teaching statistics marty triola [email protected]
TRANSCRIPT
Insider’s Guide to Teaching Insider’s Guide to Teaching with the Triola Statistics with the Triola Statistics
SeriesSeriesFor adjuncts and full-time profs:For adjuncts and full-time profs: How to teach statisticsHow to teach statistics Comments, objectives, activitiesComments, objectives, activities Choosing a technologyChoosing a technology General teaching tipsGeneral teaching tips Syllabi, supplements, extra data Syllabi, supplements, extra data
setssets
ASA: GAISE ASA: GAISE RecommendationsRecommendations
1.1. Statistical literacy and Statistical literacy and statistical thinkingstatistical thinking
2.2. Use Use realreal data data
3.3. UnderstandingUnderstanding rather than rather than proceduresprocedures
4.4. Foster Foster activeactive learning learning
5.5. Use technologyUse technology
6.6. Use assessmentsUse assessments
In addition to In addition to teaching statistics, we teaching statistics, we can help our students can help our students growgrow through through developing …developing …
Important Life SkillsImportant Life Skills
Critical thinkingCritical thinkingTechnologyTechnologyCollaborationCollaborationSpeakingSpeaking
Implementing GAISEImplementing GAISE
Beyond formulas, much Beyond formulas, much interpretationinterpretation
Project!!!!!!!!!!Project!!!!!!!!!! Real dataReal data Technology for technologyTechnology for technology Technology for new topicsTechnology for new topics Technology for different methods:Technology for different methods:
Simulation, bootstrapSimulation, bootstrap
Beyond FormulasBeyond Formulas
Find P(20 girls in 20 births).Find P(20 girls in 20 births).
Is 20 girls in 20 Is 20 girls in 20 births…births…
unusual?unusual? Why? Why?
Beyond FormulasBeyond Formulas
Data from Atkins weight loss program:Data from Atkins weight loss program:
n n = 40, mean loss = 4.6 lb, SD = 10.6 = 40, mean loss = 4.6 lb, SD = 10.6 lb.lb.
Test the claim that the diet has no Test the claim that the diet has no
effect. effect. Would you Would you recommend it? recommend it?
Why or why not?Why or why not?
Beyond FormulasBeyond Formulas
TeachingTeaching
standard deviationstandard deviation ……
Single bank line: 4, 7, 7Single bank line: 4, 7, 7→→→→→→
■■ ■■ ■■
Multiple lines: 1, 3, 14Multiple lines: 1, 3, 14↓↓ ↓↓ ↓↓
■■ ■■ ■■
Project!!!Project!!!
Give someone a fish and Give someone a fish and you have fed them for you have fed them for today.today.
Teach someone to fish Teach someone to fish and you have fed them and you have fed them for a lifetime.for a lifetime.
Tell me something Tell me something and I’ll forget.and I’ll forget.
Show me Show me and I’ll remember.and I’ll remember.
Involve meInvolve me and I’ll learn.and I’ll learn.
Touch TherapyTouch Therapy
Emily Rosa: 9 yrs oldEmily Rosa: 9 yrs old280 trials: 44% 280 trials: 44% correctcorrect
JAMAJAMA
SurveySurvey1.1. ___Female ___Male___Female ___Male
2.2. Eye color: __________Eye color: __________
3.3. Enter five random digits:__ __ __ __ Enter five random digits:__ __ __ __ ____
4.4. Enter height in inches: __________Enter height in inches: __________
5.5. Enter last 5 digits of SSN: __ __ __ __ Enter last 5 digits of SSN: __ __ __ __ ____
6.6. Record pulse rate for 1 min.: ______Record pulse rate for 1 min.: ______
7.7. Do you smoke? _____Do you smoke? _____
8.8. Do you exercise? _____Do you exercise? _____
George Cobb article about evaluating George Cobb article about evaluating introductory statistics textbooksintroductory statistics textbooks
("Introductory Textbooks: A Framework for evaluation", ("Introductory Textbooks: A Framework for evaluation", Journal of the American Statistical AssociationJournal of the American Statistical Association, Vol. 82, , Vol. 82, No. 397):No. 397):
““Are the Data Sets Real or Are the Data Sets Real or Fake? . . .Fake? . . .I hope that soon we will I hope that soon we will have seen the last of the have seen the last of the infamous XYZ infamous XYZ Corporation and Hospitals Corporation and Hospitals A, B, C, . . ."A, B, C, . . ."
Data TypesData TypesFabricated: Bank Fabricated: Bank LinesLines
SimulatedSimulatedReal: Real: GOLD GOLD STANDARDSTANDARD
With REAL data, With REAL data, students see . . .students see . . .
some some purposepurpose in what they are in what they are doing.doing.
examples from fields they might be examples from fields they might be pursuing.pursuing.
that statistics is more than an that statistics is more than an abstract mental exercise. Statistics abstract mental exercise. Statistics is used in the real world.is used in the real world.
