AP Stats- Chapter 12

• Based on data in which no manipulation of factors has been employed

• The researchers merely observe what is happening or what happened in the past

  • Two types: Retrospective and Prospective

    • Not possible for either type to demonstrate a casual relationship

• An observational study

• Subjects are selected and then their previous conditions/behaviors are determined

  • ex: first identified subjects who studied music and then collected data on their past grades

• Does not usually need to be based on random sampling

• Usually focuses on estimating differences between groups or associations between variables

• Can have errors because these are based on historical data

  • someone could not fully remember etc.

woah that so retro and old

• An observational study

• Subjects are followed to observe future outcomes

• Identifying subjects in advance and collecting data as events unfold

  • Again, since this is a type of observational study, no treatments are deliberately applied

• Usually focuses on estimating differences among groups that might appear as the groups are followed during the course of the study

• Manipulated factor levels to create treatments

• Randomly assigns subjects to these treatment levels, then compares the responses of the subject groups across treatment levels

To be valid, an experiment must assign experimental units to treatment groups at random

An explanatory variable whose levels are manipul;aged by the experimenter

Experiments attempt to discover the effects that differences in factor levels may have on the responses of the experimental units, randomly assigned to subjects

factor = explanatory variable

factory ends in a y and what comes before y? x-explanatory

• Values are compared across different treatments

• In a randomized experiment, large response differences can be attributed to the effect of differences in treatment level

Individuals on whom an experiment is performed

ex: rats, days, petri dishes of bacteria

When the individuals on whom an experiment is performed are human they are called…

The specific values that the experimenter chooses for a factor

Called the “levels of the factor”

The combination of specific levels from all of the factors r that an experimental unit receives

• different levels of a single factor

  OR

• combinations of levels of two or more factors

• Control

• Randomize

• Replicate

• Block

It is imperative that an experiment…

controls sources of variation (other than the factors we are testing) by making conditions as similar as possible for all of the treatment groups

o get and find randomization

It is imperative that an experiment…

randomizes/equalizes the effects of unknown or uncontrollable sources of variation

How you will randomize it, be specific

ex: randomly assign dog #’s 1-14 etc.

OR

list of dogs and randomly assign groups 1-4, stop after 15 groups, 1’s 2’s 3’s 4’s…

It is imperative that an experiment…

replicates, because it often happens that subjects of the experiment are not a representative sample from the population of interest aka drawing conclusions about the world is impossible unless we replicate/repeat our results

Ways to implement replication in an experiment:

• Apply each treatment to a large number of subjects/objects within one experiment

  • because the outcome of an experiment on a single subject is an anecdote, not data.

    • ex: 90 people within the study

      OR

  • The entire experiment is repeated on a different population of experimental units

To reduce the effects of identifiable attributes of the subjects (that may affect their responses but can’t be controlled)

• If we group similar individuals together

• and then randomize treatment assignments within each of these blocks

  • we can account for much of the variability due to the differences among the blocks

    • so we can see the differences caused by the treatments more clearly

ex: you could block by dog breed, by current weight of the dog, or age of the dog (harder to lose weight as they get older)

Identify what characteristic will have the biggest impact and then decide to block

Blocking!

Blocking

an experimental design where subjects or experimental units are grouped into blocks, with the different treatments to be tested randomly assigned to the units in each block

The randomization of an experiment occurs only within the blocks

ex: plants from one store can’t be assigned to treatment groups for the other store plant group

All experimental units have an equal chance of receiving any treatment

• When an observed difference is too large for us to believe that it is likely to have occurred by chance (this difference was not due to chance)

• Therefore the difference must be due to the treatments and is statistically significant!

Sample surveys try to estimate population parameters

whereas

experiments try to assess the effects of treatments

The experimental units assigned to the control treatment (a baseline, default, null, placebo treatment)

The control group’s responses provide a basis for comparison

• Any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups is said to be blinded

• Used to combat a possible source of confounding

• Two main classes of individuals who can affect the outcome of an experiment:

  • Those who can influence the results

    • subjects, treatment administrators, etc.

  • Those who evaluate the results

    • judges, treating physicians, etc.

When every individual in either of these classes (those who can influence the results and those who can evaluate the results) is blinded

When everyone in both classes(those who can influence the results and those who can evaluate the results) is blinded

A treatment known to have no affect

Administered to one group so that all groups experience the same conditions

The tendency of many human subjects (20% or more) to show a response even when administered a placebo

Only by comparing with a placebo can we be sure that the observed effect of a treatment is not simply due to the placebo effect

ex: a person struggling with insomnia takes a placebo (sugar pill) but instantly falls asleep because they believe they are receiving a sleep aid like Ambien or Lunesta.

In an observational study

Subjects who are similar in ways not under study may be matched and then compared with each other on the variables of interest

Like blocking, matching can be used to reduce unwanted variation/variability

• BAD!!

• When the levels of one factor are associated with he levels of another factor in such a way that their effect can’t be separated

• Think: like pouring two miscible liquids together, they cant be secreted from one another

  • This is just like how the effects of two confounded explanatory variables can’t be separated either

• Can occur from a two-factor combination as well

• Lurking variable: associated with both x and y, make it appear as though x is causing y, causes the other two variables to have a relationship

• Confounding variable: We can’t tell whether any effects as caused by out factor, by the confounding variable, or by both working together, affects the response variable

• randomized

• comparator el

• double-blind

• placebo-controlled

A special case of randomized block design, where an experiment only has two treatment conditions. The participants are grouped together into pairs based on an equivalent variable, such as age or gender. Within each pair, subjects are randomly assigned to one of two treatments.