Assignment 3: Sampling Fields

Instructions

Download the assignment03.Rmd file from Canvas and open it in RStudio. Complete this assignment by filling in the answers below in the R Markdown Notebook document. Click the Knit button to generate a formatted PDF or Word document.

You will work with a partner to design and conduct the spatial sample. First, find a partner in class to work with. Go onto this Canvas course, select People on the sidebar menu, Groups, then select a group for you and your partner to join. Once you and your partner have joined a Canvas group, retrieve an infrared radiant thermometer for your group from Dr. Allen and tell him your group number.

Research Question

The University is trying to detect underground water main leaks and is interested to know how surface temperature varies between the following surfaces:

1. Grass
   
2. Concrete
   
3. Dirt
   
4. Mulch

Before you go outside, work with your partner in the classroom to plan your spatial sampling approaches to measure surface temperature. As a pair, you will spatially sample the outdoor region mapped below, located between Halbouty and Doherty Buildings:

Of the four spatial sampling approaches listed below, select two to implement:

• Simple random sampling
  
• Systematic sampling
  
• Stratified random sampling
  
• Random sampling within clusters (6-10 clusters please)

For each of your two sampling approaches, collect at least 40 temperature observations, with each surface having at least five observations. Use your paper map handouts to design and conduct the sampling approaches. Using a random number generator is recommended (e.g., the sample() or runif() functions in R).

Create a data table to record your observations (see below for the minimum required information to record). The table can initially be hand written or it can be created digitally using, e.g., Excel. The final data table submitted to Canvas must be formatted as a Comma Separated Value (CSV) spreadsheet. Note that this data table will be the basis of future class assignments so please take care to collect high-quality observations.

1. Approach (Simple Random, Systematic, etc.)
   
2. Surface (Grass, Concrete, Dirt, Mulch)
   
3. Date (MM/DD/YYYY)
   
4. Time (HH:MM:SS)
   
5. Longitude (decimal degrees) - using your phone GPS
   
6. Latitude (decimal degrees) - using your phone GPS
   
7. Temperature (degrees Celsius) - using the radiant thermometers
   
8. Notes - any additional information you wish to record

Deliverables

For this assignment, each person should submit to Canvas the following items:

1. A CSV spreadsheet containing your observations (e.g., assignment03_data.csv)
   
2. A completed .Rmd file
   
3. A PDF (or Word) file knitted from the completed .Rmd file

Spatial Sampling Approaches

Most studies draw a sample from a population, which is ultimately of greatest interest in our research. Your final results are only as good as how you sampled the population and then applied your statistics. In this respect, it is critical that prior to starting a study, you decide on what to measure, where, when and how often.

In general, we can obtain an unbiased sample by giving every member of a population an equal chance of being included in the sample.

• Simple random sampling: each individual has an equal chance of being included in a sample. Random samples are, however, prone to error. For example, quite by chance a random sample might contain a disproportionately large number of individuals with specific characteristics.

• Systematic sampling: every nth individual is selected or individuals are sampled every nth minute/hour etc.

• Stratified random sampling: the population is divided into strata and samples are drawn randomly (from the above methods) from each strata. In this assignment, you and your partner must decide whether conducting a proportional or disproportional random sampling is more appropriate.

• Cluster sampling: groups of individuals or samples within specific areas, with the individuals in each cluster drawn at random. A strength and a weakness of cluster sampling is that individuals from each cluster tend to be homogeneous.

The opposite of unbiased sampling is to collect a sample of convenience, in which the investigator chooses the individuals to sample out of convenience.

It is important to remember that sampling by its nature is biased and that you do not place too much confidence in your results- do not assume your results have concreteness.

Questions

Please work individually to answer the questions below, they should not be the same words as your partner.

1. For each sampling approach taken, write a short paragraph describing the procedure that you and your partner took to collect an objectively determined sample (e.g., did you use random number generation to determine sample locations?). Refer to the map above to explain your sampling strategies. Describe the strengths and weaknesses of each of your sampling approaches.

The two sampling approaches that the group took were Systematic sampling and poportional Stratified random sampling. The first one, systematic sampling, took two even spots out of every one of the 20 blocks that the map was split into. These same two placed spots, in the middle of every block, allow infomration to be uniformily selected for data intake. The downside to this approach is the fact that some areas of the map may need more data collected from it then given by this approach (the side walk as an example). The second sampling approach is poportional stratified random sampling; in this approach the map was divided into two strata (sidewalk and dirt). Then a number of points are poportional selected to reflect the size of the two stratas in the map (there was more dirt area covereage so it will have more points). After this step, a random number generator is used to randomly select points from this area. The strength of this sampling approach is the fact that data can be more evenly representative of the different areas of the map. That being said, the weak point of it is the fact that some areas of concern or interest may be left unaccounted for due to the random nature of selection.

2. Give an example of a variable, an observation, and a data value that you collected as part of your spatial sample.

variable - type of surface (dirt, concrete, grass, etc.) observation - the list of points (ex. point 1, point 2 … point 40) data value - the numerical temperature of the readings for each point.

3. What is the spatial and temporal scale of your spatial sample?

Pictured above is the spatial scale of the spatial sample, it is the entirety of the space on the courtyard of the Halabooty building.

The temporal scale of the spatial sample is the time that was spent collecting information, for this group the temporal scale is: 10:41:10 AM - 11:15:14 AM

4. What is the data type (nominal, ordinal, interval, ratio) of the following variables? (1) Surface; (2) Date, (3) Temperature.

Surface - Nominal data type Date - Ordinal data type Temperature - Interval data type

5. Are the following variables continuous or discrete? (1) Date; (2) Temperature.

Date - discrete Temperature - Continuous

6. Name the primary spatial entity that you are sampling. Is it an object or a field?

The main spatial entity that we are sampling are vectors that represent temperature withing our grid of spatial data sample. Each point is a field that lays within the object.

7. What is the spatial dimension of your temperature observations?

The spatial dimension of the temperature observations is the range if temperatures within the spatial dimension of our data.