Sampling Techniques 1

Simple Random Sample (SRS) or just Random Sample Taking a sample from a population in which… a)Every member has the same chance of being selected b)Every member is chosen independent of each other c)Sample is taken without replacement… no one is included twice. 2

Simple Random Sample (SRS) Every member has the same chance of being selected. – How to choose a SRS of size n? Label all individuals in the population with a # 1 to N Randomly select n #’s between 1 and N Those individuals make your sample. Ex. Out of a class of 40 students (numbered 1 to 40) randomly select 5 #’s : 3, 17, 29, 33, 38 3

Simple Random Sample (SRS) Every member is chosen independent of each other – Members are independent if the fact that one individual was chosen has no effect on the probability of another individual being chosen. – If the numbers are randomly chosen, they are independent. 4

Stratified Sample – Used when the population is divided into subgroups( or strata) … AND we want to make sure each subgroup is represented in the sample Subgroups are based on similar characteristics (variables) Ex. Gender, ethnicity, etc. – A SRS is taken from each subgroup (strata) and combined into one large sample Other Types of Samples 5

Cluster Sample – Used when the population can also be divided into subgroups (or clusters) Subgroups are based on geographic groupings Ex. Counties in a state, schools within a district – One or more groups is randomly selected, and ALL members of the group(s) make up the sample 6 Other Types of Samples cont.

Systematic Sample – Starting with some member of the population, every ith member is selected for the sample. – Ex. As the student's walk into the cafeteria, every fourth student has their blood taken. Is fine as long as individuals are randomly placed in the line. Not a good way to sample humans (usually not random). 7 Other Types of Samples cont.

Convenience Sample – Consists only of available members of the population. – Ex. A survey taker in a cafeteria surveys the 10 tables closest to them 8 Other Types of Samples cont.

Voluntary Response Sample – Members of the population can choose to be part of the sample – Ex. surveys…viewer can choose to send it back or not 9 Other Types of Samples cont.

Examples: What type of sampling does the following represent? 5 randomly selected students from each of 4 classrooms at a school and is tested. The names of 80 students are put into a spreadsheet and 20 names are randomly selected. One of 4 classrooms in a school is selected, and all 20 students in that classroom are tested. 10

Voting in a presidential election 11 Examples: What type of sampling does the following represent?

Statistical Bias When the average value of the variable of interest is always different from the population mean in the same direction. – Ex. The (true) average math SAT score for all of PSB is 540. – If you sample only students in calculus courses (required by the science and engineering majors), the average SAT score will always be higher. Bias from samples occurs when the sample drawn is not representative of the population of interest. 12

Experiments vs. Observational Studies Response variable – what is measured as the outcome or result of a study Typically the main variable of interest Explanatory variable – what we think explains or causes changes in the response variable – often determines how subjects are split into groups Treatments – specific experimental conditions (related to the explanatory variable) applied to the subjects 13

An experiment was conducted to test the effect of nicotine patches to help people quit smoking. One group of smokers was given nicotine patches, and another group was given a placebo patch Is the percentage of people that quit smoking higher with those using a nicotine patch, or not? Variables: – Response: Percentage who quit smoking –Explanatory: Treatment assignment Treatments –Nicotine patch –Control patch 14 Experiments vs. Observational Studies

In an Experiment, the researcher can control the explanatory variable in the study In an Observational Study, the researcher can not control the explanatory variable – Why: impossible, or unethical – Ex. A researcher wants to study the effects of alcohol consumption during pregnancy on ave. birth weight 15 Experiments vs. Observational Studies