AP Stat Ch 4 Flashcards
Experiment
Investigates how a response variable behaves when the researcher manipulates one or more factors (or explanatory variables). The purpose is usually to determine if changes in the explanatory variable cause changes in the response variable (what you are measuring). An experiment deliberately imposes some treatment on individuals to observe their response
Observational study
Investigates characteristics of a sample in order to draw conclusions about a population
Does not attempt to influence responses.
Confounding variable
Variable related to both the explanatory variable and to the response variable
Simulation
A simulation consists of a collection of things that happen at random. There is a simulation that is repeated. These situations are called components of the simulation. Each component has a set of possible outcomes
Population
Entire group of individuals that we want information about in a statistical study
Sample
Part of the population from which we actually collect information. Use the info from the sample to draw conclusions about the entire population
Voluntary response
People who choose themselves by responding to a general appeal. This type of sample shows bias because people with strong opinions, often in the same direction, are most likely to respond.
Convenience sampling
Choosing the individuals easiest to reach. Biased
Bias
Favors some part of the population over others. The design of a study is biased if it systemically favors certain outcomes
When describing bias, identify the direction of the bias!
Simple random sample
Simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.
Use calculator or tablet in textbook
Population of interest vs inference
Population of interest is the population we want to know about and the population of inference is the population we can actually make conclusions about based on the subjects chosen in the sample.
If there is selection bias, then these populations aren’t the same
Stratified random sample
Separate the population into like strata and then randomly pick from within each group and choose porpoprtiojallg.
Cluster sample
Cluster sampling divides the population into groups, which should mirror the characteristics of the population. Then choose an SRS of these clusters. All the individuals in the chosen clusters are selected to be in the sample.
Disadvantages of SRS
large sample is hard to do
Doesn’t guarantee sample will be reperesentative of the population. Possible certain groups are over or under represented by chance
Systematic sample
k= N / n where N is popilation size and n is sample size. Every kth person selected is chosen
Variability
The variability of an estimate refers to the range of values that estimate can take in repeated sampling. If there is a lot of variability, it is difficult to be precise in our estimation.
How do sample size and population size affect variability?
Higher sample size causes less variability because closer to the mean w more values
Popilation sized doesn’t affect variability
Bias vs variability
Bias affects the center making it too high or too low. We can eliminate this by random sampling.
Variance can be reduced by increasing the sample size
Selection bias
Introduced when some part of the population is systematically underrepresented in the sample. In other words, it occurs when some groups in the population are left out of the process of choosing the sample.
Ex. Gettysburg address: smaller words were underrepresented
Ex. Homeless people are not eligible for surveys because they can’t be called or visited
Selection bias also occurs when volunteers self select themselves for a sample. People who voluntarily respond to surveys tend to have different and stronger opinions than the rest of the population
Ex. 1-900 phone in surveys, magazine mail in surveys, internet surveys…
Response bias
Occurs when our method of collecting the data tends to produce values that systematically differ from the true population value in some way. Response bias occurs once the sample has been selected. Also called measurement bias.
Ex. Using a faulty instrument
Ex. Wording of questions
Ex. Characteristics of the interviewer
Ex. Human nature
Voluntary response vs convenience sample
Voluntary response, people choose whether to respond
Convenience, interviewer makes the choice.
In both cases, personal choice produces bias.
Non-response bias
Occurs when responses are not actually obtained from subjects chosen for the sample. Could occur because an individual chosen for the sample can’t be contacted or does not cooperate.
Experiment group vs control group
Exp group receives the treatment
Control group receives a placebo
Placebo effect
So that both groups think they are receiving the treatment, this allows for the difference between the groups to be attributed to the explanatory variable and not the excitement of being in an experiment
Treatment
Factors * levels
Factors
A controlled independent variable.
Variable who’s levels are set by the experiment
Levels
Different treatments constitute different levels of a factor.
If there is salt or no salt, two levels. One factor. Two treatments
Blind
When a person doesn’t know who is receiving which treatment, that person is blind
Single vs double blind
There are two classes of individuals who can influence the results of an experiment:
- Those who could influence the results (subjects, treatment administrators)
- Those who evaluate the results
When every individual in one of these cases is blinded, single blind.
If every in both classes is blinded, then double blind.
Without blindness, experimenter could favor one group or another.
Experimental units
Smallest collection of individuals to which treatments are applied. When the units are humans, they often are called subjects
Direct control
Holding extraneous factors constant so that their effects are not confounded with the explanatory variable. Comparison of several treatments in the same environment is the simplest form of control.
Randomization
Random assignment of subjects to treatments to ensure that the experiment doesn’t systematically favor one treatment over the others. It is an essential ingredient for a good experimental design. Uses some sort of chance process.
Blocking
When subjects / experimental units are divided into homogenous groups (blocks) based on some extraneous variable and then separated randominly into different repayment groups.
Different type of experiment
Completely randomized design vs randomized block design
Matched pair
If each block has only 2 subjects, then the subjects are called a matched pair.
Matched pair design if a common type of randomized block design for comparing two treatments. Create blocks by matching pairs of similar experimental units then use chance to decide which member of a pair gets first treatment. Other member of the pair gets the other treatment.
Sometimes each pair consists of just one experimental unit that gets both treatments. Order can influence response, so randomize order for each unit
Replication
Means ensuring that there is an adequate number of observations in each treatment group. This will reduce chance variation in the results.
