A guide for gathering data 3/31/2017 11:32 PM Statistical Sampling This presentation is designed for a class that is about to do a project where they will have to gather data. It is meant to give them a high level of understanding as well as concrete examples of data collecting methods. A guide for gathering data Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Table of Contents Learning Objectives Example 1: Identifying Sampling Methods Sampling Methods Example 2: Utilizing Sampling Methods Random Sampling Systematic Sampling References Stratified Sampling Cluster Sampling Convenience Sampling Sampling Videos Sampling Relationships Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Objectives Define the five basic sampling methods Random Systematic Stratified Cluster Convenience Identify sampling methods in an example Use sampling methods to choose data There are five basic sampling methods. Random and Systematic sampling are often chosen over the other methods for their ease of use. Both Stratified and Cluster sampling employ random sampling. Be very wary of convenience sampling – it is often way too “convenient” and is fraught with potential bias. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Random Sampling The “pick a name out of the hat” technique Random number table Random number generator A simple random sample of n pieces of data from a population of data is collected in such a manner such that every sample has an equal chance of being selected and included in the sample. The data is chosen randomly using either a random number table or a piece of software called a random number generator. Hawkes and Marsh (2004) Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Systematic Sampling All data is sequentially numbered Every nth piece of data is chosen A simple random sample of n pieces of data from a population of data is collected in such a manner such that every sample has an equal chance of being selected and included in the sample. The data is chosen randomly using either a random number table or a piece of software called a random number generator. Hawkes and Marsh (2004) Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Stratified Sampling Data is divided into subgroups (strata) Strata are based specific characteristic Age Education level Etc. Use random sampling within each strata All of the data is divided into distinct subgroups or strata, based on a specific characteristic such as age, income, education level, and so on. All members of a stratum share the specific characteristics. Random samples are drawn from each stratum. Hawkes and Marsh (2004) Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Cluster Sampling Data is divided into clusters Usually geographic Random sampling used to choose clusters All data used from selected clusters The entire population of data s divided into pre-existing segments called clusters. Most often these clusters are geographic. Then clusters are randomly selected, and every member of each selected cluster is included in the sample. NOTE: Used often by government agencies and private research organizations. Hawkes and Marsh (2004) Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Convience Sampling Data is chosen based on convenience BE WARY OF BIAS! Data is chosen based on being readily available. Runs the risk of being severely biased because no real statistical method is used in order to choose the data. For example if you want to find out if people shop in a certain shopping mall your sample is going to be extremely biased if you stand outside of that mall and survey people as they walk in. Hawkes and Marsh (2004) Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Sampling Videos Random and Stratified Random Sampling (YouTube, 2009) Cluster and Systematic Sampling (YouTube, 2009) Data is chosen based on being readily available. Runs the risk of being severely biased because no real statistical method is used in order to choose the data. For example if you want to find out if people shop in a certain shopping mall your sample is going to be extremely biased if you stand outside of that mall and survey people as they walk in. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sampling Relationships Random Sampling Cluster Sampling Stratified Sampling It is important to note that when using either cluster or stratified sampling you actually have a multi-step sampling process. You need to first divide the data into clusters or strata (depending on the method chosen) and then use random sampling. For cluster sampling you use random sampling to determine the clusters and in stratified sampling you use random sampling to determine the data chosen within each strata. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Example 1: Sampling Methods In a class of 18 students, 6 are chosen for an assignment Sampling Type Example Random Pull 6 names out of a hat Systematic Selecting every 3rd student Stratified Divide the class into 2 equal age groups. Randomly choose 3 from each group Cluster Divide the class into 6 groups of 3 students each. Randomly choose 2 groups Convenience Take the 6 students closest to the teacher Now we are going to go through a some examples of how to choose 6 students out of a class of 18 by the 5 different sampling methods. After going through the slides I am going to poll the class to ask what method they would choose and why. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Example 2: Utilizing Sampling Methods Determine average student age Sample of 10 students Ages of 50 statistics students 18 21 42 32 17 19 22 25 24 23 20 29 36 27 In the second example we are going to determine the average age of 2 classes of statistics students by taking a sample of ten students using 3 of the 5 different sampling methods. We will then compare the average ages calculated using each of the 5 methods. We are also numbering the data – for example data point 1 is 18, data point 2 is 21, data point 3 is 42 and so on. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Example 2 – Random Sampling Data Point Location Corresponding Data Value 35 25 48 17 37 19 14 47 24 4 32 33 34 23 3 42 Mean 25.1 Random number generator (www.random.org) For the random sampling example we used the random number generator to find 10 data points between 1 and 50. We then used these data “points” to find the corresponding student age. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Example 2 – Systematic Sampling 5th Data Point Location Corresponding Data Value 5 17 10 22 15 18 20 21 25 30 35 40 27 45 23 50 Mean 20.8 Take every data point For the systematic sampling example since we needed 10 samples and had 50 data points we took (50/10) or every 5th data point. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Example 2 – Convenience Sampling Data Point Location Corresponding Data Value 1 18 2 21 3 42 4 32 5 17 6 7 8 9 19 10 22 Mean 22.5 Take the first 10 data points For the convenience sampling example since we needed 10 samples and had 50 data points we the first 10 samples. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling Example 2 - Comparison A comparison of the results achieved using 3 of the 5 sampling methods. Questions to pose for class – which do you think is the best and why? Which of these 3 methods would you have chosen? Why? How would you have done sampling methods for stratified and cluster sampling? Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling

Sarah DiCalogero - Statistical Sampling References Hawkes, J., & Marsh, W. (2004). Discovering Statistics (2nd ed.). Charleston, SC: Hawkes Publishing Inc.. YouTube. (2009). Random Sample. Retrieved from http://www.youtube.com/watch?v=xh4zxC1OpiA&feature=related YouTube. (2009). Types of Random. Retrieved from http://www.youtube.com/watch?v=wUwH7Slfg9E&feature=related These references are included according to APA format. Sarah DiCalogero - Statistical Sampling Sarah DiCalogero - Statistical Sampling