KNR 445Statistical Applications in

Science & Technology

Dr. Steve McCaw

Horton 227B

438-3804

smccaw@ilstu.edu

www.cast.ilstu.edu/mccaw

Why am I here?

• Interest• took an earlier course• recognize the importance

• Requirement• program• particular professor

Statistics

The science ofclassifyingorganizinganalyzing

data

Who uses statistics??

• Everyone researcher • clinicians• educators• social policy• gambler• program administrator• families

Single Parent Families

Two Main Branches of Statistics

• Descriptive Statistics• organize & summarize to

facilitate understanding• frequency

• average

• variability

• relationships

• Inferential Statistics

• reasoning from particulars to generals• draw inference (generalize)

about a population from study of a sample drawn from the population

• margin of error

• evaluating experiments• random sample

• observed differences

• expected variability

• relationships

Population & Samples

• Complete set of observations on a particular variable• height & weight ==> 2

populations• all from same subject (GRF)

• Defined by investigator• ie runners with PFP

• GRF of Donovan Baily

• this year’s stats class

• Part of a population• any subset of population

• this year’s stats class is a sample of students taking stats in CAST

• Random sample: each case of the population has equal chance of being included in the sample

Population Sample

Parameters

Statistics

Sample Properties(one of the most important slides of the whole course)

• Infinite number of samples may be drawn from a population (differ in size of sample)

• Because of sampling variation or sampling error, sample characteristics (statistics) will probably differ from• population characteristics (parameters)• characteristics of other samples drawn from the same

population

• Larger random samples will demonstrate less variability from sample to sample

Relationship & Prediction• Patterns in the world around us• Some relationship between

• chilled <> catch a cold

• diet <>HBP

• smoking<>CTD

• work out <> getting fit

• plant growth & fertilization• & fertilization & water intake & sunlight & temperature

• Knowing relationship allows for prediction• GRE & GPA ; Smoking & health care costs

Using Statistics

• Mathematical standard that helps in decision making

• Logical thought-process to aid in evaluating the “truth”

• Tool to be utilized (Volk in Family Circle) when you are

• interpreting research

• synthesizing research

• conducting research

Statistics is a TOOL

• Facilitates decision making• Leads to a more careful way of thinking/speaking

and assessing risk• Cigarettes cause cancer• Increased nitrogen in water causes birth defects• Hockey violence causes losing

• Lies, damn lies, & statistics (B. Disraeli, British PM)

• Facts are stubborn things but statistics are more pliable

Every year since 1950, the number of American children gunned down

has doubled.

Using Statistics

• Research Question (substantive questions): what drives knowledge• question of fact concerning subject matter under

investigation• derived from synthesis of theory & previous literature

(published studies)

• Example:Does ankle bracing affect joint motion when landing??

Scientific Process

• Research Question• Design study

• Variable: characteristic that may take on different values (assignment, measurement)

• Male or Female• alumni• school• winner• height• weight• motivation level• region• family income• CHO intake• sex

Simple Problems

Scientific Process

• Research Question

• Design study• Independent variable: variable systematically

manipulated by the researcher •

Scientific Process

• Research Question

• Design study• Independent variable• Dependent variable: variable measured in the study

•

Scientific Process

• Research Question

• Design study• Independent variable• Dependent variable• Extraneous\secondary\confounding variable: important

factor that might affect outcome

Scientific Process

• Research Question

• Design study

• Collect data and calculate the ROM• Would you expect the ROM to be the same in both

conditions?

Statistical Question

Is the average ROM in the two conditions so different

that chance variation (random sampling error)

alone does not account for it?

Apply a statistical procedure

Statistical conclusion

Based on outcome of the statistical procedure

Conclude (decide) ifthe observed difference

is or is notattributable only to chance (random sampling error)

Research conclusion(substantive conclusion)

Conclusion about the subject matterROM

was or was notaffected by ankle bracing

Based on : statistical decision andadequacy of research design

Scientific Process: 5 steps

• Research Question

• Statistical question (design study)

• Conduct study

• Apply statistical procedure• from statistical question ==> statistical conclusion

• Research Conclusion

Measurement

• Assign value (number or name) to an observation or characteristic (qualitative vs quantitative)

• What does a particular value mean?• 40 pounds vs 20 pounds

• 1st place vs 2nd place

• Healthy vs sick vs dying

• S.S. Stevens (1946) identified Four Scales of Measurement to facilitate interpretation and analysis of measured values• in order of complexity

Nominal Scale

• Qualitative or Categorical variables (names)• Mutually exclusive: only belong to one• Exhaustive: enough categories for all cases

• eye colour• sex• single-married• yes-no situations• “Bob & Tom” vs “Early Edition”• brace 1, brace 2, brace 3 (for ID purposes only)

Ordinal Scale

• Indicate the Order of Magnitude of some variable (creates a set of ranks)

• Exhaustive: enough categories for all cases

• Mutually exclusive: only belong to one

• Nothing implied about the magnitude of difference between the ranks• military rankings / business rankings• first place, second place, third place

Interval Scale

• Mutually exclusive

• Exhaustive

• Indicates order but interval between scores has the same meaning anywhere on the scale• aka Equal Interval Scale• value of 0 is some arbitrary reference point (set by the

investigator)• temperature in Degrees Celsius or Fahrenheit

• 0 and 32 degrees are set as freezing point of water

Ratio Scale

• Mutually exclusive

• Exhaustive

• Indicates order but scale has an absolute 0 point reflects Absence of the characteristic being measured• temperature in Degrees Kelvin (0 is Absence of heat)• distance and derivatives (height, speed, acceleration)• weight• time

Other important definitions

• Variable: characteristic that can take on different values

• Discrete variables: can only take on certain values• number of correct answers, Likert scales, # of reps

• Continuous variables: can take on any value within the range with accuracy limited by instrumentation and method of collecting data• height, weight, time, temperature• Measurement turns continuous variable into discrete

one (rounding to least significant digit)

STATE TAX SMKR18 SMKDTHS WHDR HDR CDR

Alabama 16.5 20.2 350.4 445.0 157.0 136.2

Alaska 29.0 27.8 398.2 285.0 100.5 116.9

Arizona 58.0 20.2 339.6 339.0 110.3 114.0

Arkansas 31.5 26.6 376.3 413.0 149.7 139.4

Calif ornia 37.0 19.3 366.3 373.0 114.1 114.1

Colorada 20.0 23.9 331.4 296.0 94.0 101.4

Connecticut 50.0 21.6 325.7 371.0 119.7 120.2

DC 65.0 18.2 444.7 431.0 138.3 142.2

Deleware 24.0 27.0 393.1 444.0 157.2 155.8

Florida 33.9 22.4 357.5 353.0 118.6 125.7

TAX

SMKR18

SMKDTHS Smoking deaths (per 100,00) among people over 18 years old (CDC data)

WHDR Womens death rate (per 100,000) f rom heart disease (CDC data)

HDR

CDR

tax per pack of cigarettes, in cents (CDC data)

Percent of population over 18 years old identifi ed as "smokers" (CDC data)

Heart disease death rate, per 1,000 (AARP data, 1999)

Cancer death rate, per 1,000 (AARP data, 1999)

CDC data set