Nonparametric Statistics

Nonparametric Statistics

Q1. Elephants make low-frequency sounds, inaudible to humans. Apparently these sounds are used in long-distance communication between individuals. You are interested in the response of bull and female elephants to the sound of a female who is ready to mate. You mount a giant speaker on top of your van and drive around the plains looking for elephants. When you find one, you stop 15 m away, play the sound and watch the elephant’s response.

You discover:

9 bull elephants approach the van
2 bull elephants do not approach the van
3 female elephants approach the van
11 female elephants do not approach the van

Your experiment ends prematurely when one of the bull elephants, apparently enraged by the absence of a female, tips the van over and damages the speaker. You hope that you have enough data to make a claim about males and females.

a. What is the null hypothesis?
The null hypothesis is the bull and female elephants will not have a reaction to the sound of a female who is ready to mate.

b. What statistical test should you use?
The statistical test that should be used for this is a chi-squared test of independence because the data is categorial.

c. Calculate your test statistic. Is your result statistically significant?

The Chi squared statistic is 9.0004, the degree freedom is 1, so the p-value is .002699. Since this is smaller than .05 the result is statically significant.

d. What conclusion can you draw from this experiment?

We can conclude that the elephant’s behavior is due to something other than random chance.

Q2.Male butterflies sometimes court females of other species with similar wing patterns. You are interested in how long males persist in courting the wrong female. You decide to test each male with a dead female, to control for the effectof the female’s behavior. You use three types of test females: one from the same species as the males, one from a different species with a similar wing pattern, and one from a different species with a different wing pattern. Each pair is placed in a cage, and you measure courtship time in seconds.

Female of same species: 23, 20, 17, 25, 28
Female of different species, similar pattern: 18, 27, 24, 21
Female of different species, different pattern: 22, 21, 23, 20

a. Calculate the mean, variance, and standard deviation for each group.
The means:

Female of same species- 22.6
Female of different species, similar pattern- 22.4
Female of different species, different pattern- 21.5

The variance:

Female of same species- 18.3
Female of different species, similar pattern- 15
Female of different species, different pattern-1.66667

The standard deviation:

Female of same species- 4.27785
Female of different species, similar pattern- 3.87298
Female of different species, different pattern- 1.29099
b. Qualitatively compare the means and standard deviations for each group. (Do they look very different? Very similar?)
The means are very similar for all groups, but the standard deviations show a drastic difference. The same species and the similar pattern groups have means that only have a difference of .2. When you look at their standard deviations however the same species group has the most deviation from the mean. The different pattern group has a small deviation from the mean, but the mean time of a male butterfly hanging around is less.
c. Which statistical test would you use to look for differences?
The statistical test that you would use is the Kruskal-Wallis test.
d. Perform the test. What is your test statistic? Can you reject your null hypothesis?
e. Give a biological reason why your test may have come out the way it did.

Q3.Honeybees returning from foraging convey information to bees in the hive about the location of food resources. One way they do this is through a waggle dance that other bees watch. Another way they convey information is by regurgitating some of the food they have collected to other bees, a process known as trophyllaxis. You are interested in the speed at which bees find a resource another bee “tells” them about. You decide to compare bees that have only observed a dance with bees that have observed a danceand accepted regurgitated food. You mark a lot of bees with bee tags (little numbered discs that you glue to the back of the thorax). This enables you to watch the same individual repeatedly. One day you choose a lot of bees that have seen a waggle dance but not accepted food. You measure (in seconds) how long it takes for them to find the resource. A week later you go back to the hive, and find the same individuals. This time you watch until they see a danceandaccept food, and again measure how long it takes them to reach the resource.

a. What sort of data are these? Which test should you choose?
This is ordinal data. The test that should be used is a sign test because there are only two sets of paired data.
b. What is the test statistic? The table statistic?
The test statistics are x=2 and N=12. The table statistic is .019.
c. You decide that a bee that has both watched and gotten food from another bee finds the resource faster than one that has just watched. What other factor that is a result of your experimental protocol might also explain your results?

There are a variety of factors as to why the results turned out the way they were. The bees could be going to the same areas for food. Seeing the dance and already knowing the food could affect their ability to find the site better.