Really Bad ExerciseReally Bad Exercise
Give the formula for st. Give the formula for st. dev. and use it to find the dev. and use it to find the st. dev. of the following st. dev. of the following sample data, and show all sample data, and show all work: work:
16 5 16 5 2 0 8 82 0 8 8
Worse ExerciseWorse Exercise
The following are mean The following are mean teacher salaries (in teacher salaries (in thousands) in a sample of thousands) in a sample of states. Find the mean, states. Find the mean, median, and standard median, and standard deviation:deviation:
37 42 55 29 4137 42 55 29 41
Good ExerciseGood ExerciseUse these weights (g) of new quarters. Use these weights (g) of new quarters.
5.71 5.71 5.59 5.61 5.635.71 5.71 5.59 5.61 5.63
(a) Find mean(a) Find mean (b) Find st. dev. (b) Find st. dev.
(c) Is a weight of 5.23 g (c) Is a weight of 5.23 g unusualunusual? ? Explain. Explain. (d) What’s wrong with minting (d) What’s wrong with minting quarters quarters with weights that vary too with weights that vary too much?much?
Interesting DataInteresting Data Speeding tickets: 57 42 45 . Speeding tickets: 57 42 45 .
. .. .
Body temperatures: 98.6Body temperatures: 98.6
Benford's Law: Benford's Law: USA TodayUSA Today
11stst Digit Digit Frequency %Frequency %11 30.130.122 17.617.633 12.512.544 9.7 9.755 7.9 7.966 6.7 6.777 5.8 5.888 5.1 5.199 4.6 4.6
ProjectProject
Do the leading Do the leading digits of street digits of street addresses fit the addresses fit the distribution of distribution of Benford’s Law?Benford’s Law?
Project: Toss Coin 200 Project: Toss Coin 200 TimesTimes
Actually toss a coinActually toss a coin
oror
Make up the results.Make up the results.
11 1 1 11 00 11 11 00 11 11 0011 1 1 00 00 00 00 11 11 11 0000 1 1 11 00 00 00 11 00 00 1100 1 1 00 11 00 11 11 11 00 1111 0 0 11 11 11 00 00 11 00 1111 0 0 00 00 00 11 11 11 11 0000 1 1 00 00 00 11 11 11 00 1111 1 1 11 00 00 00 00 11 00 1100 0 0 11 11 00 11 11 11 00 0011 1 1 11 11 11 11 00 00 00 1111 0 0 11 11 00 11 11 00 00 0000 0 0 11 00 00 00 00 00 00 0011 0 0 11 00 11 11 11 00 11 0011 1 1 11 11 11 00 00 00 00 0000 0 0 11 00 11 00 11 11 11 0011 1 1 11 00 11 11 00 11 11 0011 1 1 00 11 11 00 00 11 11 0000 1 1 11 00 00 00 11 11 00 0000 1 1 11 00 11 11 00 00 00 1100 1 1 00 00 11 00 00 00 00 00
Project HintProject Hint
If you don’t do If you don’t do projects now, start projects now, start with a small step of with a small step of doing just doing just oneone project.project.
Assign near beginning of Assign near beginning of course:course:
1.1. Collect a set of Collect a set of real real data.data.
2.2. Print computer display of desc. Stat’s.Print computer display of desc. Stat’s.
3.3. Write a paragraph:Write a paragraph:
-Describe the data. Anything unusual?-Describe the data. Anything unusual?
-How did you collect the data?-How did you collect the data?
-How is the sampling method flawed?-How is the sampling method flawed?
TechnologyTechnology
Any Scientific Any Scientific CalculatorCalculator
TI-83/84 PlusTI-83/84 PlusMinitabMinitabSTATDISKSTATDISKExcelExcel
Example Example
Test Test HH00: : =98.6 =98.6oo
Sample Data:Sample Data: nn = 106, ¯ = 98.20, = 106, ¯ = 98.20, ss = 0.62 = 0.62x
TITI83/84 Plus:83/84 Plus:
Uses raw data or Uses raw data or statisticsstatistics
Has "APPS" Has "APPS" capabilitycapability
PPValue = Value = 0.000000001400.00000000140
TI-83/84 Plus HintTI-83/84 Plus Hint
Use CtlgHelpUse CtlgHelpExample: Example:
2:normalcdf( +2:normalcdf( +(press + before pressing (press + before pressing [ENTER])[ENTER])
TI-83/84 Plus ProgramsTI-83/84 Plus Programs
Download from Download from www.aw.com/triolawww.aw.com/triola
(by Michael Lloyd from Henderson State U.)(by Michael Lloyd from Henderson State U.)
