Second exam study guide
This is the study guide for the second exam in Biological Statistics,
fall 2007. The exam will be on Tuesday, October 30. You may not use your
notes or textbook during the exam; if English is your second language, you
may use a dictionary. You will not need a calculator.
The exam
is cumulative; about a third of the questions will be about material
covered in the first part of the semester. You should look at the first
midterm and make sure you understand everything on it, and you should
study the topics listed on the study guide for the first midterm.
You should primarily study
your lecture notes, the web pages on different topics (linked from the
syllabus), and the homework assignments. I have revised some of the web
pages, so if you have printed them out, please look at them again. In
addition to the topics covered on the first midterm, you should be
familiar with:
- Statistics of central tendency (arithmetic
mean, median, mode);
- Statistics of dispersion (range, variance,
standard deviation, coefficient of variation);
- Standard error of the
mean
- Confidence limits
- Student's t-test
- Model I vs. Model II
one-way anova (if I describe a data set, you should be able
to say which model is appropriate)
- Partitioning of variance
components
- Planned comparisons
- Orthogonal vs. non-orthogonal planned
comparisons (you should be able to tell whether a set of comparisons is
orthogonal)
- Unplanned comparisons of pairs of means
- Gabriel's comparison intervals
- Tukey-Kramer method
- Assumptions of anova
- Bartlett's test of homogeneity of variances
- Data
transformations
- Kruskal-Wallis test
- Nested
anova
- Two-way anova
- Paired
t-test
- Wilcoxon signed-rank test
- Sign test
The exam will consist of about 15 to 20
short-answer questions. Most of them will consist of me describing an
experiment, then asking what statistical test is appropriate. On this
exam, I will not ask you to lisk the variables in an experiment and
say whether they are measurement, attribute or ranked. That is a good way
to help you decide on the appropriate statistical test, however. Here are
some example questions:
- You have placed ten egg masses, each
representing a separate family, of treehoppers on a host plant that they
don't normally eat. After one month, you measure the body length of each
treehopper. You are interested in whether there is genetic variation among
the families in ability to grow on this host plant. What are two
statistical tests you could use to test whether there is variation among
the families in body length? How would you decide which was more
appropriate?
- You are interested in the effects of fertilizer on
mitosis in onion root tips. In an onion root tip grown without fertilizer,
you count 70 cells in interphase, 28 cells in prophase, 2 cells in
metaphase, 5 cells in anaphase, and 10 cells in telophase. In an onion
root tip grown with fertilizer, you count 94 cells in interphase, 57 cells
in prophase, 9 cells in metaphase, 11 cells in anaphase, and 27 cells in
telophase. What statistical test would you use to analyze these data?
- You
have measured the height of the arch of the foot in athletes from nine
women's teams: soccer, basketball, rugby, swimming, softball, volleyball,
lacrosse, crew and cross-country. Give a set of at least three orthogonal
planned comparisons of the means from these sports.
- You want to know whether the gene that codes for mannose-6-phosphate
isomerase (MPI) is expressed differently in liver tumors than in normal
livers. You take one biopsy from each of 27 normal livers and 32 cancerous livers
and measure the amount of MPI mRNA in each one.
- Glacier-Waterton International Park is in Montana and Alberta. While
backpacking through the park, you see 8 black bears and no grizzly bears
in the Montana side of the park; after crossing the border into Canada,
you see no black bears and 6 grizzly bears in the Alberta side of the
park. Is there a difference between the two parts of the park in the
proportion of bears that are grizzly bears?
- You want to know whether 12 clonal strains of E. coli bacteria
differ in catabolic activity. You grow three lines of each strain for
2,000 generations, then take three samples of each line and measure the
catabolic activity of each sample.
- Because of the long tail feathers, male swallows mount the females
from either the right or the left. You want to know whether they have a
preference for one side, so you observe 17 pairs of mating swallows. Four
males mount from the right side, while 13 mount from the left.
- You are planning to do experiments on chicken feed with different
ratios of corn meal to soybean meal. To prepare for these experiments, you
buy 20 bags of corn meal and 14 bags of soybean meal and put them in a
cool, dry place. A few weeks later, when you finally decide to start
mixing up chicken feed, you notice that 12 bags of corn meal have moth
holes, while 2 bags of soybean meal have moth holes. Do moths prefer corn
meal?
- The repeated stress of running sometimes causes stress fractures in
the tibia (lower leg). Often just one tibia gets a stress fracture,
and you want to know whether the tibia that gets fractured had
different bone mineral density than the uninjured tibia of the same
person.
