I let students decide how they would proceed and had them record their data on a slip of paper, which I later collected. Once they were done, I proceeded to query the class about different aspects of the experiment. This allowed me to introduce different vocabulary and concepts to cover topics within experimental design. Below is an outline of the first 75 minutes of class. I followed the outline but didn't necessarily pose all of the questions listed. Information that is italicized in brackets [example] are annotations I have made;
·
Open with coin stacking
o
Ask students to stack pennies as high as
possible using dominant and non-dominant hand
o
Record data on data collection sheet
·
Coin stacking discussion
o
What are natural questions related to stacking
pennies using dominant and non-dominant hands? [wrote questions on the board]
o
What do you think the results will show for the
various questions? [only did this for a couple of the listed questions]
§
These become our hypotheses, our belief or
knowledge about what is currently true
o
What protocol did you use for penny stacking?
§
Are protocols consistent?
§
How does this affect results?
o
What was the purpose of this experiment?
§
Assume want to find out if dominant or
non-dominant hand is better at stacking
§
What if told that the purpose was really to see
what percent stacked multiple pennies at a time? [this leads directly into blinding of experimetns]
·
Experimental components
o
Blinding is when the subject, and possibly the
experimenter, of an experiment does not know the treatment they are being given
§
Blinding is not required but is desired
·
Single blind – subject does not know what
experimental treatment is
·
Double blind—both subject and experimenter do
not know what experimental treatment is
§
Placebo is a treatment that masks whether a
subject is being given a true treatment (think sugar pill)
o
Required elements of an experiment
§
Control
·
Compare two or more treatments
o
What are treatments and comparisons in penny
stacking
·
What is a control group?
o
Base to compare against—the status quo, not
nothing
§
Randomization of assignment into groups
·
How should randomization be used here?
o
Randomization of which hand gets used first
§
Replication of treatments so have ability to
detect differences
o
What is the response variable in our experiment?
§
The variable we wish to measure and understand
o
What is a factor in our experimental design?
§
A variable that impacts the response variable
and we want to measure
§
Handedness
o
What are the levels of the factor?
§
The ways that a factor varies
§
Dominant and non-dominant hand
o
What are treatments?
§
Combinations of factors
§
What if experiment added in blindfold? What are
factors, levels, and treatments?
o
Cactus example assessment of understanding [use of soil additive or not and 5 water levels]
o
Experimental design diagrams
§
Show diagram for cactus [diagram with 10 treatments displayed, completely randomized design]
o
Could the strength of dominance impact results
in coin stacking? For example, what if some people are ambidextrous? [used a hypothetical of women being better stackers]
§
What could be done in the experiment’s design to
reduce this impact?
o
Blocking provides a means to group individuals
with a similar characteristic that may affect results
o
Golf example [driving distance for 40 golfers and 5 different brand golf balls]
§
What does a completely randomized design look
like?
§
What does a block design look like?
o
Discuss diagrams
After a short break we looked at how applicable the experiment's results would be to other students on campus. This led into a discussion of sampling. I asked students to consider how they could create a representative sample of students. From this, we were able to get at the ideas of simple random samples, systematic sampling, and stratified sampling. I then discussed cluster sampling. After this, I had students work through some examples for each so they could better see how each technique worked.
Here is the outline of the remainder of the class:
·
How applicable are the coin stacking results to
other groups? [the discussion here got into issues for later questions that I did not ask]
o
Why or why not applicable to the general
population?
·
What do we mean by a sample versus a population
in statistics?
o
Population—general group we are interested in
studying or measuring
o
Sample—a subset of the population for which we
have gathered information
·
In coin stacking, who are the population and who
are the sample? [didn't pose this question]
·
What conclusion can we draw from our experiment? [didn't pose this question]
·
How reliable do you think these conclusions are
for the overall population? [didn't pose this question]
o
The idea of considering the reliability of
conclusions drawn from data is what we mean by inferential statistics
·
Suppose we wanted to make the coin stacking
results more reliable for estimating what will happen on the Auraria campus.
How could we draw samples to make our results applicable across a broader
group?
·
Discuss what students come up for sampling
o
Should be able to name a few standard techniques [students covered all but cluster sampling]
·
River Sampling – Part 1
o
Students complete sampling piece to see how each
works [modified sampling down the river activity, had students only generate sampling using SRS, systematic, cluster, and stratified; will use results later for exploratory data analysis]
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