Which statement about bias is true?
II. Bias is usually reduced when sample size is larger
The Three Big Ideas of Sampling
Idea 1: Examine a Part of the Whole
A sample from a population should give us about the same information
Idea 2: Randomize
If we select randomly select our sample we should be able to avoid bias
Idea 3: It's the Sample Size
It is the number of individuals
Simple Random Sampling
Pulling names from a hat"
Simple Random Sampling (SRS) is when every combination has an equally likely chance to be selected.
Sampling Frame - Who goes into the hat?
-the list of all individuals from which the sample is drawn.
Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are three high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly sa
Yes, because they could have chosen any 250 sutdents from throughout the district
Suppose the state decides to randomly test high school wrestlers for steroid use. There are 16 teams in the league, and each team has 20 wrestlers. State investigators plan to test 32 of these athletes by randomly choosing two wrestlers from each team.
Is
No, because not all possible groups of 32 wrestlers could have been the sample
Stratified Sampling
strata=layers
cluster sampling
#NAME?
Multistage sampling
combining multiple methods
systematic sampling
using a system of selecting every nth individual
Survey of the 2700 attendees at UVM Hockey game
Pick every 20th person through the gate
simple random sampling
Survey of the 2700 attendees at UVM Hockey game
Randomly pick 10 senior citizens, 20 college-age, and students, 10 younger children and 15 middle- aged adults
cluster sampling
Survey of the 2700 attendees at UVM Hockey game
Randomly pick 3 of the 52 sections in the hockey arena.
multistage sampling
Survey of the 2700 attendees at UVM Hockey game
Randomly generate 50 ticket numbers.
simple random sampling
The January 2005 Gallup Youth Survey telephoned a random sample of 1,028 U.S. teens aged 13-17 and asked these teens to name their favorite movie from 2004.
Napoleon Dynamite had the highest percentage with 8% of teens ranking it as their favorite movie.
all of the above
A chemistry professor who teaches a large lecture class surveys the students who attend his class on how he can make the class more interesting to get more students to attend. This survey method suffers from
A. voluntary response bias B. nonresponse bias
C. response bias
D. undercoverage
Which statement about bias is true?
Which statement about bias is true?
random
An outcome is random if we know the possible values it can have, but not which particular value it takes
generating random numbers
random numbers are hard to generate. nevertheless. several internet sites offer an unlimited supply of equilly likely random values
simulation
a simulation models a real world situation by using random- digit outcomes to mimic the uncertainty of a response variable of intrest
trial
the sequence of several components representing events that we are pretending will take place
component
a component uses equally likely random digits to model simple random occurrences whose outcomes may not be equally likely
response variable
values of the response variable record the results of each trial with respect to what were interested in
It has been shown that there is an strong positive association between the number hours studying and a students GPA.
This association is most likely due to:
lurking variable
It has been recorded that there is an string positive association between the number of firefighters at a fire and the amount of damage.
This association is most likely due to:
confounding varible
4 Principles of Good Experiment Design
1. Control
� Make conditions as similar as possible for all groups. � Control allows us to isolate the one thing that is being
studied. Helps avoid lurking variables
2. Randomize
� Equalizes the effects of variation that we cannot control.
� Distributes t
Control Group
A "baseline" group for comparison that typically receives no treatment
placebo
(fake treatment) for effective blinding
Just telling a patient that they are being treated can aid recovery. This is called the
Double-blinding in experiments is important so that
I. II. III.
The evaluators do not know which treatment group the participants are in.
The participants do not know which treatment group they are in.
No one sees which treatment any of the participants a
all of the above
Which group(s) are affected by the placebo effect?
A. The control group
B. The treatment group
C. Both the control and the treatment groups
none of the above
In an experiment the primary purpose of blinding is to reduce .
A) Bias
B)confounding
C)randomness
D) variation
Bias
Does donating blood lower cholesterol levels? 50 volunteers have a cholesterol test, then donate blood, and then have another cholesterol test. Which aspect of experimental design is present?
A. Randomization
B. A control group
C. A placebo
D. Blinding
E.
None of these
In an experiment the primary purpose of blocking is to reduce . . .
A. bias.
B. confounding.
C. randomness.
D. variation.
varition
Observational Studies
use random selection to determine who to look at past or future
simulations
use random selections for a group of participants from a populations
expierement
find a homogenous group, use random assignments to create a subgroup for treatments.
Random Phenomena Vocabulary
Trial-each time we observe a random phenomena.
outcome-the value of the trial
events- the combination of the trials outcomes
sample space the collection of unique outcomes
The Law of Large Numbers
For many trials, the proportion of times an event occurs settle down to one number, the empirical probabilty
P(a)=#times A occurs/#of trials
A fair coin has come up "heads" 10 times in a row.
The probability that the coin will come up heads on the next flip is
greater than 50% since it appears that we are in a streak of heads
The non existent law of averages
There are no "corrections" made to random events to
keep them on track!!
� No one is ever "due" an outcome to a random event
theoretical probability
formulated around equally likely outcomes
example:well shuffled deck of card
bouncing around lotter ping pong balls
Often symmetry plays a role in equally likely Dice
Coins
Equi-probabilty
Treating ALL outcomes in the sample space as equally
likely....when its not the case
example probability two people are left handed
Consider the sample space of rolling two dice and recording the total of both dice.
Do you consider the events in the sample space as equally likely?
cannot tell
Consider the sample space of a family having three children and recording the sex for each child in the order of birth.
Do you consider the events equally likely?
no
Personal Probability
What's your chance of becoming a Millionaire?
� You cannot base this on your long-run experience.
� There is no sample space of events with equal probabilities to list.
� You can only base your answer on personal experience and guesswork.
Probability Rules
Rule1-ForanyEventA, 0P(A)1
Rule 2 -For sample space S, P(S) = 1
Rule 3 - The complement rule, P(Ac) = 1-P(A)
Rule 3 - The complement rule, P(Ac) = 1-P(A)
disjoint
Disjoint - Events that do not share any outcomes
example:Think -In a single die roll: Rolling a 2 and Rolling a 4
independent
The occurrence of one event does not effect the outcomes of another.
Think -On a die Rolling a 2 and with a coin Flipping Heads
In 2007 Harvard accepted 7% of its applicants, MIT 10%. A random student applies to both of these schools.
Can we consider the events of getting accepted to these schools as:
disjoint?