-What is the best sampling method for this data set?

- Simple Random Sampling    
- Systematic Random Sampling    
- Stratified Sampling    

• Simple Random Sampling
  • subset chosen from a larger population in which the individuals are chosen randomly, all with the same probability

Simple Random Sampling

• Systematic Random Sampling
  • probability sampling method in which a random sample, with a fixed periodic interval, is selected from a larger population
    

Systematic Sampling

• Stratified Sampling
  • involves the division of a population into smaller subgroups known as strata, based on members’ shared attributes or characteristics, then independently sampled randomly
    

Stratified Sampling

• 899,164 observations
  
• 27 variables
  
• Provides information on loans that were guaranteed to some degree by the SBA between 1987 and 2014
  
• The strata are separated by the stratification variable “State” after the states are combined into categories by region
  
• “State” because geographical location may have an impact on other variables such as default rate
  

US Map

• Checking for small number of observations in each category within the variable State

• Using the R random number generator, the simple random sample was formed
  
• Table provided shows the number of observations in the sample, and the number of variables
  
• Checking to make sure the amount of variables are 5% or less of the amount of observations

• Using R to skip observations and systematically call on random variables
  
• Starting point is observation 107
  
• Jump size is 224
  
• Table created to show number of observations and variables in the new sample
  
• Checking for variables to be 5% of observation amount

• Taking a proportional amount of observations from each category in regions using frequency function in R
  
• The proportions are all even

• Default rates are compared to test the accuracy of the samples
  
• The table shows that the systematic sample is the best
  
• The stratified data is way off
  • More research is needed to explore why

• Reaffirming systematic sampling as the best fit
  
• No lines for the consistent values in systematic and stratified sampling

• After creating 3 different samples with 3 different sampling methods and stratifying the data by “State” a table was created from the default rates extracted from the samples
  
• The table and graph combined supports the idea that the systematic sampling method better represents the original population
• Now that the best sampling method is known, more analysis can be performed, exploring trends of the bank loans data