AP STATs U1 Test

Convenience Sample

Easy to reach

Voluntary Response

People choose to respond

SRS(Simple Random Sample)

Low Bias - choose group from pop so every individual and groups of individuals is equally likely.

SRS Steps

1. Label Each Individual

2. Randomize(Ex. RNG)

3. Select Individuals by Label

Stratified Random Sample

Split the population into homogenous groups(strata) and conduct an SRS in each strata. Statistical benefit only if you stratify based on response. “sample some from all groups” 

Good Estimates

A sampling method produces the best estimates if there is:

• low variability 

• low bias

Cluster Sample

Groups are heterogenous. ‘sample all from some groups’ 

Systematic Random Sample

• Random Starting Point

• Use equal intervals (ex. choose every 5)

Potential Problems with Sampling:

Undercoverage

Some people are less likely to be chosen. ex. calling landlines

Potential Problems with Sampling:

Nonresponse

cant be reached / refuse to answer

Potential Problems with Sampling:

Response Bias

Problems in data gathering process(ex. self reported and ppl lie)

Explanatory Variable

• The variable you think explains or influences changes in another variable.

• Example: The number of hours studied.

Response Variable

• The variable that is measured as an outcome.

• Example: The test score.

Confounding Variable

• A lurking variable that affects both the explanatory and the response variable, making it hard to tell if the explanatory variable is truly causing the change.

• Example: Student motivation → motivated students both study more and tend to score higher, so it confounds the relationship between hours studied and test scores.

Observational Study

No treatment imposed.

• Prospective(Looks forward)

• Retrospective(Looks back)

Experimental Study

Treatments, show causation.

Experimental Units

What/Who Treatment is imposed on

Treatments

what is done/not done to experimental units

Well-Designed Experiment

1. Comparison - 2+ Treatments

2. Random Assignment

3. Replication - more than 1 in each treatment group

4. Control - keep other variables constant

Random Assignment

1. Label

2. Randomize

3. Assign(+ specify treatment)

• to show causation

Placebo Effect

When a fake treatment(placebo) works.

Blinding

When subjects(single blind) and or/experimenters(double) don’t know about the treatments.

Block Design

Block - Group of experimental units that are similar

Randomized Block Design:

• Separate Subjects into blocks and then randomly assign treatments within

• Compare. 

Matched Pairs Design

Randomized Block Design where block size is 2 and there are 2 treatments. Make pairs by similarity(ex. old ppl pairs) and randomly assign 2 treatments to 2 ppl. 

Statistically Significant

• When results are unlikely(less than 5%) to happen by chance

• If SS, we have convincing evidence that the treatment caused the difference.

Simulation

Process:

• Assume the null hypothesis is true (no real difference/effect).

• Shuffle or simulate data many times to create outcomes that could happen by random chance.

• Compare your actual result (like a difference in means or proportions) to this simulated distribution.

• If your observed result is far in the tails (rare compared to what chance alone produces), you call it statistically significant.

Basically, plot the points of the random simulation where you assume there is no difference. Then, make a vertical line on the number line of percentage difference where the experiment showed. Make an arrow based on your hypothesis and count the amount of dots in the arrows direction of the line vs not. use that to make a fraction and see if it is below 5%. 

Scope of Inference

A Random Sample allows us to generalize our conclusions to the population from which we sampled. 

Surveys vs. Experiments

Surveys → sampling methods (SRS, stratified, cluster, systematic).

Experiments → assignment methods (completely randomized, block, matched pairs).