AP Stats 1.10 Questions & Study TypesAP Stats 1.10 Questions & Study Types

APS TAT ISTICS · UNIT1B

Investigative Questions and Study Types

Topics 1.10A and 1.10B

In one sentence: every study starts with a question, and how the data were collected (experiment or observational, random or not) decides what you are allowed to conclude.

1.10A The three-part investigative question

Component What it names What it guides

1. Variable of interest What is measured on each unit How data are

collected

2. Parameter and

direction

The true mean or proportion, and greater than, less than,

different, or just estimate

Which analysis you

run

3. Population and

conclusion

Who the results apply to, and whether cause and effect is

justified

What you can claim

Template: "Is the true [mean or proportion] of [variable] [greater than, less than, different] for [group], among all [population]?"

Example. Wait times at 6 emergency rooms, benchmark 30 minutes. (1) wait time in minutes. (2) true mean wait time, direction greater than 30. (3) all patients of these 6 ERs, no cause and effect tested. Census

A census records every individual in the population. Whether something is a census depends on which population you name. All patients seen in March is a census of March patients, but only a sample of all patients the ERs ever see.

Trap. Contacting 15 of 38 owners is a sample, not a census. A census needs every individual in the population, even when the population is small.

1.10B Observational studies and experiments

Type Definition Conclusion allowed

Observational

study

Researcher records variables, imposes no

treatment

Association only, never cause and effect

Prospective Select units now, gather data now and into the

future

Retrospective Select units now, gather data from the past

Survey Observational study using a standard set of

questions to humans

Experiment Researcher assigns treatments to experimental

units

Cause and effect if treatments were

randomly assigned

Why observational studies cannot prove cause: there may be a lurking variable that explains the relationship. Think "motivation wearing a disguise": front-row students score higher, but motivated students choose the front row.

Experiment vocabulary

Experimental unit: what receives the treatment (called subjects or participants if people). Explanatory variable (factor): the variable whose levels you impose. The levels are the treatments. Response variable: the outcome measured afterwards.

Two or more factors: treatments are every combination of levels. 3 temperatures × 2 times = 6 treatments.

Confounding variable

A confounding variable must be associated with both the explanatory variable and the response variable, and it offers an alternative explanation. Always say how it connects to each one. Random selection vs random assignment

Random selection Random assignment

What it does Chooses units from a population Puts units into treatment

groups

What it

allows

Generalizing to the population sampled Cause and effect

If missing Generalize only to people similar to those studied (volunteers,

deliberate picks)

Only association

Trap. A study can have one, both, or neither. A volunteer study with random assignment gives cause and effect for those volunteers only.

Worked examples

1. Streaming screens. 2,000 volunteers randomly assigned to Design A, B or C. Experiment (treatments imposed). Units: the 2,000 members. Explanatory: design (A, B, C). Response: still subscribed after 6 months. Generalize only to members similar to the volunteers.

2. Instrument and memory. 800 adults randomly selected from a registry, tracked 8 years. Observational and prospective. Confounder example: education (linked to playing an instrument and to memory). Generalize to adults 60+ in that registry because the sample was random.

Practice

1. A hospital measures the wait time of every patient in March and wants conclusions about all future patients. Is it a census of the population in the question?

2. Students are asked a fixed list of questions about earbud use and hearing. Name the study type. 3. Adults are selected today and their medical records from the past 10 years are collected. 4. A lab tests 3 drying temperatures and 2 drying times. How many treatments, and are they listed as temperatures or combinations?

5. Streetlights and crime are associated. Neighborhood income is proposed as a confounder. What two things must be true?

6. 250 members are randomly selected from a book club, then randomly assigned paper or e-reader. Paper wins. What conclusion fits?

7. Same study but the 250 are volunteers. What changes?

8. Write component 2 for: does a new app change mean daily steps between city and rural users? Answer key

1. No. It is a census of March patients only. For all patients it is a sample (and not a random one). 2. Survey (an observational study).

3. Retrospective observational study.

4. 6 treatments, the 3 × 2 combinations.

5. Income is associated with the number of streetlights and also with the amount of crime. 6. Paper caused higher comprehension, and it generalizes to all club members. 7. Cause and effect still holds, but it generalizes only to people similar to the volunteers. 8. Is the true mean number of daily steps different between urban and rural users?