You measure the bone mineral density in each
of the two tibias in 100 people who are about to start running. Six
months later, you find that 12 runners have a stress fracture in one leg. You look in your notes to find the bone mineral density for the stress-fractured and unfractured legs for these 12 people.
- You want to study the effect of exercise on the heart rates of mice.
You place 5 male and 5 female mice in a cage with an exercise wheel, and
you place 5 male and 5 female mice in a cage without an excercise wheel.
After one week, you measure the heart rate of each mouse.
- You have been feeding laying chickens your own custom blend of chicken
feed, and you want to know whether it's really better than commercial
chicken feed. You have the Single-Comb White Leghorn, Barred Plymouth
Rock, and Speckled Sussex breeds of chicken, with 120 hens of each breed.
Each hen is in a separate cage. You feed half of the hens your custom
chicken feed and half of them commercial chicken feed, and you count the
number of eggs each hen lays over a period of 6 months.
- You are trying to see whether the genes Jam-1 and Pax-6 are
genetically linked in zebrafish. You breed two individuals who are
heterozygous for visible, dominant mutations at both genes, and you get
1600
offspring. If the two genes are unlinked, you'd expect 100 fish that were
normal/normal, 300 that were normal at Jam-1 and mutant at Pax-6, 300 that
were mutant at Jam-1 and normal at Pax-6, and 900 that were mutant/mutant.
- You want to breed miniature schnauzers that don't bark so much, by
selecting those dogs that bark less than others to found the next
generation. You obtain 30 miniature schnauzers, raise them under similar
conditions, then record how many times each dog barks when a stranger
approaches it. You do this five times for each dog.
- Two amphipod crustaceans live high on beaches in Delaware,
Talorchestia longicornis and Talorchestia megalophthalma.
You want to know whether the proportion of each species is different on
different beaches, so you collect about a hundred amphipods at Rehoboth
Beach, Dewey Beach, Fenwick Island, and Cape Henlopen, and you count the
number of individuals of each species at each beach.
- You want to know the effect of temperature and light exposure on the
growth of eels. You put 25 young eels ("elvers"), all the same size, in
each of four tanks:
one tank with 10 C water and continuous light, one tank with 30 C water
and continuous light, one tank with 10 C water and continous dark, and one
tank with 30 C water and continuous dark. After 6 months, you measure the
length of each eel.
- A zoo has 170 turtles in an outdoor enclosure. There are three rocks
in the pen that the turtles like to bask on, one white rock, one brown
rock, and one black rock, and you want to know whether the turtles have a
preference for one rock over the others. Each rock is the same size, and
on a sunny day, all of the turtles are on a rock. You scare the turtles
off the rocks, then come back an hour later and count the number of
turtles on each rock. You do this each day for a week.
- You want to know the effect of light source on pumpkins. You grow 10
pumpkin plants under natural sunlight, 10 pumpkin plants under fluorescent
light, and 10 pumpkin plants under incandescent light. You remove excess
flowers, so each plant will have only one pumpkin. After 3 months, you
measure the diameter of the pumpkins.
- You want to know whether the presence of the malaria parasite
(Plasmodium) in mosquitoes affects the West Nile virus. You collect
1200 mosquitoes. Half of them contain Plasmodium and one-third contain
West Nile virus, so your null expectation is that one-sixth (200) of the
mosquitoes will have both Plasmodium and West Nile virus. Instead, you
find that only 148 mosquitoes have both.
- You want to know whether mice can see colors. Twenty times a day for
two weeks, you put a piece of mouse food in a small red box and put it in
a cage with one mouse. The mouse can tip the box over and get the food
out. At the same time, you also put mouse food in a blue box and a green
box; they look and smell the same as the red box, but are glued shut so
the mouse can't get the food out. Every time you put the three boxes in
the mouse cage, you record which box it tries to tip over first. You do
this with 10 mice.
- You want to test three insect species (a caterpillar, a grasshopper,
and a weevil) as biological control agents for four invasive exotic vines
(kudzu, porcelainberry, English ivy, and Japanese honeysuckle). For each
species of plant, you set up three cages: one with 50 caterpillars, one
with 50 grasshoppers, and one with 50 weevils. After one week, you
randomly select 100 leaves from each cage and measure the percentage of
the area of each leaf that has been eaten.
- You have knocked out the JAM-1 gene in mice, and as part of your
investigation of the effects of this gene, you want to know if these
genetically engineered mice can tell the difference between low-fat and
high-fat food. You have 12 of these mice in individual cages, and you put
20 pellets of low-fat mouse food and 20 pellets of high-fat mouse food in
the feeder for each cage. After three days, you count the number of each
kind of pellet remaining in each cage.
- You want to know whether keeping sheep in indoor cages affects the
weight of their offspring. You weigh 30 newborn lambs from ewes kept
full-time in cages, 30 lambs from ewes caged at nights only, and 30 lambs
from ewes kept outdoors.
- Fiddler crabs have pigment cells called melanopores; you want to know
whether they use them for camoflauge. You put 20 individually tagged
fiddler crabs on a black background for 24 hours, then measure the amount
of light reflected off their carapace. You then put the crabs on a white
background for 24 hours and measure the amount of light reflected off
their carapace.
- You want to know whether individual starfish, all of the same age, have different mean
arm lengths. You collect 27 starfish and measure the length of
each of the five arms on each starfish.
- A zoo has 17 turtles in an outdoor enclosure. There are three rocks in
the pen that the turtles like to bask on, one white rock, one brown rock,
and one black rock, and you want to know whether the turtles have a
preference for one rock over the others. Each rock is the same size, and
on a sunny day, all of the turtles are on a rock. You see 10 turtles on the
black rock, 4 turtles on the brown rock, and 3 turtles on the white rock.
- People who live in New Guinea have a diet based on sweet potatoes,
which are low in nitrogen. You want to know whether this favors the
intestinal bacterium Klebsiella, which can fix its own nitrogen.
You find 10 volunteers from New Guinea and measure the number of
Klebsiella in their intestines, then feed them a protein-rich diet
for one month. You then measure the number of Klebsiella in their
guts again.
- Fiddler crabs have pigment cells called melanopores; you want to know
whether they use them for camoflauge. You put 20 individually tagged
fiddler crabs on a black background for 24 hours, then measure the amount
of light reflected off their carapace. You then put the crabs on a white
background for 24 hours and measure the amount of light reflected off
their carapace. The differences between measurements are not normally distributed.
- You want to know the effect of temperature on the growth of eels. You
have 10 fish tanks at 10 C and 10 fish tanks at 30 C, and you put 5 elvers
in each tank. After 6 months, you measure the length of each eel.
- You want to breed miniature schnauzers that don't bark so much, but
you don't know whether there is any genetic variation for barkiness. You
obtain 7 litters of miniature schnauzers, raise them under similar
conditions, then record how many times each dog barks when a stranger
approaches it. You do this once for each dog.
- You want to know whether mice can see colors. Twenty times a day for
two weeks, you put a piece of mouse food in a small red box and put it in
a cage with one mouse. The mouse can tip the box over and get the food
out. At the same time, you also put mouse food in a green box; it looks
and smells the same as the red box, but is glued shut so the mouse can't
get the food out. At the end of the two weeks, you put the two boxes in
with the mouse for 10 more times. The mouse pushes over the red box first
eight times and the green box two times.
- You want to measure the effect of the sex of a chicken on the
incubation period of various strains of avian influenza. You inoculate
male and female chickens with one of three different strains of avian
influenza and measure how many days it takes for each bird to show signs
of respiratory distress.
- You have created a mouse model of hypercholesteremia by knocking out
the LDLR gene, and you want to know whether they have atherosclerosis
("hardening of the arteries"). You have 12 LDLR-/LDLR- mice, 12 LDLR-/+
mice, and 12 LDLR+/+ mice. You feed the mice a high cholesterol diet for
20 weeks, then prepare 4 cross-sections of the aorta for each mouse. On
each cross-section, you measure the area of atherosclerosis lesion.
- You want to know what affects the breakdown of fructose at high
temperatures (due to caramelization and Maillard reactions) in apples. You
bake 8 Winesap apples, 8 Rome Beauty apples, 8 Jonathan apples, and 8
Granny Smith apples for 90 minutes at 180 C, and you bake another set of 8
apples of each variety for 90 minutes at 200 C. You measure the amount of
fructose (in milligrams of fructose per gram of baked apple) in each
apple.
- When beaches are replenished by dumping new sand on them, the beach
animals get covered up and may die. You want to know whether the type of
sand makes a difference. You put 20 snails (Ilyanassa obsoleta) at
the bottom of each of three large containers, then you put 20 cm of fine
sand in one container, 20 cm of medium sand in one container, and 20 cm of
coarse sand in one container. After one hour, you count the number of
snails that have crawled to the surface in each container.