Sample:Sample: CDISTR CDISTR (cumulative distributions)(cumulative distributions) TVAL TVAL ((PP-value for -value for tt distribution) distribution) ANOVA2RB ANOVA2RB (2-way ANOVA)(2-way ANOVA) S2TEST S2TEST (hyp. test for variance)(hyp. test for variance) X2GOF X2GOF (Chi-sq. gooodness-of-fit)(Chi-sq. gooodness-of-fit) KWTEST KWTEST (Kruskal-Wallis test)(Kruskal-Wallis test)
Minitab:Minitab: NOW ALLOWS SUMMARY STATISTICSNOW ALLOWS SUMMARY STATISTICS Can be bundled with textbook (or $29/5 months)Can be bundled with textbook (or $29/5 months) Windows only: 98, ME, NT 4, 2000, XPWindows only: 98, ME, NT 4, 2000, XP
Minitab 16 has new “Assistant” featureMinitab 16 has new “Assistant” feature
PPValue = 0.000Value = 0.000One-Sample T One-Sample T
Test of mu = 98.6 vs not = 98.6Test of mu = 98.6 vs not = 98.6
N Mean StDev SE Mean 95% CI T N Mean StDev SE Mean 95% CI T P P
106 98.2000 0.6200 0.0602 (98.0806, 98.3194) -106 98.2000 0.6200 0.0602 (98.0806, 98.3194) -6.64 0.0006.64 0.000
STATDISKSTATDISK
FreeFree
VeryVery easy to easy to useuse
Uses raw data Uses raw data or statistics.or statistics.
PPValue = Value = 0.00000.0000
Excel:Excel:
Uses raw data Uses raw data onlyonly
PPValue = 1Value = 1 ErrorsErrors
Excel: Add-in or STATDISKExcel: Add-in or STATDISK
PPValue < .0001 from Value < .0001 from XLSTATXLSTAT
SPSSSPSS Uses raw data only.Uses raw data only. Has student version.Has student version. No confidence interval for No confidence interval for pp.. Hypothesis test: Hypothesis test:
PP-value is always -value is always two-two-tailedtailed..
Must avoid conflict with field Must avoid conflict with field width and # decimals.width and # decimals.
SPSS (continued)SPSS (continued)
Summary of Summary of PPValuesValues
TITI83/8483/84 0.000000001400.00000000140 Minitab Minitab 0.0000.000 STATDISK STATDISK 0.00000.0000 ExcelExcel 1 (whoops!)1 (whoops!) SPSSSPSS 0.0000.000 SASSAS Doesn’t work.Doesn’t work.
Statistics OnlineStatistics OnlineMyStatLabMyStatLabMathXLMathXL
Technology as a TimeTechnology as a TimeSaverSaver
After covering CI and After covering CI and HT for HT for oneone population, use population, use technology and technology and assignassign exercises with exercises with two two samples.samples.
ProjectProject
Calculation: Calculation: 8×7×6 ×5 ×4 ×3 ×2 ×18×7×6 ×5 ×4 ×3 ×2 ×1or 1 ×2 ×3 ×4 ×5 ×6 ×7 ×8or 1 ×2 ×3 ×4 ×5 ×6 ×7 ×8
Do Do NOTNOT actually compute the result. actually compute the result.
Estimate Estimate the result in less the result in less than 5 secondsthan 5 seconds, , then write it then write it down.down.
Project: Hypothesis TestProject: Hypothesis Test
Test Test =98.6 =98.6oo
1.1. PP-value-value
2.2. Traditional (critical value)Traditional (critical value)
3.3. Confidence IntervalConfidence Interval
4.4.SimulationSimulation
SimulationSimulation
Hypothesis test of Hypothesis test of μμ = 98.6:= 98.6:Sample Data:Sample Data: n n = 106= 106
Sample mean = Sample mean = 98.2098.20
s s = 0.62 = 0.62Generate samples with assumed Generate samples with assumed mean of 98.6 and mean of 98.6 and nn = 106 and = 106 and ss = 0.62 to know if 98.20 is likely = 0.62 to know if 98.20 is likely to occur by chance.to occur by chance.
Time ManagementTime Management
Should we omit some Should we omit some topics to make time topics to make time for projects and for projects and technology?technology?
YES!!! (Within Reason)YES!!! (Within Reason)
““Don’t take life too Don’t take life too seriously. You’ll seriously. You’ll never get out of it never get out of it alive.”alive.”
SummarySummary
Use Use REAL DATAREAL DATA..Do a major Do a major PROJECTPROJECT..Use technology to save Use technology to save time.time.
Go “Go “BEYOND THE BEYOND THE FORMULA.”FORMULA.”
Continued…Continued…
Closing ThoughtsClosing Thoughts
Statistics is Statistics is fun fun to teach.to teach. Statistics is Statistics is relevant relevant ; ;
after one semester, students after one semester, students can do can do realreal projects. projects.
Statistics enables us to teach Statistics enables us to teach critical thinking, technology, critical thinking, technology, collaboration, speaking.collaboration, speaking.
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