Download Introduction to Chance Models (Section 1.1) Introduction A key step

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Another Doris and Buzz study
One goal of statistical significance is to rule out random chance as a plausible (believable)
explanation for what we have observed. We still need to worry about how well the study was
conducted. For example, are we absolutely sure Buzz couldn’t see the headlight around the
curtain? Are we sure there was no pattern to which headlight setting was displayed that he
might have detected? And of course we haven’t completely ruled out random chance, he may
have had an incredibly lucky day. But the chance of him being that lucky is so small, that we
conclude that other explanations are more plausible or credible.
One option that Dr. Bastian pursued was to re-do the study except now he replaced the curtain
with a wooden barrier between the two sides of the tank in order to ensure a more complete
separation between the dolphins to see whether that would diminish the effectiveness of their
Step1: Ask a research question. The research question remains the same: Can dolphins
communicate in a deep abstract manner?
Step 2: Design a study and collect data. The study design is similar with some adjustments to
the barrier between Doris and Buzz. The canvas curtain is replaced by a plywood board. The
research conjecture, observational units, and variable remain the same.
In this case, Buzz pushed the correct button only 16 out of 28 times. The variable is the same
(whether or not Buzz pushed the correct button), but the number of observational units (sample
size) has changed to 28 (the number of attempts).
Think about it: Based on the results for this phase of the study, do you think that Doris could
tell Buzz which button to push, even under these conditions? Or is it believable that Buzz could
have just been guessing?
Step 3: Explore the data. So our observed statistic is 16 out of 28 correct attempts, which is
16/28 × 100% = 57.1% of Buzz’s attempts. This is again more than half the time, but not much
larger than 50%. A simple bar graph of these results is shown in Figure 1.5.
Figure 1.5: Bar graph for Buzz’s 28 attempts
June 27, 2014
MAA PREP workshop