UNIT 3 and UNIT 4 COMBO Flashcards
when does a trial of a simulation end?
Generally there are two cases:
- You want to know the probability of having x successes in n attempts (getting 3 smokers in a group of 5 students). Trials end when you get to n (get to 5 students). You record the number of smokers for each trial.
- You want to know how many attempts it takes to get f successes. Trials end when you get f successes. Record the number of attempts.
What type of probability when you are looking for at least one success in twelve attempts?
1 - p(NONE)
or “not zero”
1-binopdf(12, p, 0)
What is prospective study?
Prosepctive study is when you study the experimental unit’s present and futrue response variable.
RAND VARIABLE:
X has mean y and standard deviation of z.
A has mean b and standard deviation c.
Find: Mean, SD and VAR of: 5A
mean: 5b
sd: 5c
var: 25c2
what’s the difference between response bias and nonresponse bias?
response bias is anything in a survey design that influences responses falls under the heading of response bias (wording of questions).
Nonresponse bias is bias introduced to a sample when a large fraction of those sampled fails to respond.those who respond are likely to not represent the entire sample.
what is the law of large numbers?
states that in the long run.. (NOT SHORT RUN)
The relative frequency settles down to true probability.
(you’ll have 50% heads after an infinite number of coin flips with a fair coin).
Don’t make short run predictions.. coins don’t owe you “tails”
What are humans bad at ?
Humans are bad at generating random numbers.
What’s the difference between lurking and confounding?
Lurking varibles, on one hand, infer the association between the two varibles;
confounding variables, on the other hand, make it unclear which variable has had an impact on which in an experiment.
How many successes can you expect when you know p? (mean of binormial)
np.
Makes sense, if 30% like butter, out of 50 people you would expect (50)(.3)= 15 to like butter
np is the mean of the binomial distribution
What is the difference between a study and an experiment?
In a study you are basically just watching.
In an experiment you are manipulating factors and (hopefully randomly) assigning treatments.
Sometimes people call an experiment a study.
what is probability?
THE LONG RUN RELATIVE FREQUENCY!!
How are voluntary and convenience samples similar?
With voluntary, people choose them selves,
with covenience, the people are just chosen by researchers without using a random method, neither uses randomness and both are prone to BIAS.
Why blind the treatment givers?
The treatment givers may behave differently as they administer the actual meds vs when they administer the placebo.
What is a control group?
A group in an experiment without the treatment that is compared to groups with treatments to make results or conclusions.
The control group helps us see what would happen anyway. without any treatment so that we can see the true effect of the treatment.
Give examples of when you would block
Looking to see impact of different leather preservers on chairs in an airport. You might block according to proximity to window, or proximity to main entrance. The window seats will get more light and the ones closest to entrance may get more use, they will age and wear differently so you want to make sure some in each group get the different treatments.
OR, pain medicine. You might block by gender as males and females might react differently.
What is the problem with convenient sampling?
The sample may not be representative as it is not randomized to include every type of person.
Friends and family are convenient but they likely share similar opinions and thus the sample is not representative of a population.
Explain two types of experimental design.
- )Randomized Block Design: randomization occurs within the blocks only. MATCHING IS BLOCKING
- ) Completely Randomized Design: all of the experimental units have the same chance at recieving a treatment.
what is independent? What are the two equations to test for independence?
when P(A)=P(A|B) OR P(A)*P(B)=P(A and B)
When the probability of A is the same even when B is also true.
Knowing B does not affect the probability of A.
What do we call it when two things can’t happen at the same time?
disjoint OR mutually exclusive
When to use general MULT and what is it?
AND probability. Use when associated.
P(this)*P(that | this).
P(A)*P(B given A)
IT ALWAYS WORKS FOR ALL SITUATIONS.
When indep, the P(that|this) = P(that). So you end up with the simpler independent version, P(this)*P(that)
What is sample size and how does it compare with the fraction of a population?
Sample size is the number of individuals in a sample. The sample size determines how well the sample represents the population, not a fraction of the population sampled. The fraction of the population that you’ve sampled doesnt matter. Its the sample size its self thats most important.
Can you stratify in an experiment?
NO. stratification is a sampling method, blocking is method used in experiments.
They are sort of similar ideas.
RAND VARIABLE:
X has mean y and standard deviation of z.
A has mean b and standard deviation c.
Find: Mean, SD and VAR of: X + 12
mean: y+12
SD z
var: z2
can independent events be disjoint?
EXPLAIN
NO, if they are independent, then knowing one doesn’t change the probability of the other, but if they are disjoint, knowing one makes the other impossible, so it does change the probability of the other to 0
What is a factor?
A variable in an experiment that the experimenter manipulates.
What are the two types of observatinal studies?
Retrospective, and Prospective
What is area under ANY probability curve?
1 (or 100%)
How to make TREES with screening tests????
SPLIT UP POPULATION FIRST (by % with condition).
then split the groups by outcomes of the test
what is a complement?
the probability that it doesn’t happen.
1-P(it happens).
(together they add to 100%)
What is the main purpose of a placebo ?
To blind the subject that is being experimented on to avoid influence to the given variable therefore altering the response variable.
When people think they’re getting help, they often improve anyway..
What is a simple random sample? how is it different from others?
A sample where every possible sample has the same chance of being selected.
There are no impossible samples.
What is bias?
What are some common errors?
It’s any systematic failure of a sampling method.
COMMON ERRORS: Voluntary response, undercoverage of the population, nonresponse bias and response bias. We use randomness and methods like stratifying to reduce these.
How can the WORDING of the question lead to response bias
Words or phrases that impact your feelings tend to influence responses. Look for “devastating, horrific, wonderful, etc.”
