Animal Behavior Laboratory ManualSIGN TEST
To use the Sign Test, recall that you need paired observations (perhaps observations of an experimental and a control animal or observations of the same animal reacting to two stimuli). Your paired observations must allow you to make a dichotomous (two categories) classification of them. Your classification could depend, for instance, on whether your measurement of the experimental animal was greater or less than that of the control animal, or on whether the experimental animal won or lost the encounter, or on whether the experimental stimulus evoked more or less response than the control stimulus. In other words, you use the direction of the difference between paired measurements to classify them. If any pair of measurements are exactly equal (tied), or if two paired subjects have the same behavior in an encounter, then you must discard that pair from further consideration. Tied scores cannot be used in a Sign Test. For instance, suppose you had a sample of 10 experiments on reactions of a subject fish to two different test fish (perhaps your own observations combined with those of other lab teams). In 7 cases, the subject spent more time near the test fish of the same species, in 2 cases the subject spent more time near the test fish of a different species, and in one case the subject spent equal amounts of time near the two test fish. Your 10 pairs would then yield 7 positive cases, 2 negative ones, and one tie. You eliminate the tie from further consideration, so you are left with 7 positive and 2 negative cases for a sample size of N = 9. Your null hypothesis (remember the devil's advocate!) states that chance alone could reasonably explain 7 cases with the same result out of 9 comparisons, even if the subject fish had no preference for schooling with either species of test fish. The null hypothesis is equivalent to saying that 9 tosses of a fair coin should, with reasonably large probability, result in the coin landing the same side up 7 times. Scientists generally feel that anything greater than 5% is a "reasonably large probability". We could calculate the exact probability of having a fair coin land the same side up 7 times out of 9 tosses. But we are mostly interested in whether or not this probability is greater or less than 5%. So let's use a table of critical values instead. In such a table, we find how many cases must have the same result, out of a total sample of N cases, for the probability of the null hypothesis to be equal to or less than 5%. Look at the table below. To use it for the example described above, first locate the value of N in the left-hand column. For this example, N = 9. Then read the critical value of X (the larger number of cases with the same result) in the right-hand column. In this case, it is 8. According to the instructions below the table, the probability of the null hypothesis is less than 5% provided X is greater than or equal to the critical value in the table. In our case, X equals 7, and so is less than the critical value of X, which is 8. The null hypothesis has more than 5% chance of being correct. Hence we cannot reasonably reject the null hypothesis in this case. The devil's advocate might be right! To include this result in a lab report, we would write the statistical test and the relevant information about the probability of the null hypothesis after presenting the data. For instance,
"In 7 of a total of 9 trials, the fish associated more with species A than with species B (P > 0.05, Sign Test)," or Note that the results of a statistical test must always include three items:
Because we cannot reject the null hypothesis in this case, we cannot accept the alternative hypothesis that these fish prefer to school with one species more than the other.
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