Using JMP Scripts in Introductory Statistics

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Using JMP Scripts in Introductory Statistics
Amy G. Froelich
William M. Duckworth
Creighton University
Iowa State University
Concepts from Introductory Statistics

• Relationship Between Mean and
• Median
• Normal Quantile Plots
• Regression and Residual Plots
• Sampling Distributions
• Central Limit Theorem
• Normal Distribution vs. t distribution
• Confidence Intervals
• Variability
• Relationship Between Sample
• Size and Width of CI
• Connection Between Coverage
• Rates and Confidence Level

• Hypothesis Testing
• Connections Between
• CIs and Two-Sided Testing
• Between Rejection Rates and a
• Relationships Among Testing
• Conditions and Power
• Sample Size
• Alpha Level
• Difference Between True and
• Hypothesized Parameter
• Contingency Table
• Test for Two Proportions
• Fishers Exact Test

Advantages over Java applets available on web

• Script output in same format as JMP data
  analysis output.
• Flexibility to create script to match and expand
  different activities.
• Internet access not required.

Disadvantages over Java applets available on web

• Programming knowledge of JMP scripting language
  required.
• Dependent upon JMP platform.

Some Resources for JMP Scripts

• JMP Scripting Library
• http//www.jmp.com/support/downloads/jmp_scrip
  ting_library/
• Statistics Education Materials Repository at
  Iowa State University
• http//stated.stat.iastate.edu/
• Commercially Available Scripts
• Predictum Management Sciences
  (www.predictum.com)

This material is based upon work supported by
the National Science Foundation under Grant No.
0231322.
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Inference for the Mean
Population of 200 Female Heights
Hands-On Activity

• Random samples from this population
• Sample sizes 10 and 20
• Two samples of each size per group
• Sample Mean Height
• Calculate 90 CIs for Population Mean Height
• Conduct Hypothesis Test for Population Mean
• Height Under True Null Hypothesis (a 0.1)
• Learning Outcomes
• Discover variability of CI
• Discover effect of sample size on CI width
• Hypothesize about meaning of confidence
• Hypothesize about Type I error and alpha level

Confidence Interval Script
100 95 CIs for the Population Mean Height

• Replicates Hands-on Activity
• Sample from Larger Population
• 80, 90, 95 CIs
• Population Mean Height of Females
• Example Coverage Rates
• 80 CI 84/100
• 90 CI 91/100
• 95 CI 95/100

95 out of 100 CIs Contain the True Population
Mean Height
Hypothesis Testing Script
Type I error Replicates Hands-on Activity Ho µ
µTRUE vs. Ha µ ? µTRUE Vary sample size (5,
25, 50) alpha level (0.1, 0.05, 0.01)
Power Ho µ µFALSE vs. Ha µ ? µFALSE Vary
sample size (5, 25, 50) alpha level
(0.1, 0.05, 0.01) Value of µFALSE
100 z-test statistics with sample size 25 and a
0.05
100 z-test statistics with sample size 25 and a
0.05
4 out of 100 z-test statistics will reject Ho.
29 out of 100 z-test statistics will reject Ho.
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Inference for the Proportion
Hands-on Activity
Population of 200 Eye Colors

• Random samples from this population
• Sample sizes 10 and 20
• Two samples of each size per group
• Proportion of each sample with Blue Eyes
• Calculate 90 confidence intervals for
• Proportion in population with Blue Eyes
• Learning Outcomes
• Discover variability of CI
• Discover effect of sample size on CI width
• Hypothesize about meaning of confidence

Confidence Interval Script

• Replicates Hands-On Activity
• Sample from Larger Population
• 90, 95, 99 CI
• Proportion in Population with
• Blue Eye Color
• Example Coverage Rates
• 89/100 90 CI
• 97/100 95 CI
• 98/100 99 CI

100 90 Confidence Intervals for Proportion of
Population with Blue Eye Color
89 of the 100 Confidence Intervals Contain the
True Proportion of Population with Blue Eye Color
Plus 4 Method Confidence Interval Script
100 95 Traditional CIs for Proportion of
Population with Hazel Eye Color

• Sample from Larger Population
• Sample Size 10
• 95 CI for Proportion in
• Population with Hazel Eye Color
• Compare Two Methods
• Traditional
• Plus 4 Method
• Example Coverage Rates
• Traditional 81/100
• Plus 4 Method 91/100

81 of the 100 Traditional CIs Contain the True
Proportion of Population with Hazel Eye Color
100 95 Plus 4 Method CIs for Proportion of
Population with Hazel Eye Color
91 of the 100 Plus 4 Method CIs Contain the True
Proportion of Population with Hazel Eye Color
4
Randomization in the Design of Experiments
Hands-on Activity
Comparison of Mean Yields of Two Corn Varieties
Convenience Assignment
Alternating Assignment
No significant difference in mean yields between
two varieties.
No significant difference in mean yields between
two varieties.
The Importance of Random Assignment
The True Yields Per Plot for Each Variety
One Random Assignment of Varieties to Plots
Variety A Variety B by 12 bushels in each plot.
Significant difference in mean yields between two
varieties.
Hypothesis Testing Script
100 t-test statistics when true difference 12
bushels

• Replicates Hands-on Activity
• Random Assignments of Varieties to Plots
• Distribution of Sample Mean Differences Between
  
• Varieties
• Number of Rejections of Null Hypothesis of Equal
  
• Means
• Vary alpha level (0.05, 0.01)
• true difference between Varieties A
  and B
• Example Rejection Rates (a 0.05)
• 99/100 True Difference 12
• 43/100 True Difference 6
• 13/100 True Difference 3

99 out of 100 t-test statistics will reject Ho.
100 t-test statistics when true difference 6
bushels
43 out of 100 t-test statistics will reject Ho.
100 t-test statistics when true difference 3
bushels
13 out of 100 t-test statistics will reject Ho.
Original Activity Developed by W. Robert
Stephenson and Hal Stern. See their article in
STATS, Spring 2000, No. 28, 23-27. Programming
Assistance provided by Mark Bailey, SAS
Institute, Inc.