Sampling

Introduction to Sampling What is population? What is a sample? What is sampling? What is a representative sample? What is sampling bias? What makes a sample representative?

Population A population is “the aggregation of all elements in which we are interested.” The research question defines de population..

Population Research question How many undocumented immigrants in the US have health insurance? What is the obesity rate in the US? What percentage of CHHS students live on campus? Population All Undocumented immigrants in the US All the people in the US All students in CHHS major

Population In most cases we will not be able to observe the entire population to answer our research question. So… we rely on a sample It turns out that if we obtain a representative sample of the population, we do not need to observe the population to understand it fairly accurately.

Sample A sample is a subset of the population It is a collection of elements from the population Population: ALL CHHS students (ALL 250 of them) Sample of CHHS students: A group of 25 CHHS students

Sampling Sampling is the process of obtaining a sample from the population. The goal is to make the sample as representative of the population as possible.

What is a Representative Sample? A representative sample is the result of an unbiased selection of elements from the population. Thus, differences between the composition of a representative sample and the population are due to chance and not by a systematic selection of some elements over others.

What is a Representative Sample? In other words, a representative sample is a sample that was obtained in an unbiased way (i.e. there was no systematic way of including or excluding a elements of the population while selecting the sample). It could be very different from the population (in its composition), but if it was collected in an unbiased way it is still representative. Lets see some examples….

Total population = 100 people = 65 (65 % of the population is orange) = 9 (9% of the population is green) = 22 (22% of the population is blue) = 4 (4% of the population is pink) Population of CHHS students Suppose I select this group of students as my sample because they are in my CHHS 385 class Is that a representative sample ? No, It is not non-representative because the sample’s composition is different from the population (90% blue and 10% orange), but because me selecting them as a result of them being in my class systematically excluded the rest in their probability of being selected and therefore introduced bias in the sampling. Example 1

Total population = 100 people = 65 (65 % of the population is orange) = 9 (9% of the population is green) = 22 (22% of the population is blue) = 4 (4% of the population is pink) Population of CHHS students Suppose I select this group of students as my sample because they volunteered to be in the study. Is that a representative sample ? No, It is not non-representative because the sample composition is different from the population (80% orange and 20% green), but because they selected themselves by volunteering and systematically excluded the rest of students in their probability of being selected and therefore introduced bias in the sampling. Example 2

Total population = 100 people = 65 (65 % of the population is orange) = 9 (9% of the population is green) = 22 (22% of the population is blue) = 4 (4% of the population is pink) Population of CHHS students Suppose I select this group of students as my sample because they were the first 10 CHHS students to walk in the classroom. Is that a representative sample ? No It is not non-representative because the sample composition is different from the population (90% orange and 10% blue), but because me selecting them based on showing up early systematically excluded the rest of students in their probability of being selected and therefore introduced bias in the sampling. Example 3

What is a Representative Sample? In summary when you select the elements in the sample based on some criteria the sample is biased and therefore not representative. When the elements select themselves to be in the sample, you sample will be biased and therefore not representative.

How to get a representative Sample? The only way to obtain a representative (unbiased) sample is by selecting the elements randomly. In representative samples elements are selected purely by chance. Examples….

Total population = 100 people = 65 (65 % of the population is orange) = 9 (9% of the population is green) = 22 (22% of the population is blue) = 4 (4% of the population is pink) Population of CHHS students Suppose I select this group of students randomly by picking their names out of a hat that contained the names of all the students in CHHS Is that a representative sample ? YES, Notice that it does not matter that sample composition is somewhat different to the population (40% orange, 30% blue, 10% pink, and 20% green), it is still representative because elements were selected randomly so no bias was introduced in the sampling process Example 4

Summary A sample is subset from the population. We study samples because in most cases it is impossible to observe the population. The goal is to obtain a representative sample because we want it to reflect all the characteristics of the population The only way to obtain representative samples is using probability theory to select observations randomly. What makes a sample representative is not its composition, but the way it was collected. Sometimes we cannot obtain probability samples so we use other techniques that we will discuss next.

Next lectures The next lectures explain how to obtain probability samples and non probability samples. Make sure you understand what a representative sample is. Having a firm understanding of what a representative sample is will help you when we get to the statistics part of the course and will make you better consumer of information in general.