Biological Statistics
Homework 7
Due Tuesday, Oct. 23

You must type this and all other homework assignments. Do not e-mail the assignment to me; turn it in early (at 322 Wolf) for a foreseeable absence, or turn it in late after an unexpected absence from class.

Here are some practice questions for the exam. If the answer is "one-way anova," you must specify Model I or Model II; if the answer is "nested anova," you must specify Mixed Model or Pure Model II.

1. You travel to Canada and observe the snow goose, Chen caerulescens. Snow geese come in two color morphs, white or blue. You want to know whether the blue geese and white geese prefer different areas. You go to four different lakes, and at each lake you record the first 100 snow geese you see. You see 35 blue geese at Lac Oie, 24 blue geese at Lago de Ganso, 19 blue geese at Lake Anser, and 44 blue geese at Pokebutt Pond. What test should you use?

2. Blue geese and white geese mate with each other (the polymorphism is caused by two alleles at a single gene); you want to know how random the mating is. At each of the four lakes, you find a few dozen blue/white mated pairs and record how many have a blue male and white female, and how many have a white male and blue female. What test should you use?

3. You want to know whether the plumage color affects the number of offspring. You go to Lake Anser and find 19 nests with both blue parents, 36 nests with a blue male and a white female, 33 nests with a white male and blue female, and 49 nests with both white parents. You count the number of eggs in each nest. What test should you use?

4. You want to know whether the plumage color affects the weight of offspring. You go to Lake Anser and find 19 nests with both blue parents, 36 nests with a blue male and a white female, 33 nests with a white male and blue female, and 49 nests with both white parents. You weigh every gosling in each nest. What test should you use?


5. Students in my section of BISC413, Advanced Genetics Lab, collected data on codon bias in different genes in Drosophila melanogaster. Codon bias is when some synonymous codons are used more often than others; for example, TTC and TTT both code for phenylalanine, but in Drosophila, TTC is more common. One measure of codon bias is called the Codon Bias Index, or CBI. Each student found the CBI for several genes in a region of a chromosome. At the bottom of the page are data for three regions of the X chromosome and three regions of the third chromosome. Analyse the data using a nested anova, and write a couple of sentences interpreting the results. Then pool together all of the X-chromosome data, pool together all of the third-chromosome data, and analyze using a single-classification anova (or a t-test). Compare the results of the two tests; what does analyzing the data with a nested anova tell you that you wouldn't get from a single-classification anova?

(Note--please don't copy these data into a spreadsheet by retyping them. Instead, copy the whole data set from this web page, paste into a blank spreadsheet, then use the "Text to columns" command to separate the numbers into different columns. You can then copy the numbers from the blank spreadsheet into the nested anova spreadsheet.)

Chromosome  Region    Gene          CBI
     1        7D     singed        0.366
     1        7D     CG1409        0.224
     1        7D     CG15326       0.165
     1        7D     CG2175        0.125
     1        7D     CG15327       0.202
     1        7D     CG15325       0.264
     1        7D     CG1543        0.329
     1        7D     CG15333       0.066
     1        7D     CG2233        0.125
     1        7D     CG2252        0.205
     1        7D     CG1560        0.296

     1        13F     sd          -0.081
     1        13F     chc          0.282
     1        13F     CG32582     -0.224
     1        13F     CG8565       0.142
     1        13F     Aats-arg     0.161
     1        13F     CG8509       0.191
     1        13F     PGRP-LE      0.17
     1        13F     CG15602      0.114

     1        16A     CG8611       0.276
     1        16A     CG5488       0.246
     1        16A     CG5445       0.253
     1        16A     CG8661       0.395
     1        16A     CG8664       0.612
     1        16A     CG5424       0.359
     1        16A     CG5529       0.286

     3        75C     thick veins  0.205
     3        75C     virile      -0.012
     3        75C     white        0.358
     3        75C     wrinkled    -0.083
     3        75C     zerknult    -0.102
     3        75C     zipper       0.271
     3        75C     CG7320      -0.126

     3        93C     CG5871       0.266
     3        93C     CG3337       0.15
     3        93C     CG5874       0.235
     3        93C     ebony        0.401
     3        93C     CG5892       0.138
     3        93C     ETHR         0.416
     3        93C     Rab1         0.18

     3        94D     Heldout      0.248
     3        94D     gem          0.248
     3        94D     mei-w68      0.147
     3        94D     CG4656       0.177
     3        94D     Lnk          0.133
     3        94D     Fbp1         0.365
     3        94D     Rp513        0.614

6. McDonald et al. (1991) compared the shell morphology of three species of marine mussel, Mytilus edulis, Mytilus galloprovincialis and Mytilus trossulus, from various locations around the world. The three species can be distinguished using genetic characters, but they are very difficult to identify using just the shells. One of the characters that does show some difference among the species is the length of the anterior adductor muscle scar, or AAM length. Here are AAM lengths (standardized by dividing by total length) for a bunch of mussels. Analyze the data using a nested anova. Graph the means for the locations, grouped by species (you do not need to add error bars). Based on the results of the anova, if you were to do a followup study in which you measured 1000 more mussels, would you sample a few mussels from a lot of locations for each species (which would be a lot of work), or a large number of mussels from a small number of locations (which would be easier)?

