Binomial test

There are many other distributions used in statistics besides the normal distribution. Common ones are the yl and the F-distributions (see later) and the binomial distribution. The binomial distribution involves binomial events, i.e. events for which there are only two possible outcomes (yes/no, success/failure). The binomial distribution is skewed to the right, and is characterised by two parameters n, the number of individuals in the sample (or repetitions of a trial), and n, the true probability of success for each individual or trial. The mean is n n and the variance is nn(l-n). The binomial test, based on the binomial distribution, can be used to make inferences about probabilities. If we toss a true coin a iarge number of times we expect the coin to faii heads up on 50% of the tosses. Suppose we toss the coin 10 times and get 7 heads, does this mean that the coin is biased. From a binomiai tabie we can find that P(x=7)=0.117 for n=10 and n=0.5. Since 0.117>0.05 (P=0.05 is the commoniy... 

However, for each set of samples, a two-way binomial test (Engels, 1988) was used to determine the lowest probability of correct identification that would have given a 95% chance of assigning all samples in this set to the correct category. Thus, for the 6 samples of Rhododendron honey, the lowest probability of correct identification was 0.616 for the 8 samples of Citrus honey, this probability was 0.679 and for all 17 samples, the lowest probability was 0.835, indicating that there was a 95% chance that the probability of correct identification of the ANN used was 0.835 or better. 

A chi-square or binomial test is used to determine which phy- 7 logenetic invariants deviate significantly from zero and which do not... 

Based on your own and/or the data provided below, compare the observed number of visits to the single tile with the expected number of visits if the mouse had moved around randomly in the open field. Use a binomial test. 

Compare these results with your own data. Try to explain any differences between these and your results. If needed, use these frequencies in lieu of your own data. Use a binomial test for the difference between the observed proportion and an assumed proportion (here 1/12 of all visits by the mouse, i.e., the share of 1 tile out of 12, had the mouse moved around randomly). 

The results will be scored for departure from random choice, first for identifying self If each student randomly labeled 20 shirts as self, he/she would be correct in 1 out of 20 choices. Use a binomial test for the difference between an observed and an assumed proportion (here 1/20) for each student separately. 

For ability to discriminate gender by odor, use one subset, e.g., only five male and five female shirts. In a binomial test, compare one person s proportion of labeling shirts as male with an assumed random proportion of 0.5. 

The percentage positive deviation statistic is the percentage of the predictions that are over predicted from perfect correlation by a technique. If a predictive technique does not have a tendency to over or under predict values, i.e. over predicts as many values as it under predicts then you would expect the percentage positive deviation to be 50%. Therefore this statistic is used as a measure of the tendency of a package to over or under estimate potency. The data reported for this statistic is the distance from 50%, i.e. if positive the technique has a tendency to over-estimate the potency, if negative the technique has a tendency to under-estimate the potency whilst the further away from zero the more exaggerated this tendency. A one sample binomial test was used to identify if the identified tendency to under or over estimate the potency was significant at the 95% confidence hmit. 

Chi-.square. binomial test, runs test, one-sample Kolmogorov Smirnov test. Mann-Whitney U test. Moses test. Wald-Wolfowitz test. Kruskal Wallis te.st, Wilcoxon signed rank test. Friedman s test. Kendall s W test, Cochran s Q test... 

We first verified that males have no preference when exposed to chemical cues from two same-sized females. An average, sexually-mature adult female newt has a mass of approximately 3 g. We used matched pairs of females that differed by less than 0.05 g in mass, placing one into each side arm of Y-maze, When subject males were allowed to choose between two same-size females, no preference was observed (Table 1, I one-tailed binomial test, P = 0.37). 

To determine whether a pheromonal repelling response occurs, we first placed one of two same-sized females into each arm of the Y-maze, and then added three males to one side to mimic a state of high male-male competition. In this experiment, the stimulus males and female were allowed to interact for 5 min in the side arm before each test begins. We found that subjects strongly preferred the arm containing a single female compared with that containing a female plus three males (Table 1, II one-tailed binomial test, P = 0.017). 

To determine whether chemical cues from three males alone are sufficient to repel conspecific males, we placed three males in one arm of the Y-maze and left the other arm empty. Subject males were then allowed to choose between the two arms. Subjects significantly preferred the arm containing three males to the arm containing nothing but plain water (Table 1, III one-tailed binomial test, P = 0.003). 

Experiment (no. of subjects) Sources of chemical cues used No. of times chosen One-tailed binomial test (P)... 

In the next experiment, we determined whether behavioral interactions between the stimulus males and females are necessary to produce a repelling response. The set-up for this experiment was similar to that described for Experiment II, above, except that we inserted a solid barrier between the stimulus female and the stimulus three males that were placed in one arm of the maze. In this experiment, subject males displayed no preference between the two arms of the maze that is, no repelling response occurred (Table 1, IV one-tailed binomial test, P = 0.27). 

To determine whether female fecundity affects male choice, we determined whether or not subject males display a preference when presented with large and small females. We placed one large (3.75 0.57 g, n = 5) and one small (2.67 0.18 g, n = 5) female into each arm of Y-maze and allowed subject males to choose between them. Males showed a strong preference for the side containing the large female (Table 1, V one-tailed binomial test, P < 0.001). 

In this test, subject males did not show a preference for either side (Table 1, VI one-tailed binomial test, P = 0.13). 

Table 3. Laboratory tests of trail-following in newborn Crotalus horridus conducted in a Y-maze. Probability values for control condition were calculated using a two-tailed binomial test and with a one-tailed binomial test for experimental conditions. Modified from Brown and MacLean, 1983,... 

Table 5. Ability of male plains garter snakes, Thamnophis radix to determine direction of a female pheromone trail under three different physical conditions. For experiments I and II a one-tailed binomial test of the hypothesis that the males would follow the trail in the direction of the female was conducted. For experiment III the hypothesis tested was that the males would go the direction the pegs "indicated . From Ford and Low (1984). 

Thamnophis radix complex. P values were calculated using a one-tailed binomial test for preference of the conspecific trail. From Ford (1982), Ford and Schofield (1983), and Ford and O Bleness (in press). 

The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial when n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is n x repeated Bernoulli trial. The binomial distribution is the basis for the popular binomial test of statistical significance. 

The expected value was then used in the Binomial test for sample sizes where N>25 in formula (2), where x = the observed transition frequency between behavior (A,B) and N was the expected value ... 

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