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In the actual study, Buzz really did push the correct button 15 times out of 16, an outcome that we just determined would rarely occur if Buzz was just guessing. So, our coin flip chance model tells us that we have very strong evidence that Buzz was not just tossing a coin to make his choices. This means we have strong evidence that Buzz wasnât just guessing. Therefore, we donât believe the âby chance aloneâ explanation is a good one for Buzz. The results mean we have strong enough evidence to be statistically significant, not a result that happened by chance alone, and to convince us that something other than ârandom chanceâ was at play. Definition: A result is statistically significant if it is unlikely to occur just by random chance. If our observed result appears to be consistent with the chance model, we say that the chance model is plausible or believable. What next? A glimpse into Steps 5 and 6 The steps we went through above have helped us evaluate how strong the evidence is that Buzz is not guessing (Step 4 of the Statistical Investigation Method). In this case, the evidence provided by this sample is fairly strong that Buzz isnât guessing. Still, there are some important questions you should be asking right now, such as: If Buzz isnât guessing what is he doing? Step 5: Formulate conclusions. We should also ask ourselves: if Buzz wasnât guessing, does this prove that Buzz and Doris can communicate? And if so, what does this say about other dolphins? As weâll find in later chapters, the answers to these questions hinge mainly on how the study was designed and how we view the 16 attempts that we observed (e.g., we assume Buzz couldnât see the light himself, the light signal displayed each time was chosen randomly so Buzz couldnât figure out a pattern to help him decide which button to push; Buzzâs 16 attempts are a good representation of what Buzz would do given many more attempts under identical conditions; but we might still wonder whether Buzzâs behavior representative of dolphin behavior in general or are there key differences among individual dolphins). Step 6: Look back and ahead. After completing Steps 1-5 of the Statistical Investigation Method, we need to revisit the big picture of the initial research question. First, we reflect on the limitations of the analysis, and think about future studies. In short, we are now stepping back and thinking about the initial research question more than the specific research conjecture being tested in the study. In some ways, this is the most important step of the whole study because it is where we think about the true implications of the scientific study weâve conducted. For this study, we would reflect on Dr. Bastianâs methods, summarize the results for Buzz, and reflect on ways to improve the study to enhance the conclusions we can draw. The 3S Strategy Let us summarize the overall approach to assessing statistical significance that we have been taking in this section. We observed a sample statistic (e.g., the number of âsuccessesâ or the proportion of âsuccessesâ in the sample). Then we simulated âcould-have-beenâ outcomes for that statistic under a specific chance model (just guessing). Then we used the information we gained about the random variation in the âby-chanceâ values of the statistics to help us judge whether the observed value of the statistic is an unusual or a typical outcome. If it is unusualâ we say the observed statistic is statistically significantâit provides strong evidence that the chance-alone explanation is wrong. If it is typical, we consider the chance model plausible. You may have noticed that we only simulated results for one specific model. When we saw that the sample statistic observed in the study was not consistent with these simulated results, we June 27, 2014 MAA PREP workshop 6