AP Stats Unit 1 Part 2 study guideAP Stats Unit 1 Part 2 study guide

Collecting Data

1F Introduction to Data Collection 1G Sampling: Good and Bad 1H Experimental Design

T H E W H O L E U N I T I N F O U R S E N T E N C E S

1. Random selection of individuals lets you generalize to the population they came from.

2. Random assignment of treatments, with a statistically significant result, lets you say cause and effect.

3. Bias is a flaw in the method that pushes estimates in one direction. A bigger sample does not fix it.

4. A good experiment has four things: comparison, random assignment, replication and direct control.

How to use this guide. Read the summary box at the top of each section, study the diagram, then cover the answer

under each Quick check and try it. The red Trap boxes are the mistakes that cost points on free-response questions.

Introduction to Data Collection

2 0 - S E C O N D S U M M A R Y

An experiment imposes treatments. An observational study only watches. Only an experiment with random

assignment can show cause and effect, because in an observational study a confounding variable may be the real

explanation. Who the results apply to depends on whether the individuals were randomly selected.APS TAT ISTICS · UNIT1 PA RT2 · V I S U A L S T U D Y G U I D ESections 1F, 1G and 1H: how data are collected, how sampling goes right and wrong, and how to design an experiment you can trust. Built from the class notes packet.SECTION1 FExperiments, observational studies, confounding, generalizing, and the investigative question.

Experiment or observational study?

Did the researchers impose treatments?

YES NO

EXPERIMENT

treatments assigned to units

OBSERVATIONAL STUDY

only observe and measure

Randomly assigned + significant result

= can conclude CAUSE AND EFFECT

Retrospective

data from the past

Prospective

follow into future

Survey

ask questions

Association only. Confounding is possible, so no cause and effect.

One question sorts every study: did the researchers assign the treatments, or did the individuals end up in their groups on their own?

TRAP

Comparing two groups does not make a study an experiment. If students choose flashcards or practice tests and you compare their scores, that is an observational study, because nobody assigned the method.

The parts of an experiment

Term What it is In the lobster example

Response variable Measures an outcome of the study. Growth of the shell

Explanatory variable May help explain or predict changes in the

response.

The diet

Factor An explanatory variable that is manipulated in an

experiment.

Protein amount; L:CHO ratio

Level One of the values of a factor. 400 or 500 g/kg; low, medium,

high

Treatment A specific condition applied to the units. With

more than one factor, a treatment is a

combination of levels.

500 g/kg protein with a low

ratio

Experimental unit The item or individual a treatment is assigned to.

Called subjects when they are people.

The lobsters

2 factors: protein (2 levels) x L:CHO ratio (3 levels) = 6 treatments

Low ratio Medium ratio High ratio

400 g/kg protein Treatment 1

400 + low

Treatment 2

400 + medium

Treatment 3

400 + high

500 g/kg protein Treatment 4

500 + low

Treatment 5

500 + medium

Treatment 6

500 + high

Experimental units = the lobsters. Response variable = growth of the shell.

Count treatments by multiplying the levels, never by adding them: 2x3 = 6, not 2 + 3 = 5.

TRAP

The experimental unit is whatever the treatment was assigned to, not whatever was measured. If 24 classrooms are randomly assigned a type of lighting and 600 students are tested, there are 24 experimental units, not 600.

QUICK CHECK

An experiment uses 3 temperatures and 4 humidity settings on 96 trays, equally divided. How many treatments, and how many trays per treatment?

Answer: 3x4 = 12 treatments, and 96 / 12 = 8 trays each.

Kinds of observational study

Units selected NOW

PAST FUTURE

RETROSPECTIVE

look back at existing records

PROSPECTIVE

collect data now and going forward

Retrospective looks back, prospective looks forward. A survey is an observational study that collects data from people by asking a common set of questions.

Confounding

An extraneous variable is any variable other than the explanatory variable that may affect the response. It becomes a confounding variable only if it is associated with both the explanatory variable and the response. Then you cannot tell which one caused the change.

EXPLANATORY

visits the coast often

RESPONSE

better health

CONFOUNDING VARIABLE

income

causes? can't tell

higher income =

more trips

higher income =

better care

It must be linked to BOTH. Linked to only one side = not confounding.

The two red arrows are the proof. To show confounding on a free-response question, you must explain both links. Sentence frame for confounding: "[Variable] is a possible confounding variable. People who [have more of it] are more likely to [be in this explanatory group], and people who [have more of it] also tend to [have this response]. So we can't tell whether [explanatory] or [the variable] is the cause of [response]."

TRAP

"Study time affects GPA" is not enough to make study time a confounder in a breakfast-and-GPA study. You must also say how study time is related to eating breakfast. One link only = extraneous, not confounding. Scope of inference: what can you conclude?

Were treatments RANDOMLY ASSIGNED?

YES NO

Were individuals

RANDOMLY SELECTED? YES

NO

Cause and effect: YES

Generalize to population: YES

Cause and effect: NO

Generalize to population: YES

Cause and effect: YES

Only for units like those studied

Cause and effect: NO

Only for units like those studied

Random selection decides WHO it applies to. Random assignment decides WHETHER it is causal. Two separate questions, two separate kinds of randomness. Most experiments use volunteers, so they land in the bottom-left box: cause and effect, but only for individuals like the ones in the study.

QUICK CHECK