Targets 3A-3G

Question 1

Population

Answer 1

The larger group we hope to learn something about

Question 2

Census

Answer 2

Collect data from all members of a population

Question 3

Sample

Answer 3

Subset of the population that actually gets examined or measured

Question 4

Inference

Answer 4

Drawing a conclusion about a population based on data from a sample

Question 5

Sampling Variability

Answer 5

We don’t expect the statistic from a sample to be the same as if we calculated it from the population; each sample produces a different result.

Question 6

Random Sampling

Answer 6

typically produces a sample that is representative of the population

allows us to use the laws of probability to construct a margin of error

Larger ones give better information about a population than smaller ones

Question 7

Sample survey

Answer 7

A study that uses an organized plan to choose a sample that represents some specific population

Question 8

Good sample

Answer 8

representative of the population and will provide a good estimate of the value of interest

Question 9

Biased sample

Answer 9

Systematically over or under represents a portion of the population and would consistently overestimate or underestimate the value of interest

Question 10

Random Sampling Process

Answer 10

Use a chance process to determine which members of a population are included in the sample

Sampling without replacement: a member of the population can only be selected once

Sampling with replacement: a member of the population can be selected more than once

Question 11

Sampling frame

Answer 11

the list of all the potential subjects in a population

Question 12

Chance processes

Answer 12

flipping a coin, rolling dice, drawing names out of a well-mixed hat, random number generator, random digit table

Question 13

Random Sampling Benefits

Answer 13

is the number 1 way to fight bias. It avoids favoritism by the sampler and self-selection by the respondents.

Question 14

Simple Random Sampling (SRS) Characteristics

Answer 14

Every group of n individuals in the population has an equal chance of being selected for the sample.

Equivalent to throwing all members of a population into a hat, mixing them up, and then drawing without replacement

NOT the only legitimate method of random sampling

Question 15

Simple Random Sampling (SRS) Process

Answer 15

Choosing a sample of size n from a population of size N

1. Assign random numbers between 1 and N to each member of the population
2. Use randomness (calculator or table) to select n unique numbers. Be sure to state: ignore unused numbers; ignore repeats (for sampling without replacement)
3. The subjects corresponding to the chosen numbers are in the sample.

Question 16

Stratified Random Sampling

Answer 16

Split the sampling frame into homogeneous groups, then pick a random sample from each group.

Benefit :1 Reduces variability in the sample statistic (Field of Dreams Lab)

Benefit 2: Guarantees that all subgroups are represented in the sample; allows for subgroup comparisons

Question 17

Cluster Random Sampling

Answer 17

Split the sampling frame into heterogeneous clusters (members that are in close proximity to each

other), then randomly choose several clusters.

Sample ALL subjects in the randomly chosen clusters.

Benefit 1: Can make sampling less expensive by reducing travel time

Question 18

Systematic Random Sampling

Answer 18

Begin with a randomly selected individual; every nth!” member after that will be in the sample.

Larger values of n generate smaller samples. Smaller values of n generate larger samples.

Benefit: Can be easier to use than an SRS especially if the population is lined up (or listed) already

If we want a sample of size 3, we’ll choose every 5th member of the population. (15 ÷ 3 = 5)

To begin, we choose a random number between 1 and 5. Our random number was 4, so the 4th

member is the first one for the sample. We also include every 5th member after that.

Question 19

Biased Sample

Answer 19

Systematically over or under represents a portion of the population and would consistently overestimate or underestimate the value of interest.

Question 20

Convenience Sample

Answer 20

select individuals from the population who are easy to reach

Example: A farmer brings a juice company several crates of oranges each week. A company inspector looks at

10 oranges from the top of each crate before deciding whether to buy all the oranges.

Question 21

Voluntary Response Bias

Answer 21

happens when the sample is made up of subjects who chose to participate

Example: In 2016, Britain’s Natural Environment Research Council used an online poll to choose the name of

its new $300 million ship. The winning name “Boaty McBoatface” received 124,000 votes, far more than more

serious candidates “Shackleton”, “Endeavor”, and “Falcon”.

Question 22

Undercoverage Bias

Answer 22

happens when a subgroup of the population has little to no chance of being chosen

Example: In 1936 legitimate polling organizations such as Gallup were just getting started. That same year the

magazine Literary Digest, used the phone book to send out a presidential poll. 2.4 million out of 10 million

mailed ballots were returned. 57% said they would vote for Alf Landon (Rep) and 43% said they would vote

for Franklin Roosevelt (Dem). In the actual election, Landon only won electoral votes from two states.

Question 23

Response Bias / Question Wording bias

Answer 23

happens when the method of the survey (or the wording of the questions) influences the responses given by subjects

Example: How do the results from the Pierre, SD survey illustrate response bias?

Question 24

Nonresponse bias

Answer 24

happens when a portion of the chosen sample does not respond to the survey; the non-respondents may share a common characteristic such as being stressed or busy

Example: With our modern-day caller ID feature, many people do not answer their phone when a polling

organization calls.

