Review- ch. 4 AP Stats notes (copy)

Bias

• A deviation from the truth in data collection

• tendency to favor the selection of certain members of the population

• ALWAYS check for bias when collecting data→ no recovery from a biased sampling method AFTER the sample is collected.

Selection bias

• A type of bias when the sample is not representative of the population.

• technique for selecting

• Types

  • size bias

  • voluntary response bias

  • undercoverage bias(inadequate representation of certain groups)

• done when using convenience samples or judgment samples(professional opinion only)

Convenience Bias

• Choosing individuals whoo are easy to reach

Disadvantages:

• Data collected tens to be highly unrepresentative of the entire population

human mistake

• a careless human mistake

• a real concern of researchers

size bias

• tendency to believe outcomes are more likely to occur if they are part of a large category than part of a small category.

Sample Size

• The most important is not the fraction of the population, but rather the actual sample size

“bad sample”

• if have enough bias→ sample could be worthless

Proportional Sampling

• EACH stratum(homogenous groupings) sample size is DIRECTLY proportional to the population size of the ENTIRE population

• a “ratio”

Convinience Bias

• Based on choosing easy-to-reach individuals

Disadvantages:

• tend to produce data unrepresentative of the ENTIRE population

voluntary response bias

• Individuals CHOOSE whether they want too respond

• Example

  • survey

• Result:

  • Typically give too much emphases to those who feel STRONG opinions

undercoverage bias

• inadequate representation of certain groups

Response bias

• the tendency of participants to answer questions inaccurately

• Based on participant response

• Types:

  • non-response bias

  • questionnaire bias(misleading influence due to non neutral wording)

  • incorrect response bias(very obvious what the right answer is)

• Impact: distorts research findings, reduces validity of results

• Minimize: careful wording, field test survey questions, use randomized response technique, ensure the anonymity of responses

non-response bias

bias that occurswhen survey participants are unwilling or unable to respond to a survey question or an entire survey.

questionnaire bias

• misleading influence due to non neutral wording

incorrect response bias

• very obvious what the right answer is

Sample Surveys

• poll, questions to small groups in hopes of learning something about the population

Advantages:

• best when a random sample(not chosen by the creator nor volunteered) of ppl is surveyed.

• Cheaper and quicker than experiments

Disadvantages:

• tend to produce data unrepresentative of the ENTIRE population

• usually subject to bias → very hard to conclude cause & effect, only can suggest relationships

Sampling frame/Parameter

• list of the population units in which the sample is drawn form

  • could be the whole population of interest

Random Sampling

• use of choice in selecting a sample from a population

• necessary in order to be able to generalise findings to the population

Census

• collecting data from the whole population

• no inference procedures are required later

• a poorly run census→ can provide less info and be less accurate than a well-designed survey

Population

• entire group of individuals does not mean everyone in the world

• Numerical summary= parameter

  • “population parameter”

Sample

• part/subset of the population

• Numerical summary= statistic

  • “sample statistic”

Sampling variation/error

*variability

• natural variation BETWEEN samples

  • When different samples give different sample statistics for the estimate for the same population parameter

• can never be eliminated

• smaller for smaller sample size(n)

• never an error

• not higher with bias

Randomize

unpredictable chance

Variability

• the mean that VARIES from 1 sample to the next

Strata

• homogeneous subgroup

• can be considered unacceptable if there are overlaps

Good sample design

• No personal bias/reference

• avoids undercoverage, nonresponse, and response bias

• the wording of the question matters

• does’t use old data(date+time) for a later date

• Larger sample → more detailed and accurate result

Simple Random Sample(SRS)

• randomly choosing a number from units

• the SAME probability for everyone in the populations

• Requirements: numbering everything

• example:

  • pick out of a hat

  • rolling a dice

  • random number generator

Stratification( Stratified random sample)

Steps

1. Units divided into strata(homogeneous groups)

2. Do an SRS on EACH grouping(from 1)

3. COMBINE to form a full sample(the stratified random sample)

• Advantages:

  • Convenient, coverage, precision

  • helps with diversity

  • easier and more cost-effective than SRS

• Notes

  • nonequal chance of selection

  • not considered an SRS, but includes it

3. Cluster Sampling

1. Units divided into clusters(heterogeneous groups)

2. Do an SRS to choose grouping(s) (from 1)

3. test ALL the units that were chosen (from 2)

4. 2 stage cluster sampling

1. Units divided into clusters(heterogeneous groups)

2. Do an SRS to choose A grouping(s) (from 1)

3. A SECOND SRS for chosen groupings(from2) → chose an individual unit(or a few) in EACH grouping

5. Systematic Sample with random Start (1 in k)

• random start, from ___to ___ every kth term

• reasonable as long as the original order of the list is not related to the variable under condition

• Not a “random” sample

Cluster

• heterogeneous groups

• Should be representative of the population → EACH cluster should look similar

• Depends on the amount of time and money

Observational study

• Study where individuals are observed and SPECIFIC variables of interest are measured

