KNR 445 Statistical Applications in Science

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KNR 445Statistical Applications in Science
Technology
What are you enrolled in?

• Dr. Steve McCaw
• Horton 227B
• 438-3804
• smccaw_at_ilstu.edu
• www.castonline.ilstu.edu/mccaw

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Why am I here?

• Interest
• took an earlier course
• recognize the importance
• Requirement
• program
• particular professor

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Statistics
The science of classifying organizing analyzing da
ta
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Who uses statistics??

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

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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

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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

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Relationship Prediction

• Patterns in the world around us
• Some relationship between
• chilled ltgt catch a cold
• diet ltgtHBP
• smokingltgtCTD
• work out ltgt getting fit
• plant growth fertilization
• fertilization water intake sunlight
  temperature
• Knowing relationship allows for prediction
• GRE GPA Smoking health care costs

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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

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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

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What about this statement?
Every year since 1950, the number of American
children gunned down has doubled.
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What they really said.
The number of American children killed each
year by guns has doubled since 1950.
Childrens Defense Fund, The state of Americas
Children Yearbook 1994.
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CDC data set
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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)
• Examples
• Does ankle bracing affect joint motion when
  landing??
• Do holding promotional nights increase
  attendance?

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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
• attendance

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Scientific Process

• Research Question
• Design study
• Independent variable variable systematically
  manipulated by the researcher
• Male vs female
• brace vs no-brace conditions
• Promotion vs no promotion game

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Scientific Process

• Research Question
• Design study
• Independent variable
• Dependent variable variable measured in the
  study
• The score one receives
• joint range of motion
• attendance
• toilet paper

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Scientific Process

• Research Question
• Design study
• Independent variable
• Dependent variable
• Extraneous\secondary\confounding variable
  important factor that might affect outcome
• previous injury, familiarity with landing,
  height, speed, style of landing, ???
• Examples affecting attendance?

Control them or measure them
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Scientific Process

• Research Question
• Design study
• Collect data and calculate the ROM
• Would you expect the ROM to be the same in
  repeated trials of the same condition?
• Would you expect the ROM to be the same in trials
  of both conditions?

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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
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Statistical conclusion
Conclude (decide) if the observed difference is
or is not attributable only to chance (random
sampling error)
Based on outcome of the statistical procedure
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Research conclusion(substantive conclusion)
Conclusion about the subject matter ROM was or
was not affected by ankle bracing
Based on statistical decision and adequacy of
research design
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Scientific Process 5 steps

• Research Question
• Statistical question (design study)
• Conduct study
• Apply statistical procedure
• from statistical question gt statistical
  conclusion
• Research Conclusion

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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
• Two types of variables
• Numeric
• String (alphanumeric characters)

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Review 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)

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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)

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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

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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

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Ratio Scale

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