Sometimes there is a background story like “Many americans lose jobs to illegal aliens every year, how do you feel about the border wall?”
What type of probability when you are looking for the first success on or before the fifth attempt?
Geocdf(p, 5)
What four things do you need in an experimental design? (trick)
NEED only 3: control , randomization, replication..
MAKE SURE YOU COMPARE
Use blocking when appropriate
When to use general add and what is it?
OR probability.
Use when not disjoint. (subtract overlap)
P(this OR that) = P(this)+P(that) - P(this and that)
(IT ALWAYS WORKS IN ALL SITUATIONS, when disjoint, P(this and that)= 0, so you end up with the simpler disjoint version)
Why is it called “binomial”
These numbers come from the coefficients of expanded binomials..(x+y)1, (x+y)2, (x+y)3
What is diff between 3X and X+ X+ X
(mean and st. dev)
3X is just tripling one play. Mult mean and SD by 3.
X+X+X is playing 3 times, Mult mean by 3,
BUT… must add variances, square SD’s add 3 times then sqrt.
What is the difference between a cluster sample and random sample?
A cluster sample is when the population is first divided into sections of clusters that have all of the traits that the population has, so the clusters are representative. You grab a cluster as your sample.
A random sample is all names in a hat so you could get any group.
Give three examples of events that are not mutually exclusive (not disjoint)
- Being a DOG and being SMELLY
- Being a FRESHMAN and being FEMALE
- Liking ICE CREAM and liking HAMBURGERS(both can be true simultaneously)
How can you simulate a coin flip with random number table?
Assign heads to odd numbers and tails to even numbers.
What is a quality of SRS that is not a quality of Systematic, Stratified or Clustering?
In an SRS, all samples are possible and all possible samples have the same chance of being picked.
The other methods have lots of “impossible sample groups”
.Stratified- an impossible group would be all girls (you’re taking some boys and girls)-
Clustered- an impossible group would be all girls (each cluster has boys and girls)-
systematic- an impossible group would be 4 people that are right next to eachothe (you are taking every nth person)
what is the best way to reduce bias?
randomness.
sophisticated answer: make as many things as random as possible
RAND VARIABLE:
X has mean y and standard deviation of z.
A has mean b and standard deviation c.
Find: Mean, SD and VAR of: 3X + 5A
mean: 3y+5b
sd: SQRT(9z2+25c2)
var: 9z2+25c2 (same as (3z)2 + (5z)2)
What is easy way to assign treatments with random number generator?
Assign everyone a 2 digit number (toss out repeaters),
then simply sort from lowest to highest.
The lowest n get treatment 1, next n get treatement 2, next n get treatment 3, etc….
What is the law of averages?
a misinterpretation of the law of large numbers.
thinking things will even out..
Using this law, if you flipped 4 heads in a row, you’d expect the next one to be a tails because it should even out in the long run. Not true, 5 flips is not the long run. Infinity is. The next flip still has a 50% chance of being another head. You may hear someone say “he’s do for a hit” or “it’s bound to rain soon” both bad.
what is n! ?
it is “n factorial” example: 5! = 5*4*3*2*1= 120.
tells you how many ways you can arrange n objects.
Why do you have to block?
You don’t have to,
But you might want to if you feel that the experimental units (subjects) may respond differently to the treatment because of confounding variables.
Like if you were testing out new deoderant. You might want to block according to activity level so you don’t get all of the active people in one group (they sweat more).
What is response bias?
How do you avoid it?
Response bias is any influence that may sway the respondent to give a more favorable answer e.g wording of the question, interviewer’s behavior/background.
Therefore, in a survey, ask questions that allow respondents to answer comfortably and honestly.
Keep the wording “indifferent” or neutral in some way in order to unduly favor one response over another.
CONTROL the environment so that it is similar for all subjects.
What is the “hot hand?”
a misinterpretation of the law of large numbers. Using this law, if you flipped 4 tails in a row, you’d expect the next one to be another tails, because tails is “hot.” A baseball player who gets three hits in a row, you expect another hit? wrong. Streaks happen randomly (actually there is a little evidence for hot hand in some sports, but more research needs to be done)
Give three examples of independent variables
- Being tall and having a high GPA
- If it is snowing and whether it is a Thursday or not
- Whether a person likes pizza and their gender(notice, knowing one bit of information does not impact the likelihood of the other being true also)
Do we say things are “dependent?”
NO! we say associated
How to find likelihood of being pregnant, given the test says you are? (tree)
Split population by %pregnant and %not who take test, then each of those into what test says.
Then look just the groups that the test said pregnant. Then find: %pregnant/(total percent in both groups).
RAND VARIABLE:
X has mean y and standard deviation of z.
A has mean b and standard deviation c.
Find: Mean, SD and VAR of: X + A
mean: y+b
SD SQRT(z2+c2)
var z2+c2
what does binomial model tell us about?
exactly x successes in K trials.
What is likelihood of exactly 3 heads out of 13 flips?
binopdf(13, .5, 3)
What is the standard sampling method?
A Simple Random Sample (SRS) is our standard. Every possible group of n individuals has an equal chance of being our sample. That’s what makes it simple.
geopdf (inputs)
FIRST SUCCESS ON THIS ATTEMPT
geopdf (p,x)
probability of FIRST SUCCESS being ON the Xth trial
What type of probability when you are looking for more than 5 successes in twelve attempts?
6 or more
same as not 5 or less
1- (5 or less)
1 - binocdf(12, p, 5)
What type of probability when you are looking for exactly 5 or more successes in twelve attempts?
(more than 4)
not 4 or less
1-(4 or less)
1 - binocdf(12, p, 4)
What is retrospective study?
A retrospective study is a study that looks backwards in time. They focus on estimating differences between groups or variable association because they are not based on random samples.
