Unit 3 & 4 review
Unit 3: collecting data
Simple Random Sample (SRS): Every group of a certain size has an equal chance of being selected
Cluster Sample: Divide the population into heterogeneous groups [all from some]
Stratified Random Sample: Divide the population into strata of homogeneous groups [some from all]
Why stratify by X, explain why individuals in those strata would have different responses as opposed to some other variable
Stratifying has less variability but more precision
Bias Types: Undercoverage, nonresponse, response bias (inaccurate) - always say if it leads to over/underestimate of a response
EXPERIMENTS ASSIGN TREATMENTS
Experiments have a comparison, random assignment (creates roughly equivalent groups of variables among treatment groups), control (helps avoid confounding & lowers variability in the response variable), & replication (any difference in effects of treatments can be distinguished from chance differences between groups)
Randomized block design: random assignment of treatments is carried out separately in each block
Blocks share a variable that may impact response lower variability in the response variable, and allow for easier comparison of treatments
Marched pairs = compare 2 treatments in block size
Guenther notes:
Random sampling: Allows for generalization to the population
If not, can only be applied to the sample or those similar to the sample
Random Assignment: establishes a cause-and-effect relationship of treatments to groups
if not, can only claim an association
Experimental Design:
Random Assignment
Control of confounding variables
Comparison of treatments
Replication - statistically significant - done so many times that it is unlikely to occur by chance
Types of Experimental Design:
Completely Random Design:
Random assignment occurs from the whole group
Blocking:
The whole group is blocked by a common trait (EX: male/female)
Random assignment occurs from each block
Matched pairs:
Pairs are created from the whole group
One person in each pair was randomly assigned to a treatment
General notes:
Factor: General variable that you are applying
Explanatory variable
Levels: Amount of that factor you are giving
Specific things you are doing
Treatments: Specific things being applied in the experiment
Factor and level included
Experimental unit/subjects: people o things that you are performing the experiment
AKA your sample
Random Assignment gives you causation, explanatory causes response
Cause and effect
Random Sampling: generalization to the whole population
an say association
FRQ Phrase:
Assign each subject to a ______-digit number from [01-____]. Using a random number generator to assign the first _______ to treatment group 1- [actual treatment], assign the next ______ to treatment group 2 - [control treatment], [any more groups needed same outline]. Ignore any repeated numbers or any numbers produced that are 00 or [n+1} or above
Unit 4: Probability, Random Variables, & probability Distributions:
Probability: the chance of an event occurring, expressed in a decimal
Must be between 0-1
P (event) = successful outcomes/total outcomes
Completment of an event P(not event) is equal to 1-P(event)
Common compliments = at least, at most, greater/less than
P(A and B) = P(A∩B) = probability that BOTH events A and B occur
In a 2-way table = the intersection of the two events is divided by a full total of the two events
Using conditional probability = P(A) * P(B|A)
P (A or B) = P(A U B) = probability that either events A or B occur
P(A) + P(B) -P(A and B)
Events mutually exclusive if P(A or B) = P(A) + P(B)
Events mutually exclusive if P(A or B) = P(A) + P(B)
Events are independent if P(A|B) = P(A) or if P(A and B) = P(A) x P(B)
Random variables are quantitative and take numerical values determined by the outcome of a chance event
Discrete = has a set number of values like number of coins that land heads or composite ACT score
P(X = event) must add up to 1
Expected value (OR MEAN)
Continuous random variable takes on all values in an interval of numbers, represented by a normal distribution
Binomial random variables: multiple trials of the same event
CONDITIONS: Binary, Independent (10%), Number of fixed trials, Same probability of success p
Parameters: n (number of trials) & p (probability of success on any trial), x = successes
Geometric random variables are still independent with a fixed probability of success without trials set previously
Check binary, independence, same probability of success p
Guenther Notes:
Binomial Random Variable:
B: binomial - only 2 outcomes
I: each trial is independent
N: set n value
S: the probability of success is the same for each trial
EXPECTED VALUE IS THE SAME AS MEAN
Geometric value:
Same as binomial but there is no set n value
UNTIL
When in doubt a tree diagram may help
Other notes:
If the outcome of a chance process is a numerical value, then a random variable X can be used to describe the outcomes
Two types of Random Variable:
Discrete Random Variables: The outcomes can only take on a distinct set of listable (or countable) values
Continuous Random Variables: The outcomes can take on an infinite number of values
TRANFORMING A RANDOM VARIABLE:
is simply changing the UNITS that the random variable is measured in
When transforming a random variable MULTIPLY both the mean and standard deviation by the conversion factor
Transforming can also be adding (or subtracting) a constant to the outcomes as well as multiplying by a constant.
COMBINING random variables:
together means either combining two or more different random variables together OR repeating one random variable multiple times (must be independent)
The mean of the sum or difference of random variables is the sum or difference of the individual means
The standard deviation for the sum or difference of a random variable is the square root of the SUM of the variables
Even in examining the difference of two random variables the variance still adds! then take a square root for the combined variance to get a final total standard deviation.