chapter 11- · chapter 11-a statistical analysis of the effects of injecting mice with the dna...

Chapter 11-A statistical analysis of the effects of injecting mice with the DNA

chromosome associated with down syndrome

Here I will look at the weights of mice that have been injected with a strand of the 21st chromosome associ-

ated with down syndrome and compare them to the weights of mice without gene present. The first thing I will

do is sort the data into a category based on if the 21-chromosome is present in their DNA or not. Once I have

complied these two lists I will plot a histogram of each an preform some basic statistics to determine if either

distribution is normal and if the data suggests mice with this syndrome are generally more obese.

data =

Import@"http:��www.stat.berkeley.edu�users�statlabs�data�mouse.data", "Data"D;

data = Delete@data, 881<, 8-1<<D;

Length@dataD

532

dnadata = Cases@data, x_ �; x@@3DD == 1D;

birthweightdnadata = dnadata@@All, 6DD;

birthweightnondna = Cases@data, x_ �; x@@3DD == 0D;

Length@birthweightnondnaD

256

Length@dnadataD

276

Histogram@birthweightdnadataD

25 30 35 40

10

20

30

40

50

60

Kurtosis@birthweightdnadataD

2.62198

Printed by Wolfram Mathematica Student Edition

Skewness@birthweightdnadataD

0.194869

Mean@birthweightdnadataD

29.4909

Quartiles@birthweightdnadataD

826.3, 29.6, 32.1<

nondna = Cases@data, x_ �; x@@3DD � 0D;

weighthealthy = nondna@@All, 6DD;

Histogram@weighthealthyD

25 30 35 40

10

20

30

40

50

60

70

Kurtosis@weighthealthyD

3.0515

Mean@weighthealthyD

28.3672

Skewness@weighthealthyD

0.736127

Quartiles@weighthealthyD

825.4, 27.35, 31.<

Needs@"HypothesisTesting`"D

MeanCI@weighthealthyD

827.883, 28.8513<

MeanCI@birthweightdnadataD

829.034, 29.9479<

2 ch11Project.nb


MeanCI@weighthealthy, ConfidenceLevel ® .99D

827.7291, 29.0052<

MeanCI@birthweightdnadata, ConfidenceLevel ® .99D

828.8889, 30.093<

From these tests we can see the average weight of mice with the 21-chromosome detected was approxi-

mately 1 gram heavier than those without the chromosome. The confidence intervals really provide

some insight into the relation between obseity and the syndrome. The 95% confidence interval for the

uninfected mice was between 27.7 - 29, while the mice with the syndrome had a CI of 28.8-30.1. To

further analyze this data I will look at each of the four strands of DNA that was found in the transgenic

mice by the sex of the mouse. Males tend to be heavier than females, which may cause the data to

provide skewed results.

Seperating the data sets from the 4 strands of mice into male/female:

dna1 = Cases@data, x_ �; x@@1DD � 1D;




dna1pos = Cases@dna1, x_ �; x@@3DD == 1D;

fdna1pos = Cases@dna1pos, x_ �; x@@4DD == 0D;

mdna1pos = Cases@dna1pos, x_ �; x@@4DD � 1D;

fdna1pos = fdna1pos@@All, 6DD;

mdna1pos = mdna1pos@@All, 6DD;











dna4pos = Cases@dna4, x_ �; x@@3DD � 1D;



ch11Project.nb 3




F1 = Histogram@fdna1pos, 10DM1 = Histogram@mdna1pos, 10D

22 24 26 28 30

2

4

6

8

10

30 35 40

5

10

15

20

25

4 ch11Project.nb



24 26 28 30 32

1

2

3

4

5

6

7

28 30 32 34 36 38

1

2

3

4

5

6

7

ch11Project.nb 5



25 26 27 28 29

0.5

1.0

1.5

2.0

30 32 34 36 38

0.5

1.0

1.5

2.0

6 ch11Project.nb



23 24 25 26 27 28 29

1

2

3

4

5

6

26 28 30 32 34 36

2

4

6

8

10

Calcualting the mean weights, standard deviations, and 95% confidence interval of

the data:

Mean@mdna1posDStandardDeviation@mdna1posDMeanCI@mdna1posD

32.0984

2.80603

831.3975, 32.7994<


33.2103

2.45226

832.4153, 34.0052<

ch11Project.nb 7



32.45

2.8476

830.8058, 34.0942<


30.2465

2.33374

829.5283, 30.9647<

Mean@fdna1posDStandardDeviation@fdna1posDMeanCI@fdna1posD

24.9825

2.13023

824.3012, 25.6638<


28.2677

2.05075

827.5155, 29.02<


26.3714

1.49634

824.9875, 27.7553<


25.6553

1.68871

825.1002, 26.2103<

Comparing the weights of the 4 strands of dna to mice without the DNA:

In these results we find the mean confidence interval of female mice with the second strand of DNA

(27.5-29.02) is larger than the female mice without the mutated DNA (25.5,26.2). The male DNA of mice

without the gene was {31.3381,32.5172}. The males with the second strand of the chromosome exhibited

an increase in the 95% confidence interval {32.4153,34.0052}.

8 ch11Project.nb


Comparing the weights of the 4 strands of dna to mice without the DNA:

In these results we find the mean confidence interval of female mice with the second strand of DNA

(27.5-29.02) is larger than the female mice without the mutated DNA (25.5,26.2). The male DNA of mice

without the gene was {31.3381,32.5172}. The males with the second strand of the chromosome exhibited

an increase in the 95% confidence interval {32.4153,34.0052}.

fnondna = Cases@nondna, x_ �; x@@4DD � 0D;

fnondnaweight = fnondna@@All, 6DD;

mnondna = Cases@nondna, x_ �; x@@4DD � 1D;

mnondnaweight = mnondna@@All, 6DD;

Mean@fnondnaweightDMeanCI@fnondnaweightD

25.8914

825.5381, 26.2446<

Mean@mnondnaweightDMeanCI@mnondnaweightD

31.9276

831.3381, 32.5172<

Histogram@fdna1posD

22 24 26 28 30 32

2

4

6

8

10

12

14

ch11Project.nb 9


Histogram@mdna1posD

30 35 40

5

10

15

20

25

Histogram@fnondnaweightD

24 26 28 30 32 34

10

20

30

40

Histogram@mnondnaweightD

25 30 35 40

5

10

15

20

25

30

10 ch11Project.nb


chapter 11- · chapter 11-a statistical analysis of the effects of injecting mice with the dna...

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