• No cause-and-effect relationship can be determined

• No treatment imposed

• Usually MORE cost and time-effective than an experiment

Retrospective

• Looking backward, examining old data

• Advantages:

  • tend to be smaller scale, quicker to complete, less expensive

• Disadvantages:

  • Less control due to past record keeping(usually done by others)

  • subjects inaccuracy

  • possible bias

Prospective

• Watch for outcomes, tracking individuals into the future

• Advantages:

  • less susceptible to recall errors from subjects

  • researchers do OWN record keeping→ can monitor SPECIFIC variables of interest

• Disadvantages:

  • Expensive, time-consuming

  • follow a large number of subjects for a long time

Experiment

A research method in which one or more variables are manipulated to observe the effect on another variable.

• Individuals placed in particular treatment-measured response

• experiments ≠ observation

• Examples

  • clinical trial, randomized comparative experiment

  • placebo, fake treatment

Statistically significant Experimental results

• An observed effect/results that is unlikely to occur by chance

Treatment Group

• CHANGING independent variable may affect the results

• at least 2

*random assignment MUST be used to determine which experimental units go into which treatment group

Comparison Group

treated “SAME” as treatment group

Control Group

*placebo

• No change in the independent variable

• may not be necessary(use context)

Good Experimental Design

1. Control/comparison group → Best to establish a cause-and-effect relationship

2. Randomization →reduced by confounding

3. Replication→ SAME treatment for DIFFERENT units

Notes

• Should have an EQUAL chance of being assigned to a treatment and assigned in a random way

1. Completely Randomised Design(CRD)

1. Number units t to n

2. n/(number of treatments wanted)

3. Randomly put treatment numbers into treatment groups

2. Randomised Pair Comparison Design(matched pairs)

1. Place 2 homogeneous units in a pair

2. randomly decide who gets what treatment

• A special case of blocking, where EACH pair is a “block”

• reduces variability because pairs are already in homogeneous groups

3. Randomised Block Design

1. block units based on homosimilarity

2. Do a CRD with EACH block

• randomization occurs ONLY within groups of blocks(homogenous experimental units)

4. Randomized comparitive Design

1. Compare ONLY 1 or 2 treatments at a time → Controls lurking variables

2. Replicate experiment → reduce variation and ensure efficiency

5. Double Blind Study

• "subject & designer don’t know what the experiment treatment is.

Treatments

• a combination of factors x levels that an experimental unit receives

• block what you can and Randomize what you cannot.

Factors

NO. of groups(“title”)

Levels

• NO. of groups within groups

• eg. height, length

Experimental Unit

• unit that treatment is being applied to

Confounding

• cause confusion in response

  • uncertainty with regard too which variable causes an effect→vairables are confounded→not propper conclusions

• Impossible to SEPARATE the effect on the response

• can reduce through random assignment, control groups

*variables considered in the study

Lurking variable

• Doesn’t cause confusion in response

• effects outcome, as it drives 2 other variables into a mistaken cause-and-effect relationship

• not included in the analysis

  *variables not considered in the study

Random assignment(randomisation)

• Best solution to reduce confounding because there is only 2 main causes for a difference in response

  1. Chance

  2. Treatment itself

• source of variation cancels out

• not SAME as listing out

• subjects are randomly assigned to treatments to even out effects over which have no control

  *random assignment!

Blocking

• Block variables with a STRONG association to results and impact them

• Grouping together homogenous units

• Decreases the change of variation and lurking variables

• make conclusions MORE specific by controlling certain variables and bringing them into the picture

• allows us to clearly see a difference caused by treatments

  • especially when we can’t control certain variables

Random Digit Table

1. Simulation start: Random place on the graph

2. Assign digits to correspond to things

3. record results and make a frequency distribution of the number of trials needed until success

Self selection

• kinda like voluntary response, but in this case you just chose what to do, not hv to be inn regards to a survey

Examining and goal of Sampling vs Experiments

Sample: Examining the population and its response→ Describe the characteristics of the population

Experiments: Examining the treatment response → Different treatments lead to different responses

Randomisation in Sampling vs Experiments

Sample: Take an SRS from the population

Experiments: Reduce the likelihood of a confounding variable by randomly assigning treatments to available units

Controlling variation in Sampling vs Experiments

Sample: Variation can be controlled through stratification( combining SRS of strata( homogenous groups))

Experiments: Variation can be controlled by blocking based on homogenous

Threats to inference in Sampling vs Experiments

Sample: 2 bias’s: section bias, response bias

Experiments: Confounding variables

Placebo Effect

• Many people respond to ANY kind of perceived treatment

best way to minimize the placebo effect

• binding and Control groups

Blinding

• Subjects don’t know which treatment they’ve received

• sometimes it can be impossible in an experiment

  • eg. ppl are told to not do something that those in the other treatment is doing

Double Blinding

• BOTH subjects and those evaluating responses don’t know which treatment was received.