Statistics 101Exam #2 Iowa State University

Random Every Day Meaning

-Proceeding, mode or occurring without definite aim, reason or pattern.

Random Meaning in Statistics

-Behavior with a predictable long term structure.

-Long term structure produces fair results.

Random Events

-Outcome unknown before even occurs.

-No structure in short term.

-Structure in long term

-Must be found

Examples of Random Events

-Flipping a coin

-Rolling a die

-Shuffling a playlist

-The lottery

Simple Randomly Sample (SRS)

-Every combination of population members HAS EQUAL CHANGE of being selected for sample.

Stratified Random Sample

-Large populations will be made up of SMALLER HOMOGENOUS GROUPS

- Total sample is collection of SIMPLE RANDOM SAMPLES from each group.

-Group members can be included in analyses.

Cluster Sample

-Difficult to get sampling frame for large population.

-Divide population into CLUSTERS.

-Randomly select a certain # of clusters.

-Interview ALL PEOPLE in selected clusters

-Only need sampling frame for clusters selected.

Multi-Stage Sampling

-Combination of SRS, Stratified, and Clustering

-Government: ex, Current population survey.

Experimental Units

-Humans, Subjects

-Need one experimental unit per trial in experiment.

Factors

-Need at least one for every experiment

-Variables you can manipulate

-Explanatory Variables

Levels

-Values used within a factor

-Need at least 2 for each factor

-Can be Categorical or Quantitative

Treatments

-The combination of factors and levels given to experimental units.

Treatment Group

-Group of experimental units given a treatment

Control Treatment

-If one treatment= 'Nothing'

-Experimental units assigned to this treatment are called CONTROL GROUP.

-Different than control in an experiment.

Placebo Effect

-Just receiving a treatment can affect response.

-Psychology of humans-doing something is better than doing nothing.

-Causes problems in comparing control group to treatment group.

SOLUTION- Placebo

-Fake treatments that resembles the real treatment in an experiment.

-Part of CONTROL in an experiment.

Blinding

-Subjects should not know which treatment they are receiving.

-Could influence response.

Double Blinding

-People in direct contact with subjects should not know which treatment they are receiving.

-Could influence way subjects are treated.

Blinding and Double Blinding are....

-Part of CONTROL in an experiment.

4 Principles of Experiments

1. Control

2. Randomization

3. Replication

4. Block

1. Control

Control of outside variables

2. Randomization

Randomly assign experimental units to treatment goups

3. Replication

Apply each treatment to many experimental units

4. Block

Use blocking to remove identifiable sources of variation in experimental units

Probability of a Random Event

1. Subjective

2. Empirical

3. Theoretical

1. Subjective

-Personal

-Based on feeling or opinion

example: Levi didn't thing this event was likely

2. Empirical

-Based on experience

3. Theoretical

-Formal

-Based on mathematical model with assumptions

Law of Large Numbers

-For repeated trials of an event, the long run relative frequency of the event gets closer to the theoretical probability of the outcome

LLN Example

Deck of cards has 52 cards

-26=Red

-26=Black

What is the probability of drawing a red card?

Of drawing a heart or spade?

What type of random event is this?

26/52= .5

26/52= .25

(13+13)/52= .5

These are all Theoretical Events