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# Scientific Inquiry SCI 105.020 PowerPoint PPT Presentation

Scientific Inquiry SCI 105.020. Statistical Models and Probability. Recap: Ex 2.7. Analyze the findings reported in the May 8, 1987 issue of Science Identify the four components involved in Model Evaluation process

Scientific Inquiry SCI 105.020

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## Scientific Inquiry SCI 105.020

Statistical Models and Probability

### Recap: Ex 2.7

• Analyze the findings reported in the May 8, 1987 issue of Science

• Identify the four components involved in Model Evaluation process

• Run the six-step program described in the text to summarize what you see from the report

### The Four Components

Real World:

Dinosaurs extinct 65m-yr ago:

What caused it?

Fit

Model:

Single catastrophic

Event—extraterrestrial

body hitting—caused it

Observation

Reasoning

Calculation

Prediction:

Cracks in quartz +

Debris blocking sunlight for

months or years 

Climate cooled down 

Death of habitants on earth

Agree

Data:

Unique crack patterns

in quartz particles +

Unusually high concentration

of iridium found all over the world

Size and speed: fit or not?

### The Evaluation Process

• RW: extinction of dinosaurs: What caused it?

• Model: two alternative theories

• Single catastrophic event  hit by an extraterrestrial body

• A series of volcanic eruptions

• (New) Data: found all over the world

• Unique crack patterns in quartz particles, and

• Unusually high concentration of iridium

• Prediction:

• same as what the new data shown

• Size and speed prediction: seemed reasonable

• Data-prediction agreement: GOOD  Model fit RW

### Why Statistical/Probabilistic Models?

• Widely used in science

• Social/behavioral sciences

• Public polls and surveys

• Testing theories like: sunlight helps prevent depression

• Bio-medical sciences

• Can also be used in daily life

• Professional sports:

• AFC vs. NFC: which conference has stronger teams?

• NBA: is the belief in “hot hand” supported by historical data?

### Modeling with Statistical Hypothesis

• Statistical hypothesis seem to be the only rational way to answer certain questions

• What percentage of American women between the ages of 20 to 30 hold a full-time job?

• Exceedingly difficult

• Very costly

• It’s impractical or even impossible to seek for characteristics in large populations

• Instead, we can proximate them using small samples

### Casual Models & Casual Hypothesis

• Behavioral/bio-medical scientists concern about causes of characteristics exhibited by individuals

• Does the dietary intake of cholesterol cause heart attacks in men?

• Cause or Correlation?

input

output

blackbox

### The Elements of a Statistical Study

• Terms associated with RW phenomenon

• Population: the object of the investigation

• A property is a characteristic that may exhibit in the population

• Also known as a variable in the sense that it can be measured or classified to describe the property

• Also known as a parameter as defined in the handout

• Terms associated with model

• Sample: selected members of the population

• Statistics: a number computed from data that describes a characteristic of a sample

### Stats as Predictions to Parameters

• Theme:

A statistic is computed from a sample to predict the parameter for the whole population.

• Ex 1: average height of a Mercer Student

Population

size: 8000+

Population:

Havg = XXX

Sample:

havg = xxx

Sample

size: 200

### Descriptive Statistics

• A graphical display of data

• Histograms

• Numerical summaries of data

• Center

• Shape

• Outlier

(See handout and sample

worksheet for details)

Super Bowl Scores (1967-2001)

### Announcements

• H/W Assignment 2

• Ex 7: p 8 in the handout

• Create a histogram

• Draw a boxplot and more as specified

• Read the sections 5.3 through 5.7 (pp 124-137) in Giere’s text