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### Stats Review

Chapter 3

3.1 First Step in Producing Data

Experiment Design

The arrangement or patterns for producing data

- How many individuals to collect data from?
- How to select individuals?
- How to form groups if needed?

Anecdotal Evidence

Based on haphazardly selected individual cases which come to our attention because they are striking in some way. Not a reliable source of statistical data.

Observational Study vs. Experiment

- Observational Study observes individuals and measures variables of interest but does not attempt to influence responses
- Experiment deliberately imposes some treatment on individuals in order to observe their responses

3.2 Experiment Design

Factors – Explanatory variables in an experiment

Treatment – A specific experimental condition applied to the individuals in an experiment

Comparative Experiments

Treatment is given to one group and the response is observed.

A dummy treatment (placebo) is given to another group (called the Control Group) and the response is observed

This type of experiment defeats lurking and confounding variables.

Bias

The systematic favoring of certain outcomes in the experiment

Randomization

Using impersonal chance to select individuals for the experiment and the treatments they will receive.

Principles of Experimental Design

- Control – comparing several treatments to control the effects of lurking variables
- Randomization – using impersonal chance to assign experimental units to treatments
- Replication – conducting the experiment with many units to reduce the variation of results.

Matched Pairs Experiment

- Choose blocks of 2 units that are as closely matched as possible.
- We assign one of the treatments to each unit randomly.
- Can be done on the same individual by giving one treatment then the other. The individual serves as their own control group. Order of treatments are randomized in this case

Block Experimental Designs

A block is a group of experimental units or subjects that are known before the experiment to be similar in some way that is expected to affect the response to the treatments. In block design, the random assignment of units to treatments is carried out separately within each block.

Ex.) Separating subjects into blocks of men and women then conducting the same experiment within each group

Tree Diagram of a Block Design

GROUP 1 THERAPY 1

MEN GROUP 2 THERAPY 2 COMPARE

GROUP 3 THERAPY 3

SUBJECTS

GROUP 1 THERAPY 1

WOMEN GROUP 2 THERAPY 2 COMPARE

GROUP 3 THERAPY 3

3.3 Sampling Design

Simple Random Sample (SRS)

A SRS of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.

Stratified Random Sample (SRS)

The population is divided into groups of similar individuals, called strata. Then a SRS is chosen from each stratum and combined to form the full sample.

3.4 Statistical Inference

Sampling Distribution

The distribution of values taken by the statistic in all possible samples of the same size from the same population.

Describing a Distribution:

Shape: Does it look normal? Is it skewed? Granularity? Outliers?

Center: Mean is used when the distribution is more normal. Median when there is a skewed distribution.

Spread: St. Dev. is used with mean. IQR is used with median.

Bias

How close of an accurate estimator the statistic is to the parameter.

Variability

How spread out the distributions outcomes are.

4 Targets Example on page 273

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