HPR 445 Statistical Applications in Science & Technology

Statistics in Applied Science & TechnologyDr. Pete SmithMcCormick 265G438-3553peter.smith@ilstu.edu1

2Click on the speaker to hear the audio for each slidehere first

and here second.

Getting startedRelation of this course to 497; values, variables, measurement scales1

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A quick word on purposeResearch methods and stats (497 and 445)Heres what I believe about themNot everyone likes themBut nobody can do or critique quantitative research well without understanding their contentI dont want to argue, but these courses are not going away, so you might as well accept them. There are, honestly, very good reasons for keeping them.12

497 & 445Our way of teaching research methods

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497 & 445The KNR way of teaching research methods497 dealt with internal, external and construct validity Stats deals with conclusion validityStatistics are ways of representing large collections of numbersThese numbers can be used to tell a storyConclusion validity is the extent to which this story is true

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Conclusion ValidityFrom Trochim (the 497 text from last semester for most of you [I think]): Conclusion validity is the degree to which conclusions we reach about relationships in our data are reasonable.Stats is largely about answering that question.There is an issue here with descriptive vs. inferential stats that will followRead about Trochims description here:http://www.socialresearchmethods.net/kb/concval.htm

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2 Main Branches of StatisticsDescriptive...organize & summarize to help understandingfrequencyaveragevariabilityrelationships

Inferential...reasoning from particulars to generalsinfer (generalize) to a population from studying a sample drawn from the populationmargin of errorevaluating experimentsrandom sampleobserved differencesexpected variabilityrelationships1234

Population & SamplesPopulation Complete set of observations on a particular variableE.g. height & weight ==> 2 populationsCan be all from same subject (height over lifespan)Defined by investigatorthis years stats class

Sample Part of a populationany subset of populationthis stats class is a sample of students taking stats in CASTRandom sample: each case of the population has equal chance of being included in the sampleParametersStatistics1234

Conclusion validity & Descriptive researchDoes not attempt to generalize, so conclusion validity is [relatively] simple:Are your measurements and computations accurate and do they fully represent the patterns that are in the data?1234

Conclusion validity & Inferential researchAs for descriptive, plus the notion that your inference from the sample to the population is reasonable(Non-) violation of assumptions (if you violate assumptions of the statistical procedures, the tests simply dont work the same way they are quite intricate)Effect sizeType I and type II errorPower123

Whats covered in 445?For an overall picture, see inside cover of Cronk its a nice summaryAs we proceed, Ill note what sections of Cronk the slides, assignments, and applets refer toJava programs that run in a web browser (netscape, internet explorer, firefox, safari, etc) that give a dynamic graphical interpretation of the concepts we are trying to learn12

Whats covered in 445?AppletsExample: applet for mean, median, mode (measures of something called central tendency well cover them 2 weeks from now])http://www.ratrat.com/histogram_explorer/he.html12

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First week objectivesGet started with SPSS statisticsNeed to open the program and do a few things just to make sure you can get things goingnice and easy start so that you dont get despondent too soonGet started with the conclusion validityMany assumptions of statistical tests depend on levels or scales of measurementso we need to familiarize ourselves with them1

Levels of MeasurementAssign value (number or name) to an observation or characteristic (qualitative vs quantitative)What does a particular value mean?40 pounds vs 20 pounds1st place vs 2nd placeMale vs FemaleS.S. Stevens (1946): Four Scales of Measurement to facilitate interpretation and analysis of measured valuesin order of complexity12

NominalIn nominal measurement the numerical values just "name" the attribute uniquely. No ordering of the cases is implied. For example, jersey numbers in basketball are measures at the nominal level. A player with number 30 is not more of anything than a player with number 15, and is certainly not twice whatever number 15 is. (Trochim)Qualitative or Categorical variables (names)Mutually exclusive: only belong to oneExhaustive: enough categories for all casesEthnicitysexsingle-married12

OrdinalIn ordinal measurement the attributes can be rank-ordered. Here, distances between attributes do not have any meaning. For example, on a survey you might code Educational Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college; 4=college degree; 5=post college. In this measure, higher numbers mean more education. But is distance from 0 to 1 same as 3 to 4? Of course not. The interval between values is not interpretable in an ordinal measure. (Trochim)Exhaustive: enough categories for all casesMutually exclusive: only belong to oneNothing implied about the magnitude of difference between the ranksmilitary / business rankingsfirst place, second place, third place12

IntervalIn interval measurement the distance between attributes does have meaning. For example, when we measure temperature (in Fahrenheit), the distance from 30-40 is same as distance from 70-80. The interval between values is interpretable. Because of this, it makes sense to compute an average of an interval variable, where it doesn't make sense to do so for ordinal scales. But note that in interval measurement ratios don't make any sense - 80 degrees is not twice as hot as 40 degrees (although the attribute value is twice as large).Mutually exclusiveExhaustiveIndicates order but interval between scores has the same meaning anywhere on the scaleaka Equal Interval Scalevalue of 0 is some arbitrary reference point (set by the investigator)E.g. temperature in Degrees Celsius or Fahrenheit0 and 100 degrees are set in Celsius as freezing & boiling point of waterWhy is 0 f set there?Zero Fahrenheit was the coldest temperature that the German-born scientist Gabriel Daniel Fahrenheit could create with a mixture of ice and ordinary salt (may be apocryphal see Wikipedia)1234

RatioFinally, in ratio measurement there is always an absolute zero that is meaningful. This means that you can construct a meaningful fraction (or ratio) with a ratio variable. Weight is a ratio variable. In applied social research most "count" variables are ratio, for example, the number of clients in past six months. Why? Because you can have zero clients and because it is meaningful to say that "...we had twice as many clients in the past six months as we did in the previous six months. (Trochim)Mutually exclusiveExhaustiveIndicates order but scale has an absolute 0 point reflecting absence of the characteristic being measuredtemperature in Degrees Kelvin (0 is Absence of heat)distance and derivatives (position, velocity, acceleration)Weight1

Interval & Ratio MeasurementsEasy way of telling if scale is interval or ratio:If you divide a score on the scale by two, is the amount half as much as it was?Temperature 25 degrees C is not half as hot as 50 C (interval)Weight 25lbs is half as heavy as 50lbs (ratio)1

Other important definitionsVariable: characteristic that can take on different valuesDiscrete variables: can only take on certain values# correct answers, Likert scales, # repsContinuous variables: can take any value within the range. Accuracy limited by instrumentation, data collection methodheight, weight, time, temperatureMeasurement turns continuous variable into discrete one (rounding)Things you should know:Independent variable, dependent variable1

For next timeA quiz on this stuff is posted in reggienetJust measurement scales, and identifying values, variables, independent variables and dependent variablesComplete the practice exercises in Cronk, chapters 1 and 2.Let me know if you have problemsAll computer labs in CAST should have SPSS installed on the computersListen to lots of slides for 1.25.15 central tendency, spread, z-scores, graphing.1