Wednesday, September 21
We're starting a unit on observational studies and experimental design. This will align with Chapter 5 in the text.
TEST October 13.
The concepts for today's lesson were
sampling
experiments
observational studies
sample / population
sampling method
probability sampling methods
Simple Random Sample
Stratified Random Sample
Cluster Sample
Elements of good experimental design: randomness, replication, control
HW: problems 1-5 on the paper handed out in class today
Preview topic for Thursday here.
Need something to do since there's no football game this week? Moneyball hits theaters this weekend (PG-13 language). I have recommended this book for years. It is the story of how the Oakland As used statistics to create a championship team using statistics instead of the usual scouting system.
Interesting article from Clearwater today about a highly unlikely event. (Warning--health related topic)
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Thursday, September 22
We looked at randomness and replication again today. Students picked up a handout with a discussion of the need for both. We also looked over the homework. Please be prepared with the homework every day. Some students did not do the homework and received 0/2 points today for preparedness.
HW: use the table of random digits provided and the example on the back side of that page to work problems 11-13.
Two online activities related to today's topics are http://www.nsa.gov/academia/_files/collected_learning/high_school/statistics/random_number_table.pdf
and http://www.mdk12.org/share/clgtoolkit/lessonplans/RandomDigitTables.pdf
You don't have to do all the sections in these activities, but the more you understand, the better prepared you will be.
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Friday, September 23
We looked at test scores today. Many students did very well. If you were one of those who didn't do well, let's make some plans for improvement. Have you come in before school for help? Have you done all your homework? Have you taken notes every day in class? What can we do to help you "get it?"
We also investigated blocking. We block an experiment when we believe that there is an existing characteristic of some of the experimental units that will influence the response significantly, possibly more significantly than the treatment itself!
Example: imagine a pool of seniors and second graders. We're going to divide them up to train them using one of two different reading programs. Complete randomization would yield results that had really high scores and really low scores because the people had such differing skills going into the experiment. It would be difficult to tell which program was better.
If we blocked on grade, then we are breaking the experiment into two smaller experiments. The range of results for the second graders will be shorter, so it should be easier to differentiate between the results of the two programs. This improves the "power" of the test. Similarly, the scores of the seniors should be closer together than the original sets of scores, so this should follow suit.
HW problems 3 and 4 from the 2001 AP Exam. Email me if you need a copy. __________________________________________________________________________________
September 26 & 27, 2011
We've been splitting our time between simulations and blocking. You should have completed problems 13-15 on the page of problems, plus the fish tank problem from the 1997 exam. Also, if southpaws (left-handed people) make up 10% of the population, use simulation (your calculator or the TORD) to estimate how many people you would have to meet UNTIL you met a left-handed person. Repeat this 19 more times. Formulate a reasonable theoretical estimate for this value.
September 28 & 29, 2011
Thank goodness for the old books! We used the older version of the textbook in pairs to practice simulation. The problems included 54-59 and 78-82. If you need a copy of 78-82, please swing by the classroom and pick up a copy from the pocket on the door.
You will recall that the focus for this week has been split between experimental design and simulation. The two topics intersect in the descriptions of how to randomize.
Experimental design: must include a treatment applied to experimental units. Good experimental design incorporates control, randomness, and replication. Completely randomized designs have no blocking. Blocking MAY be implemented in order to reduce the variability in the results that stems from a pre-existing condition. After blocking into two (or more) groups that are DIFFERENT from each other but homogeneous within the group, the units within the blocks are randomly allocated to treatment groups.
2 blocks x 3 treatments means 6 different treatment groups.
The videos about mathemagic that we saw in class can be found online at http://www.math.hmc.edu/~benjamin/mathemagics/video.html
Be prepared for a quiz over experimental design at any time.
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Tuesday, October 4, 2011
We got books today and covered them to protect them. I DO expect the books to remain covered, and that you will bring them to class every day for the next three weeks. We have a lot of catching up to do.
In the last two days we investigated the biases associated with survey design. Specifically, we looked at response and wording bias (both can lead to answers that do not represent the truths for the people surveyed--a validity problem), non-response bias (stemming from the chosen people's refusal to contribute, either actively or passively), undercoverage (when your sampling frame does not cover your population), and the Garbage-in-garbage out twins: voluntary response bias and convenience samples.
We took a moment to discuss validity and reliability. Like the precision and accuracy concepts from science class, these topics are not synonyms, but they are commonly addressed at the same time. Look online for more information about how these concerns are addressed in practice.
HW from the book :) due Wednesday: problems 5.33-5.36. The three pagtes prior to the questions have great explanations of the terms in the problems. Use them!
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Friday and Monday, October 7 and 10
We considered two problems from previous AP exams, the shampoo problem, and the tai chi problem. Both of these questions deal with experimental design. You were supposed to write up good answers in the journals. I hope that you used your time wisely.
Today we looked at completely randomized designs and blocked designs for experiments and contrasted the methods with stratified sampling for surveys. Both blocking and stratifying break a large group into partitions based on a previously-existing condition because the responses may vary systematically between these groups. In experimental design, the purpose is to reduce the variability in the responses so you can differentiate between the two groups' responses. For survey design, you sample from each of the partitions (strata) and throw the selected participants into one group that should mimic the responses of the entire population. We stratify to make sure that each portion of the population is adequately represented in the sample.
Multistage sampling requires a series of random selections--for instance randomly picking a class period, then randomly picking 10 classes held that period, then randomly picking 10 kids from each of those 10 classes.
Systematic sampling involves some randomness to start, then an arbitrary method of selecting the rest of the participants based on the one random selection.
Simple random sampling is distinguished from these other sampling methods because every possible sample of size n has an equal chance of being selected. In the other methods there are possible combinations of participants that have NO chance of being selected.
Brush up on your methods for using a TORD to select a sample or randomly allocate experimental units to groups.
HW: problems 5.15-5.20 AND at least 4 of these 5.27 - 5.32. If you are weak at these problems, then you need to work MORE of them, not fewer of them!
You will have a test on Thursday over Chapter 5.
