet。