The abstract below is a corrected version of the one submitted for the Statistics exercise in a previous semester. This example has good clarity of writing and the level of understanding is outstanding. In a few places I inserted important exerpts from other students. The original indeed fit onto one page, but with all the additions I have made, it is now probably too long. It is good to use each other as resources and as editors to improve each others' writing. Of course I am always happy to help you too.
A Comparison of Hand Size in the Classroom, an Experiment in Bean Weight and Volume, and a Statistical Evaluation of Coin Toss and Dice Throwing Outcomes.
Primary Author and Lab Parner
In Biology, as in the other disciplines which incorporate the scientific method, environmental forces act upon living things in ways which influence their subsequent reactions. In studying these reactions, one must also be aware of the degree to which chance events influence results before arriving at conclusions. This laboratory exercise emphasizes the importance acknowledging and incorporating these chance events into biological studies through the use of statistics (descriptive, parametric and non-parametric testing). First, comparisons of hand widths of each individual and of the entire class were made, most of which were not equal. Descriptive statistics were then calculated (mean and standard deviation) from the class data in order to decide whether or not the data were normally distributed. Since the data were distributed normally, a Student T-test (parametric) was run on a computer program producing a t-statistic that was less than a T-table value. By following the decision rule, it was decided that the left and right hand measurements were not significantly different. Again a Student T-test was used in an experiment that compared the mass of dry versus water-soaked beans. The test supported the hypothesis that soaked beans were heavier. While supposing that the normal distribution could not be demonstrated, the data were then analyzed with the Wilcoxon Rank-Sum test (non-parametric). A computer calculated rank-sums for the dry and wet seeds. The lesser of the two numbers (known as the W-statistic) was then compared to a table value that incorporates a 5% error. The hypothesis of equality was rejected by the decision rule because the table value was less than the W-statistic. Next, in comparing the volumes (displacement of water) of the dry and soaked beans, it was also found that the average soaked bean occupied 200% of the dry bean volume. This gave only one result, therefore there was no degree of freedom and no statistical test could be done. Such large differences between treatment and control seldom require statistical analysis. The last two exercises involved experiments where more than one outcome was likely. Tosses of balanced and unbalanced coins and dice were used to create data that might be skewed in one sample (most likely the unbalanced). A Chi-square test was used to detect any disproportionate number of outcomes in both the coins and dice. This test effectively detected the unbalanced die, however this was not the case with the two coins where the outcomes of "heads" and "tails" were not significantly different. Since we knew just by looking that the hybrid coin was not balanced, we must conclude that either the coin was not weighted enough to make a statistical difference or we did not do enough tosses to accurately decide. This is an example of a Type II statistical error: not rejecting a false hypothesis. In summary, the exercises having to do with hand widths effectively emphasized the source of measuring error, such as the amount of pressure applied to the surface of the ruler and the angle from which the hands were viewed when measuring. This exercise also shows how a parametric test can be used to detect significant differences between samples of normal distribution. The Wilcoxon Rank-Sum test effectively found a difference between the masses of dry vs soaked beans when normal distribution was not necessarily tested. Finally the Chi-square test detected the disproportionate number of occurrences of a particular outcome upon tossing an unbalanced die. In all cases it was important to construct the hypothesis so that it could be eliminated, narrowing down possible hypotheses to the likely true one. Although these exercises are simplistic, they demonstrate the important part chance events and statistics play in the application of the scientific method. It is clear that the use of statistics is a useful way of interpreting and analyzing data in an unbiased manner, but statistics cannot make up for an experiment that is poorly designed.
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