Statistics in Applied Science & Technology

1 2 Click on the speaker to hear the audio for each slide…here first… Statistics in Applied Science & Technology Dr. Pete Smith McCormick 265G 438-3553 peter.smith@ilstu.edu …and here second.

1 2 Getting started… Relation of this course to 497; values, variables, measurement scales

A quick word on purpose… • Research methods and stats (497 and 445) • Here’s what I believe about them • Not everyone likes them • But nobody can do or critique quantitative research well without understanding their content • I don’t 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. 1 2

497 & 445 • Our way of teaching research methods 1

497 & 445 • The KNR way of teaching research methods • 497 dealt with internal, external and construct validity • Stats deals with conclusion validity • Statistics are ways of representing large collections of numbers • These numbers can be used to tell a story • Conclusion validity is the extent to which this story is true 1 2

Conclusion Validity • From 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 follow • Read about Trochim’s description here: • http://www.socialresearchmethods.net/kb/concval.htm 1 2

Descriptive... organize & summarize to help understanding frequency average variability relationships Inferential... reasoning from particulars to generals infer (generalize) to a population from studying a sample drawn from the population margin of error evaluating experiments random sample observed differences expected variability relationships 2 Main Branches of Statistics 1 3 4 2

Population Complete set of observations on a particular variable E.g. height & weight ==> 2 populations Can be all from same subject (height over lifespan) Defined by investigator this year’s stats class Sample Part of a population any subset of population this 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 Parameters Statistics Population & Samples 3 1 2 4

Conclusion validity & … 1 • Descriptive research • Does 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? 2 3 4

Conclusion validity & … • Inferential research • As 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 don’t work the same way – they are quite intricate) • Effect size • Type I and type II error • Power 1 2 3

What’s covered in 445? • For an overall picture, see inside cover of Cronk – it’s a nice summary • As we proceed, I’ll note what sections of Cronk the slides, assignments, and applets refer to 1 2 Java 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 learn

What’s covered in 445? • Applets… • Example: applet for mean, median, mode (measures of something called central tendency – we’ll cover them 2-3 weeks from now]) • http://www.ratrat.com/histogram_explorer/he.html 1 2 3

First week objectives • Get started with SPSS statistics • Need to open the program and do a few things just to make sure you can get things going…nice and easy start so that you don’t get despondent too soon • Get started with the conclusion validity • Many assumptions of statistical tests depend on levels or scales of measurement…so we need to familiarize ourselves with them 1

Levels of 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 • Male vs Female • S.S. Stevens (1946): Four Scales of Measurement to facilitate interpretation and analysis of measured values • in order of complexity… 1 2

Nominal • “In 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 one • Exhaustive: enough categories for all cases • Ethnicity • sex • single-married 1 2

Ordinal • “In 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 cases • Mutually exclusive: only belong to one • Nothing implied about the magnitude of difference between the ranks • military / business rankings • first place, second place, third place 1 2

Interval • In 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 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) • E.g. temperature in Degrees Celsius or Fahrenheit • 0 and 100 degrees are set in Celsius as freezing & boiling point of water • Why 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) 1 4 2 3

Ratio 1 • “Finally, 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 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 (position, velocity, acceleration) • Weight

Interval & Ratio Measurements • Easy 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 definitions 1 • Variable: characteristic that can take on different values • Discrete variables: can only take on certain values • # correct answers, Likert scales, # reps • Continuous variables: can take any value within the range. Accuracy limited by instrumentation, data collection method • height, weight, time, temperature • Measurement turns continuous variable into discrete one (rounding) • Things you should know: • Independent variable, dependent variable

For next time 1 • A quiz on this stuff is posted on the web • Just measurement scales, and identifying values, variables, independent variables and dependent variables • Complete the practice exercises in Cronk, chapters 1 and 2. • Let me know if you have problems • All computer labs in CAST should have PASW Statistics installed on the computers

Statistics in Applied Science & Technology