ap stats

undercoverage bias

Some groups of the population are left out of the sampling process, or have a much smaller chance of being chosen.
Example: A phone survey that only calls landlines misses people who only have cell phones, who tend to be younger.

Voluntary response bias

People choose themselves to be in the sample, usually because they feel strongly about the topic. Strong, often negative, opinions end up overrepresented.
Example: An online poll asking “Should the school day be shorter?” mostly gets answers from students who really want it shorter.

Nonresponse

People were selected for the sample but don’t respond, or can’t be reached. If the people who don’t respond differ from those who do, the results are skewed.
Example: A survey on work hours gets few replies from people working two jobs, because they’re too busy to answer.

Response bias

Anything that leads people to give inaccurate or untruthful answers. The next three are specific types of response bias.

Question wording bias

The way a question is phrased pushes people toward a certain answer. Causes include loaded words, leading questions, and confusing wording.
Example: “Don’t you agree that the dangerous new highway should be stopped?” The word “dangerous” and the “don’t you agree” phrasing both steer the answer.

Interviewer bias

Something about the interviewer influences the responses, such as their tone, appearance, reactions, or who they are.
Example: People asked about their opinions on police by a uniformed officer may answer more favorably than they really feel.

Self-reporting bias

People misreport information about themselves. They may make themselves look better (social desirability), misremember, or exaggerate.
Example: People asked how often they exercise or how much they drink tend to overstate the exercise and understate the drinking.

Convenience sample

This happens when you pick the people who are easiest to reach instead of choosing randomly. The people who are easy to get usually aren’t representative of the whole population, so the results are skewed.

Example: To find out how much students at your school study, you survey only the people sitting near you in the library. Students in the library probably study more than average, so your estimate would be too high.

population mean

mew u

sample mean

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When using Simple random sample…

Label (assign with numbers 1-++)

Randomize with RNG to select integers from ___ to ____

Select assign ____ integers to find the mean

cluster random sample

Sample all people from some groups

EX: pick 2 mini bags of candy/10 and only sample skittles and m&ms, but completely miss out from the twizzlers and sour patch groups.

systematic random

You pick a random starting point, then pick every nth individual from a list.

EX:You want 50 students from a list of 1,000. Since 1,000 ÷ 50 = 20, you randomly pick a number from 1 to 20, say 7. Then you choose students #7, #27, #47, #67, and so on.

Stratified random sampling

Divide populations into groups (called stratas) based on characteristics like grade levels, gender, or age and then take a seperate sample from each group and combine them.

Example: Your school has 400 freshmen, 300 sophomores, 200 juniors, and 100 seniors. To survey 100 students, you randomly pick 40 freshmen, 30 sophomores, 20 juniors, and 10 seniors.

Why use it: It guarantees every group is represented, and it usually gives more precise estimates when the groups differ from each other on what you’re measuring.

Key idea: People within each stratum should be similar to each other, and the strata should be different from one another.

Observational study

researcher observes individuals and measures variables but doesn’t impose any treatment or try to change anything

*cannot determine causation, can only show association

Experiment

The researcher deliberately imposes a treatment on individuals to see how they respond.
Example: Researchers randomly assign 100 adults to drink either 3 cups of coffee a day or none for a month, then measure their blood pressure.

only a well-designed experiment can show cause and effect

explanatory variable

may explain or cause changed in another variable. In an experiment it is what the researcher changes (IV)

Response variable

Outcome being measured, variable may change because of the explanatory variable (sometimes the dependent variable)

Confounding variable

A third variable that affects the response variable

Ice cream sales and drowning deaths rise together. Ice cream doesn’t cause drowning. Hot weather increases both.

A well designed experiment includes….

a randomization of subjects, replication of treatments, control of confounding variables and comparison of response variable results

Single-blind

Either the subjects or the people measuring the results don’t know which treatment each subject received but not both

Double blind

Neither the subjects nor the people interacting with them and measuring the response know who received which treatment

Why it’s better: It removes bias from both sides, so the results reflect the treatment itself rather than anyone’s expectations.

Randomized block design

Sort experimental units into groups (blocks) that are similar in some way that could effect the results and within each block you randomly assign the treatments

Example: You’re testing 2 fertilizers on 60 tomato plants. But 30 plants are in a sunny part of the greenhouse and 30 are in a shady part. Sunlight affects growth, so:

1. Make two blocks: sunny plants and shady plants.

2. In the sunny block, randomly give 15 plants Fertilizer A and 15 Fertilizer B.

3. Do the same in the shady block.

4. Compare the fertilizers within each block

Why use it: Sunlight can no longer mess up the comparison, because each fertilizer is tested on both sunny and shady plants, and you compare like with like.

In simple words: Group similar things together first, then randomize inside each group.

Matched pairs design

A special type of block design where each block has only 2 units (or 1 unit used twice) and there are 2 treatments.

Example: Testing whether caffeine improves reaction time, each person is tested once with caffeine and once without. A coin flip decides which comes first, so getting tired or getting practice doesn’t unfairly favor one treatment.