Sullivan – Statistics: Informed Decisions Using Data – 2 nd Edition – Chapter 1 Section 2 – Slide 1 of 21 Chapter 1 Section 2 Observational Studies, Experiments,

Sullivan – Statistics: Informed Decisions Using Data – 2nd Edition – Chapter 1 Section 2 – Slide 1 of 21

Chapter 1Section 2

Observational Studies, Experiments,and Simple Random Sampling


Chapter 1 – Section 2

● Learning objectives Distinguish between an observational study and an

experiment Obtain a simple random sample2

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● There are different ways to collect data Census Existing sources Survey sampling Designed experiments

● These are good methods of data collection, if done correctly



● 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)


(this is only an example though)● Advantages

Answers have 100% certainty


(this is only an example though)● Advantages

Answers have 100% certainty● Disadvantages

May be difficult or impossible to obtain Costs may be prohibitive



● An existing source is An appropriate data set has already been collected That can be used for this study


● Advantages Saves time and money


● Advantages Saves time and money

● Disadvantages There may not be an applicable data set



● A survey sample 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



value of the variable of interest● Advantages

Saves time and money



value of the variable of interest● Advantages

Saves time and money● Disadvantages

Choosing an appropriate sample could be difficult



● A survey sample is an example of an observational study An observational study is one where there is no

attempt to influence the value of the variable An observational study is also called an ex post facto

(after the fact) study



(after the fact) study● Advantages

It can detect associations between variables



(after the fact) study● Advantages

It can detect associations between variables● Disadvantages

It cannot isolate causes to determine causation



● A designed experiment 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



● Advantages Can analyze individual factors

● Disadvantages Cannot be done when the variables cannot be

controlled Cannot apply in cases for moral / ethical reasons



● 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


under analysis while designed experiments do Because variables are uncontrolled in an

observational study, the results can only be associations


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



● A danger in observational studies are lurking variables

● 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



● 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





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● A simple random sample is when every possible sample of size n out of a population of N has an equally likely chance of occurring

● A simple random sample 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



● 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



● 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?



● 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



● 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



● 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)



● 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


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

Documents

Sullivan – Statistics: Informed Decisions Using Data – 2 nd Edition – Chapter 1 Section 2 – Slide 1 of 21 Chapter 1 Section 2 Observational Studies, Experiments,