Question 25

Observational Study

Answer 25

researchers observe their subjects

no treatment is imposed on the subjects

there is no control over other variables

vulnerable to confounding variables

Question 26

Retrospective observational study

Answer 26

data are collected from past events or records; could be unreliable if subjects must recall information

Question 27

Prospective observational study

Answer 27

subjects are identified at the beginning of the study and measurements are taken as the study unfolds; this could get expensive

Question 28

Explanatory variable

Answer 28

a variable that we think explains or causes changes in the response variable

Question 29

Response variable

Answer 29

the outcome being measured

Question 30

Confounding Variable

Answer 30

a variable that is related to the explanatory variable and influences the response variable. It may create a false perception of an association between the explanatory and response variables.

Question 31

Writing about a confounding variable

Answer 31

1. Link the confounding variable to the explanatory variable.
2. Link the confounding variable to the response variable.

Question 32

Experiment

Answer 32

researchers randomly assign treatments to the subjects

Question 33

Nature

Answer 33

Was a treatment randomly assigned to the subjects?

• No! We can only draw the conclusion that the two variables are associated.

• Yes! We can draw a cause-and-effect conclusion.

Question 34

Scope

Answer 34

Was the sample randomly chosen?

• No! We may not generalize our conclusions to the larger population.

• Yes! We may generalize our conclusions to the larger population.

Question 35

experimental unit / subject

Answer 35

the individuals to which treatments are applied

Question 36

explanatory variables / factor

Answer 36

variables whose levels are manipulated intentionally

Question 37

levels

Answer 37

dosages or durations of a factor

Question 38

treatments

Answer 38

the specific combinations of levels that are imposed on the groups of subjects

Question 39

placebo

Answer 39

a treatment that has no active ingredient but is otherwise like other treatments

Question 40

placebo effect

Answer 40

subjects show an improvement after receiving a placebo simply because they expect an

improvement

Question 41

blinding

Answer 41

keeping human participants unaware of the treatment applied in order to reduce response bias

Question 42

single blind study

Answer 42

subjects do not know which treatment they are receiving, but members of the

research team who interact with them do, or vice versa

Question 43

double blind study

Answer 43

neither the subjects nor the members of the research team who interact

with them know which treatment a subject is receiving

Question 44

inference

Answer 44

using the results from a sample to draw a conclusion about the population

The results of a study are considered to be statistically significant when the observed results are too unusual

to be explained by chance alone.

Question 45

Comparison

Answer 45

compare two or more treatment groups

Question 46

Random Assignment Benefits

Answer 46

creates roughly equivalent groups of subjects

to balance the effects of unknown variables; also reduces bias

Question 47

Control

Answer 47

control the levels of the explanatory factor and keep all other variables as similar as possible;

control prevents confounding

Question 48

Control Group

Answer 48

group that receives the currently accepted treatment or no treatment at all; this

counts as one of the levels

Question 49

Replication

Answer 49

apply the treatments to many subjects; also, run the study multiple times (in another location)

Question 50

Random Chance Experiments

Answer 50

We rely on random chance to create groups that resemble each other so that the only differences between the

groups are the treatments imposed.

If we find that one group’s results are better than the other’s we can be reasonably certain that the explanatory

variable caused the difference.

Question 51

Random Assignment of Treatments

Answer 51

If group sizes don’t need to be equal we can use a coin flip, roll dice or use a random digit table,

allowing repeats.

If group sizes must be equal we can write treatments on slips of paper or use a random digit table,

ignoring repeats.

Don’t flip a coin until one group is filled. Putting the rest of the subjects in the other group could

unintentionally create a confounding commonality in that group.

Question 52

Describing a Completely Randomized Experiment

Answer 52

1. Begin with a group of subjects.
2. Randomly assign subjects to the treatment groups. State the treatments in context and explicitly link

each random outcome to a treatment.

3. State the response variable in context that will be compared at the end of the experiment.

Question 53

Randomized Block Experiment

Answer 53

The pool of subjects is purposely divided into blocks of homogenous subjects.

Within each block subjects are randomly assigned to treatments.

At the end of the experiment the measurements from each treatment group will be compared to the other treatment groups in the same block

We block on variables that we believe will affect the response variable so that the only differences between the treatment groups are the treatments

Blocking reduces variability in the results (much like stratification in sampling)

Question 54

Statistics Haiku Rule 1

Answer 54

Control what you can - make the circumstances as similar as possible for all subjects, except for the explanatory variable – reduce confounding

Question 55

Statistics Haiku Rule 2

Answer 55

Block on what you can’t control - if there is a variable that is suspected to affect the response variable, block on that variable to reduce confounding

Question 56

Statistics Haiku Rule 3

Answer 56

Randomize the rest - Random assignment creates similar treatment groups. The effects of any unknown confounding variable should be minimized if it is equally represented in all groups

Question 57

Matched Pair Design

Answer 57

The pool of subjects is purposely divided into blocks of size two (pairs)

Two subjects who are as alike as possible have treatments randomly assigned to them.

One subject provides two measurements with the order of treatments randomly determined

At the end of the experiment the differences between the 2 measurements will be analyzed

matched pair studies are very powerful because they can control for many many variables