species  location   ID number    AAM
edulis     Aarhus        26    0.150
edulis     Aarhus        27    0.179
edulis     Aarhus        28    0.164
edulis     Aarhus        29    0.129
edulis     Aarhus        30    0.147
edulis     Aarhus        31    0.157
edulis     Aarhus        32    0.128
edulis     Aarhus        33    0.166
edulis     Aarhus        34    0.119
edulis     Aarhus        35    0.167
edulis     Aarhus        36    0.190
edulis     Aarhus        37    0.160
edulis     Magdalen    1280    0.103
edulis     Magdalen    1280    0.107
edulis     Magdalen    1280    0.131
edulis     Magdalen    1280    0.108
edulis     Magdalen    1280    0.136
edulis     Magdalen    1280    0.125
edulis     Magdalen    1280    0.116
edulis     Magdalen    1280    0.116
edulis     Magdalen    1280    0.115
edulis     Magdalen    1280    0.133
edulis     Magdalen    1280    0.121
edulis     Magdalen    1280    0.111
edulis     Shinnecock  1526    0.118
edulis     Shinnecock  1529    0.115
edulis     Shinnecock  1533    0.128
edulis     Shinnecock  1534    0.108
edulis     Shinnecock  1535    0.117
edulis     Shinnecock  1536    0.123
edulis     Shinnecock  1539    0.106
edulis     Shinnecock  1540    0.108
edulis     Shinnecock  1541    0.129
edulis     Shinnecock  1547    0.105
edulis     Shinnecock  1548    0.119
edulis     Shinnecock  1549    0.139
gallo      HongKong       3    0.114
gallo      HongKong       4    0.100
gallo      HongKong      12    0.078
gallo      HongKong      24    0.091
gallo      HongKong      25    0.093
gallo      HongKong      27    0.092
gallo      HongKong     f20    0.122
gallo      HongKong     f26    0.115
gallo      HongKong     m14    0.089
gallo      HongKong     m15    0.094
gallo      HongKong     m22    0.066
gallo      HongKong     m23    0.086
gallo      SanDiego    m110    0.060
gallo      SanDiego     m16    0.084
gallo      SanDiego    sd17    0.085
gallo      SanDiego    sd21    0.077
gallo      SanDiego    sd22    0.101
gallo      SanDiego    sd28    0.083
gallo      SanDiego    sd30    0.073
gallo      SanDiego    sd32    0.072
gallo      SanDiego    sd34    0.072
gallo      SanDiego   sd809    0.083
gallo      SanDiego   sd810    0.092
gallo      SanDiego   sd812    0.067
gallo      Venice         1    0.090
gallo      Venice         2    0.062
gallo      Venice         3    0.049
gallo      Venice         4    0.084
gallo      Venice         5    0.061
gallo      Venice         7    0.071
gallo      Venice         8    0.072
gallo      Venice         9    0.050
gallo      Venice        10    0.096
gallo      Venice        11    0.088
gallo      Venice        12    0.096
gallo      Venice        13    0.063
trossulus  Magadan     2228    0.069
trossulus  Magadan     2229    0.068
trossulus  Magadan     2231    0.083
trossulus  Magadan     2234    0.075
trossulus  Magadan     2235    0.078
trossulus  Magadan     2238    0.073
trossulus  Magadan     2239    0.103
trossulus  Magadan     2240    0.076
trossulus  Magadan     2241    0.066
trossulus  Magadan     2243    0.068
trossulus  Magadan     2244    0.091
trossulus  Magadan     2249    0.070
trossulus  Newport      226    0.072
trossulus  Newport      228    0.091
trossulus  Newport      230    0.075
trossulus  Newport      234    0.065
trossulus  Newport      235    0.091
trossulus  Newport      238    0.074
trossulus  Newport      239    0.082
trossulus  Newport      241    0.084
trossulus  Newport      244    0.087
trossulus  Newport      245    0.085
trossulus  Newport      247    0.067
trossulus  Newport      249    0.066
trossulus  Posyet      2251    0.096
trossulus  Posyet      2254    0.101
trossulus  Posyet      2255    0.121
trossulus  Posyet      2256    0.108
trossulus  Posyet      2257    0.103
trossulus  Posyet      2265    0.116
trossulus  Posyet      2266    0.107
trossulus  Posyet      2268    0.097
trossulus  Posyet      2268    0.100
trossulus  Posyet      2271    0.119
trossulus  Posyet      2274    0.117
trossulus  Posyet      2275    0.092
trossulus  Petersburg   901    0.097
trossulus  Petersburg   905    0.106
trossulus  Petersburg   915    0.115
trossulus  Petersburg   928    0.121
trossulus  Petersburg   929    0.135
trossulus  Petersburg   930    0.105
trossulus  Petersburg   943    0.106
trossulus  Petersburg   946    0.082
trossulus  Petersburg   948    0.106
trossulus  Petersburg   955    0.097
trossulus  Petersburg   961    0.102
trossulus  Petersburg   963    0.114

Return to the Biological Statistics syllabus

Return to John McDonald's home page

This page was last revised October 18, 2007. Its URL is http://udel.edu/~mcdonald/stathw7.html