Chapter 1 Section 2

1. Chapter 1Section 2 Observational Studies, Experiments, and Simple Random Sampling

2. 2 1 Chapter 1 – Section 2 • Learning objectives • Distinguish between an observational study and an experiment • Obtain a simple random sample

3. 2 1 Chapter 1 – Section 2 • Learning objectives • Distinguish between an observational study and an experiment • Obtain a simple random sample

4. Chapter 1 – Section 2 • There are different ways to collect data • Census • Existing sources • Survey sampling • Designed experiments • These are good methods of data collection, if done correctly

5. Chapter 1 – Section 2 • A census is a list • Of all the individuals in a population • That records the characteristics of the individuals • An example is the US Census held every 10 years (this is only an example though) • A census is a list • Of all the individuals in a population • That records the characteristics of the individuals • An example is the US Census held every 10 years (this is only an example though) • Advantages • Answers have 100% certainty • A census is a list • Of all the individuals in a population • That records the characteristics of the individuals • An example is the US Census held every 10 years (this is only an example though) • Advantages • Answers have 100% certainty • Disadvantages • May be difficult or impossible to obtain • Costs may be prohibitive

6. Chapter 1 – Section 2 • An existingsource is • An appropriate data set has already been collected • That can be used for this study • An existingsource is • An appropriate data set has already been collected • That can be used for this study • Advantages • Saves time and money • An existingsource is • An appropriate data set has already been collected • That can be used for this study • Advantages • Saves time and money • Disadvantages • There may not be an applicable data set

7. Chapter 1 – Section 2 • A surveysample is • A study when only a subset of the population is considered • A study where there is no attempt to influence the value of the variable of interest • A surveysample is • A study when only a subset of the population is considered • A study where there is no attempt to influence the value of the variable of interest • Advantages • Saves time and money • A surveysample is • A study when only a subset of the population is considered • A study where there is no attempt to influence the value of the variable of interest • Advantages • Saves time and money • Disadvantages • Choosing an appropriate sample could be difficult

8. Chapter 1 – Section 2 • A survey sample is an example of an observationalstudy • An observational study is one where there is no attempt to influence the value of the variable • An observational study is also called an expostfacto (after the fact) study • A survey sample is an example of an observationalstudy • An observational study is one where there is no attempt to influence the value of the variable • An observational study is also called an expostfacto (after the fact) study • Advantages • It can detect associations between variables • A survey sample is an example of an observationalstudy • An observational study is one where there is no attempt to influence the value of the variable • An observational study is also called an expostfacto (after the fact) study • Advantages • It can detect associations between variables • Disadvantages • It cannot isolate causes to determine causation

9. Chapter 1 – Section 2 • A designedexperiment is an experiment • That applies a treatment to individuals • Often compares the treated group to a control (untreated) group • Where the variables can be controlled • A designedexperiment is an experiment • That applies a treatment to individuals • Often compares the treated group to a control (untreated) group • Where the variables can be controlled • Advantages • Can analyze individual factors • A designedexperiment is an experiment • That applies a treatment to individuals • Often compares the treated group to a control (untreated) group • Where the variables can be controlled • Advantages • Can analyze individual factors • Disadvantages • Cannot be done when the variables cannot be controlled • Cannot apply in cases for moral / ethical reasons

10. Chapter 1 – Section 2 • Observational studies and designed experiments have some fundamental differences • Observational studies and designed experiments have some fundamental differences • Observational studies do not control the variable under analysis while designed experiments do • Observational studies and designed experiments have some fundamental differences • Observational studies do not control the variable under analysis while designed experiments do • Because variables are uncontrolled in an observational study, the results can only be associations • Observational studies and designed experiments have some fundamental differences • Observational studies do not control the variable under analysis while designed experiments do • Because variables are uncontrolled in an observational study, the results can only be associations • Because variables are controlled in a designed experiment, the results can be conclusions of causation

11. Chapter 1 – Section 2 • A danger in observational studies are lurkingvariables • In an observational study, two variables can be determined to be associated • Associated does not mean that one causes the other • A simple observational study may find that smoking and cancer are associated • Cannot conclude that smoking causes cancer • Cannot conclude that cancer causes people to smoke

12. Chapter 1 – Section 2 • Usually only a part of the population can be analyzed • How do you choose your sample? • The process is called sampling • We will discuss • Simple random sampling • Stratified sampling • Systematic sampling • Cluster sampling • Convenience sampling

13. 1 2 Chapter 1 – Section 2 • Learning objectives • Distinguish between an observational study and an experiment • Obtain a simple random sample

14. Chapter 1 – Section 2 • A simplerandomsample is when every possible sample of size n out of a population of N has an equally likely chance of occurring • A simplerandomsample is when every possible sample of size n out of a population of N has an equally likely chance of occurring • Examples • For a simple random sample of size n = 1 from a population size of N = 5, each of the 5 possible samples has an equally likely chance of occurring • For a simple random sample of size n = 2 from a population size of N = 4, each of the 6 possible samples has an equally likely chance of occurring

15. Chapter 1 – Section 2 • Simple random sampling requires that we have a list of all the individuals within a population • This list is called a frame • If we do not have a frame, then a different sampling method must be used

16. Chapter 1 – Section 2 • A simple (but not foolproof) method • Write each individual’s name on a separate piece of paper • Put all the papers into a hat • Draw a random paper from the hat • Physical methods have some issues • Are the papers sufficiently mixed? • Are some of the papers folded?

17. Chapter 1 – Section 2 • A method using a table of random numbers • List and number the individuals • Decide on a way to pick the random numbers (how to choose the starting point and what rule to use to select which digits to choose after that) • Select the random numbers • Match the numbers to the individuals • With the technology available today, this method is outdated

18. Chapter 1 – Section 2 • A method using technology • List and number the individuals • Use software (a calculator, software such as MINITAB or Excel) to generate random numbers • Match the random numbers to the individuals • The method must be decided in advance … it is not statistically correct to choose a series of samples until a “good” one comes up

19. Chapter 1 – Section 2 • Simple random sampling example • We wish to select a random sample of 3 out of a group of 30 students • To choose the first student • Simple random sampling example • We wish to select a random sample of 3 out of a group of 30 students • To choose the first student • We generate a two digit random number • If it is between 01 and 30, we select the student with this number • If it is not between 01 and 30, we select another two digit random number (until we get a number that can be used)

20. Chapter 1 – Section 2 • To choose the second student • To choose the second student • We generate a two digit random number • If it is between 01 and 30, and not equal to the number of the first student, then we select the student with this second number • If it is not between 01 and 30, or if it is equal to the first number selected, then we select another two digit random number (until we get a number that can be used) • To choose the second student • We generate a two digit random number • If it is between 01 and 30, and not equal to the number of the first student, then we select the student with this second number • If it is not between 01 and 30, or if it is equal to the first number selected, then we select another two digit random number (until we get a number that can be used) • We repeat the process to choose the third student

21. Summary: Chapter 1 – Section 2 • There are different ways of collecting data • A census uses the entire population • An existing source use an existing data set • An observational study measures the characteristics of a sample without influencing the variable of interest • A designed experiment applies a treatment to a sample to isolate the effects of a variable • The method of simple random sampling can be used to select the sample