KNR 445 Statistical Applications in Science & Technology Dr. Steve McCaw Horton 227B

Why am I here? Interest took an earlier course recognize the importance Requirement program particular professor

Statistics The science of classifying organizing analyzing 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 PopulationSample 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) if the observed difference is or is not attributable only to chance (random sampling error)

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

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)

CDC data set