- When a click beetle is on its back, it rapidly flexes its body with an
audible "click," flipping itself into the air and hopefully landing
right-side-up. You want to know whether this flipping is random or whether
the beetles tend to land on their feet. You catch a click beetle, put it
on its back, and watch it click. You repeat this 12 times. The beetle
lands on its feet 8 times and on its back 4 times.
- You want to know whether fruit flies carrying the 8J16 mutation in
their Wingless gene differ in the amount of wingless protein. You dissect
out a wing imaginal disc from 15 embryos of flies with the mutation, stain
for wingless, and measure the amount of stain at 4 random spots in each
disc. You do the same for 15 embryos of flies without the mutation.
- You want to know whether mice can see colors. Twenty times a day for
two weeks, you put a piece of mouse food in a small red box and put it in
a cage with one mouse. The mouse can tip the box over and get the food
out. At the same time, you also put mouse food in a blue box and a green
box; they look and smell the same as the red box, but are glued shut so
the mouse can't get the food out. After the two-week training period,
you put the three boxes in with the mouse for 50 times, and you record
which box it tries to tip over first. You do this with for five mice.
- You have been observing a large troop of monkeys in the Philadelphia
zoo. By careful observation of their social interactions, you have figured
out the dominance heirarchy: which monkey is dominant over all, which
monkey submits only to the most dominant, etc., all the way down to the
poor monkey that submits to every other monkey. You want to know whether
monkeys born at the Philadelphia zoo tend to dominate monkeys brought from
other zoos.
- You want to know whether mice can see colors. Twenty times a day for
two weeks, you put a piece of mouse food in a small red box and put it in
a cage with one mouse. The mouse can tip the box over and get the food
out. At the same time, you also put mouse food in a blue box and a green
box; they look and smell the same as the red box, but are glued shut so
the mouse can't get the food out. At the end of the two weeks, you put the
three boxes in with the mouse for 10 more times. The mouse pushes over the
red box first seven times, the green box two times, and the blue box one
time.
- You want to know the effect of light source on pumpkins. You grow 10
pumpkin plants under natural sunlight and 10 pumpkin plants under
fluorescent light. You remove excess flowers, so each plant will have only
one pumpkin. After 3 months, you measure the diameter of the pumpkins.
- You are studying the species diversity of algae in the highlands of
Ecuador, and you want to know whether different taxonomic groups of algae
are favored in different areas. In a pond at 400 meters elevation, you
isolate 5 species of green algae and 3 species of cyanobacteria
("blue-green algae"); in a pond at 1500 meters, you isolate 6 species of
green algae and 7 species of cyanobacteria.
- You are studying the effects of bone marrow transplants on the level
of T-cells in the blood. You want to know whether recipients of bone
marrow tend to have more or fewer T-cells than the person who donated bone
marrow
to them. You find 17 people who received
bone marrow
transplants more than 10 years ago, and you also find the bone-marrow
donor for each person. You measure the level of T-cells in each person's
blood. You notice that the differences between donor and recipient are not
normally distributed.
- You have knocked out the JAM-1 gene in mice, and as part of your
investigation of the effects of this gene, you want to know if these
genetically engineered mice have a food preference. You have 20 of these
mice in individual cages, and you put a small pile of low-fat mouse food
in one corner of each cage and an equal-sized pile of high-fat food in the
other corner. After three days, the uneaten food has been mixed in with
the litter, so it would be too difficult to weigh it. However, 5 of the
cages have piles of uneaten low-fat food that are obviously smaller than
the high-fat food piles, 12 cages have piles of high-fat food that are
smaller than the low-fat piles, and 3 cages have equal-sized food piles.
- It has been hypothesized that bright colors in birds are a signal to
potential mates that the brightly colored individual is healthy and
therefore would be a good parent. To test the relationship between
healthiness and brightness, you buy 20 healthy parakeets and take a
picture of each one. You then infect the birds with avian malaria, and
after a month of the birds being sick, you take another picture. You show
the two pictures for each bird to your collaborator (without saying which
is the sick bird) and ask which one looks more brightly colored.
- You want to know whether aspirin taken during pregnancy has an effect
on the sex of offspring. You ask 1072 new mothers whether they took
aspirin during the first three months of their pregnancy, and you also ask
them whether they had a boy or a girl.
- You want to know whether the JAM-1 gene affects the thickness of mouse
corneas, so you genetically engineer mice that are missing JAM-1. You have
5 mice that are missing JAM-1 and five mice with JAM-1. You pluck out both
eyes from each mouse and measure the thickness of the cornea at 3 random
points.
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This page was last revised October 25, 2007. Its URL is
http://udel.edu/~mcdonald/statstudy2.html