SCI 105.020 Scientific Inquiry

Evaluating Causal Hypotheses

Causation vs. Correlation-similarities

Relationships between two variables Associations in sample statistics can be observed and

analyzed in the same way Direction Strength Margin of error (ME)

Small

Large

Red Green

Not E

E

x-group k-group

A random experimentA jar of marbles

Causation vs. Correlation-differences

Correlation is a symmetric relationship, whereas causation is not

In a causal relationship There is a clear temporal order between the cause and effect

variables: you cannot cause something happen in the past Causes produce their effects in the causal production

10/40 (or 25%)Large

45/60(or

75%)Large

Red Green

15/45 (or 33%)Red

45/55(or

82%)Red

Large Small

Being Large is positively correlated to being Red, and vise versa.

Use ashtray

Lung cancerSmoking

correlation

causation

causation

Differences In Hypothesis Evaluation

Evaluating correlation The real-world population

Population sampled vs. population of interest

The sample data Sample sizes and observed

frequencies The statistical model Random sampling

Representativeness and possible biases

Evaluating the hypothesis Strength of correlation

Summary

Evaluating causation The real-world population &

causal hypothesis Identify C & E variables and

state the hypothesis The sample data Design of the experiment

Random/prospective/ retrospective

Random sampling Evaluating the hypothesis

Effectiveness of the causal factor

Summary

The Ideal Case

Ideally, we’d like to divide the real-world population into two disjoin group: Subjects exposed to the cause variable Subject not exposed to the cause variable

exposed

not exposed

x-group

k-group

Not E

E

x-group k-group

Random Experiment

In reality, one can only mimic the ideal condition by random sampling

exposed

not exposed

x-group

k-group

population of interest

population sampled

Randomsample

Not E

E

x-group k-group

Randomsampling

Principles of Experimental Design

The fundamental principle is control The key is to control for possible effects of extraneous

variables

Principles of control include Comparison: observe any differences in effect variable Randomization: impacts of extraneous variables

can be balanced out These can then be attributed directly to the cause variable

Blindness: further improve the effectiveness of the experiment by resolving the placebo effect

Prospective Studies

Not controlled experiments, inherently not as strong

Widely used in various medical contexts where a real controlled experiment is not applicable

Efforts can still be made to minimize the impacts from other variables (O) Select only subjects not exposed to O Select only subjects exposed to O and make sure there

is no interaction between o and the suspected cause Matching the subjects according to their values in O

Prospective Studies-an illustration

x-group

k-group

population of sampled

Randomsampling

E E

C Not C

Starting from a real population in which its instances have selected their groups already

Random sampling is still achievable in selecting subjects from the divided population

Retrospective Studies

Retrospective studies mean to survey the past Just opposite to prospective studies, which look into the

future Starting from a x-group with subjects that are

known to have the effect and a k-group which is free from the effect Ideally the subjects in the k-group will match up with the

x-group subjects in all other aspects Efforts are needed to verify it as far as possible

The result of the study was presented as percentages of subjects who had the cause, not percentages of those who developed the effect

Retrospective Studies vs. Survey Sampling Both employ techniques such as interviewing Both can come up with various frequency

values A survey can also select subjects randomly Why should one bother to do a retrospective

study? The difference

is numbers!Cases Controls

All women 62% 52%

Women w/ children 61% 52%

Women w/o children 65% 51%

Women using pills before 22 yrs 68% 69%