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This criticism only applies to two-tailed tests, where the null hypothesis is "Things are exactly the same" and the alternative is "Things are different." Presumably these critics think it would be okay to do a one-tailed test with a null hypothesis like "Foot length of male chickens is the same as, or less than, that of females," because the null hypothesis that male chickens have smaller feet than females could be true. So if you're worried about this issue, you could think of a two-tailed test, where the null hypothesis is that things are the same, as shorthand for doing two one-tailed tests. A significant rejection of the null hypothesis in a two-tailed test would then be the equivalent of rejecting one of the two one-tailed null hypotheses.

Approximately13,000 years ago, the Laurentide Ice Sheet’s retreat was interrupted by a return to glacial climatic conditions that persisted for over 1,000 years. The events precipitating the dramatic, millennial long climatic cooling, known as the Younger Dryas, remain both a mystery and the subject of debate. It has recently been hypothesized that a fragmented comet or asteroid might have simultaneously initiated the YD and formed the Carolina Bays. However, Carbon 14 dating and pollen analysis indicates an earlier genesis. While this research does indicate the bays were formed during prior glacial epochs, the bays also appear to be repositories of a significant amount of materiel considered evidence of an extraterrestrial impact including carbon and magnetic spherules and nanodiamonds.

We can see below the ANOVA table, another table that provides the sample sizes, sample means, and sample standard deviations of the 4 samples. Beneath that table, the pooled StDev is given and this is an estimate for the common standard deviation of the 4 populations.

GPA), the descriptives output gives the sample size,mean, standard deviation, minimum, maximum, standard error, and confidence interval for each level of the (quasi) independent variable.

There are different ways of doing statistics. The technique used by the vast majority of biologists, and the technique that most of this handbook describes, is sometimes called "frequentist" or "classical" statistics. It involves testing a null hypothesis by comparing the data you observe in your experiment with the predictions of a null hypothesis. You estimate what the probability would be of obtaining the observed results, or something more extreme, if the null hypothesis were true. If this estimated probability (the *P* value) is small enough (below the significance value), then you conclude that it is unlikely that the null hypothesis is true; you reject the null hypothesis and accept an alternative hypothesis.

**Mentor**: Dr. Dewayne Branch, Dr. Malcolm LeCompte

Undergraduate Research Experience in Ocean, Marine, and Polar Science, ECSU**Abstract**

Buried beneath the East Antarctic Ice Sheet is a mountain range similar to the European Alps whose age estimates range from 35 to 500 million years. Expeditions during the International Polar Year are seeking to reveal the sub-glacial topography of the range and obtain hints to solve the mystery of their formation. The tools they are using include a combination of ice-core samples and ice penetrating RADAR.

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You must choose your significance level before you collect the data, of course. If you choose to use a different significance level than the conventional 0.05, people will be skeptical; you must be able to justify your choice. **Throughout this handbook, I will always use P** If you are doing an experiment where the cost of a false positive is a lot greater or smaller than the cost of a false negative, or an experiment where you think it is unlikely that the alternative hypothesis will be true, you should consider using a different significance level.

The significance level you choose should also depend on how likely you think it is that your alternative hypothesis will be true, a prediction that you make *before* you do the experiment. This is the foundation of Bayesian statistics, as explained below.

and is computed by summing the squared differences between each observation and its group mean (i.e., the squared differences between each observation in group 1 and the group 1 mean, the squared differences between each observation in group 2 and the group 2 mean, and so on). The double summation ( SS ) indicates summation of the squared differences within each treatment and then summation of these totals across treatments to produce a single value. (This will be illustrated in the following examples). The total sums of squares is:

and is computed by summing the squared differences between each treatment (or group) mean and the overall mean. The squared differences are weighted by the sample sizes per group (n_{j}). The error sums of squares is:

The probability that was calculated above, 0.030, is the probability of getting 17 or fewer males out of 48. It would be significant, using the conventional *P**P*=0.03 value found by adding the probabilities of getting 17 or fewer males. This is called a one-tailed probability, because you are adding the probabilities in only one tail of the distribution shown in the figure. However, if your null hypothesis is "The proportion of males is 0.5", then your alternative hypothesis is "The proportion of males is different from 0.5." In that case, you should add the probability of getting 17 or fewer females to the probability of getting 17 or fewer males. This is called a two-tailed probability. If you do that with the chicken result, you get *P*=0.06, which is not quite significant.

The relative costs of false positives and false negatives, and thus the best *P* value to use, will be different for different experiments. If you are screening a bunch of potential sex-ratio-changing treatments and get a false positive, it wouldn't be a big deal; you'd just run a few more tests on that treatment until you were convinced the initial result was a false positive. The cost of a false negative, however, would be that you would miss out on a tremendously valuable discovery. You might therefore set your significance value to 0.10 or more for your initial tests. On the other hand, once your sex-ratio-changing treatment is undergoing final trials before being sold to farmers, a false positive could be very expensive; you'd want to be very confident that it really worked. Otherwise, if you sell the chicken farmers a sex-ratio treatment that turns out to not really work (it was a false positive), they'll sue the pants off of you. Therefore, you might want to set your significance level to 0.01, or even lower, for your final tests.

When the F ratio is statistically significant, we need to look at the multiple comparisons output. Even though our F ratio is not statistically significant, we will look at the multiple comparisons to see how they are interpreted.

The Multiple Comparisons output gives the results of the Post-Hoc tests thatyou requested.

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