Thats a bunch of Bridget Matamoros Guyer High School Denton TX BULL Wei Simulations Work But they must be Efficient Effective Sticky One 90 minute block Get the point across clearly Engaging and concrete enough that students will remember the point ID: 763554
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That’s a bunch of Bridget MatamorosGuyer High SchoolDenton, TX BULL!! Wei
Simulations Work! But they must be:EfficientEffective Sticky ~One 90 minute block Get the point across clearly Engaging and concrete enough that students will remember the point
Minitab ROCKS! 30 seat perpetual license = $1,000
Took quite a bit of time to cut out the population data. A student aide (or spouse) is helpful here. 300 Numbers to sample from in each population simulated from Minitab
Groups of 3-4 students randomly selected a population identified only by a letter. They did not know any characteristics about the population. 2 bags of the same population per group to increase speed of sampling
Students worked in pairs to take samples of size 30 and calculate sample means. After 20-30 sample means were obtained they created histograms.
Then came The Big Reveal…
Descriptive Statistics: Normal Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Normal 300 14.620 0.288 4.991 0.000 12.000 15.000 18.000 30.000 where is the mean and is the standard deviation
Descriptive Statistics: Chi-Squared DF=10 Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum ChiSquare 300 9.887 0.253 4.378 1.000 7.000 9.000 12.000 30.000 where is the parameter for the degrees of freedom and denotes the gamma function
Descriptive Statistics: Uniform [0, 30] Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Uniform 300 14.510 0.513 8.886 0.000 7.000 14.000 22.750 30.000 where a and b are the interval minimum and maximum
Descriptive Statistics: Gamma Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Gamma 300 9.853 0.384 6.645 0.000 5.000 8.000 13.000 40.000 where is the shape parameter is the scale parameter and denotes the gamma function
Descriptive Statistics: Triangular Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Triangular 300 18.893 0.371 6.424 0.000 15.000 20.000 24.000 30.000 where a and b are the interval minimum and maximum and c is the mode
Descriptive Statistics: Laplace Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Laplace 300 15.380 0.242 4.187 0.000 13.000 15.000 18.000 30.000 where is the location parameter and is the scale parameter
Descriptive Statistics: Beta*30 Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Beta*30 300 15.147 0.715 12.381 0.000 1.000 16.000 28.000 30.000 where are the shape parameters and denotes the gamma function
Descriptive Statistics: Weibull Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Weibull 300 8.877 0.720 12.478 0.000 1.000 4.000 11.000 100.000 where is the shape parameter and is the scale parameter
Outcomes Expected Observed Approximately normal sampling distributions for almost all groups Only a handful were approximately normal Students to bore quickly with monotonous calculations They actually worked fairly efficiently Lingering confusion about the CLT Students internalized the CLT more effectively by comparing populations Activity to take only one class period We barely finished histograms and closed up discussion the next day
Un-Expected Results Exposure to the Nearly Normal ConditionWeibull and others were SO skewed that a sample size of 30 was not sufficient to produce an approximately normal sampling distribution Populations that were unimodal and not severely skewed produced sampling distributions closer to normal Later reinforcement of the Nearly Normal Condition I referred to the activity and in particular the Weibull distribution numerous times for T inference procedures.
Improvements Play music during sampling to keep energy up (student recommended) Write a calculator program instead PRO: Faster sampling CON: Not concrete enough for some students to get the pointJIGSAW Method might work better
JIGSAW Method Students go to different groups where they work together to create the sampling distribution. Each member produces their own copy of the histogram. They go back to their original groups to share/compare results before whole class discussion.
Want more bull? bmatamoros@dentonisd.org