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Basics Skills: Capstone Table of Contents:) Inferential Statistics: Introduction (2.) Inferential Statistics: An Example (3.) Using Inferential...

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I do not understand what are the step to fallow in the experimental design (factors affecting leaf size)
I am confused; I don't know how to gather the data and complete the activity sheet (Basic Capstone)
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PS: the document is ESA21 Environmental Science Activities for the 21st Century Basic skills: Capstone
Basics Skills: Capstone Table of Contents: (1.) Inferential Statistics: Introduction (2.) Inferential Statistics: An Example (3.) Using Inferential Statistics (4.) The t-test (5.) The t-test - An Example (6.) t-tests and Statistical Assumptions - A Word of Caution (7.) Answers to Practice Problems (8.) Sample Problems (9.) Capstone: Putting It All Together Inferential Statistics: Introduction You have already gained experience with descriptive statistics but we will now introduce a new class of statistics that are also useful in science - inferential statistics. Before I define inferential statistics, let me show you why they are useful. In the previous section, I described a research study that sought to determine the effects of temperature on plant biomass. Upon completion of her experiment, the experimenter would have sets of biomass measurements for each group. What does she do then? Should she take the mean of the values for each group and then make conclusions based on this statistic alone? What if the mean biomass for one group is only slightly higher than that for another group - is the difference sufficient for her to make a solid conclusion? Inferential statistics allow you to make comparisons in scientific studies and determine with confidence if differences in treatment groups truly exist. Inferential Statistics: An Example Inferential statistics are used to make comparisons between data sets and infer whether the two data sets are significantly different from one another. It is important to realize that when dealing with statistics and probability, chance always plays a role. When we compare means from two groups in an experiment, we are attempting to determine if the two means truly differ from one another, or if the difference in the means of the groups is simply due to random chance. The best way to explain this concept is with an example. Chance and "significant" differences: A Case Study After losing a close game in overtime, a local high school football coach accuses the officials of using a "loaded" coin during the pre- overtime coin toss. He claims that the coin was altered to come up heads when flipped, his opponents knew this, won the coin toss, and consequently won the game on their first possession in overtime. He wants the local high school athletic association to investigate the matter. You are assigned the task of determining if the coach's accusation stands up to scrutiny. Well, you know that a "fair" coin should land on heads 50% of the time, and on tails 50% of the time. So how can you test if the coin in question is doctored? If you flip it ten times and it comes up heads six times, does that validate the accusation? What if it comes up heads seven times? What about eight times? To make a conclusion, you need to know the probability of these occurrences.
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To examine the potential outcomes of coin flipping, we will use a Binomial Distribution. This distribution describes the probabilities for events when you have two possible outcomes (heads or tails) and independent trials (one flip of the coin does not influence the next flip). The distribution for ten flips of a fair coin is shown in Figure 1. Figure 1. Binomial distribution for fair coin with ten flips Note that ratio of 5 heads:5 tails is the most probable, and the probabilities of other combinations decline as you approach greater numbers of heads or tails. The figure demonstrates two important points. One, it shows that the expected outcome is the most probable - in this case a 5:5 ratio of heads to tails. Two, it shows that unlikely events can happen due solely to random chance (e.g., getting 0 heads and 10 tails), but that they have a very low probability of occurring. Also note that the binomial distribution is rather "jagged" when only ten coin flips are performed. As the number of trials (coin flips) increases, the shape of the distribution begins to smooth out and resemble a normal curve. Note how the shape of the curve with 50 trials is much smoother than the curve for 10 trials, and more representative of a normal curve (Figure 2). Figure 2. Binomial distribution for fair coin with 50 flips
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