Assume alpha = .05

1) A golden retriever breeder is curious as to whether joint and dental problems tend to be inherited together. Dogs that are heterozygous for both traits are bred, the phenotype frequencies of their offspring are found in the table below. Fill in the blank spaces in the table, assuming hip and dental problems are recessive traits. Use chi-squared goodness of fit to determine whether the traits follow the expected 9:3:3:1 ratio.

Phenotype

No hip or dental problems

Hip problems, no dental problems

Dental problems, no hip problems

Hip and dental problems

Total

Observed frequency

32

19

24

18

Expected Proportion

Expected Frequency

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

2) Chronic wasting disease (CWD) is a brain disease of deer and elk, and it is one of a group of diseases called transmissible spongiform encephalopathies (TSEs) associated with the presence of prions (like mad cow disease). Characterized by long incubation periods, CWD takes years to develop. A study was conducted over a 3-year period. Deer were caught in the wild and tested for infection. Their age and sex was recorded, along with the region (core area or marginal area) where they were caught. The table below summarizes the infections of males and females in the area.

Infected

Not infected

Male

62

38

Female

55

71

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

3) A botanist is studying the effects of different fertilizers on wheat growth. The wheat berry production for each type of fertilizer is found below. Use a one factor ANOVA to determine whether there is difference in the wheat berries produced depending on fertilizer type.

SuperGro

CrazyPlant

Cow manure

Chicken Manure

30

38

27

32

32

32

26

31

38

30

23

29

26

37

29

27

25

32

27

32

28

27

25

30

38

31

25

30

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

4) The botanist then plans to investigate the role of temperature and fertilizer on wheat berry production. The data from this experiment is found in the table below.

SuperGro

CrazyPlant

Cow manure

Chicken manure

10C

23

19

25

21

29

34

31

32

22

26

28

30

19

14

17

12

15C

24

29

27

31

40

38

39

43

23

25

27

31

18

16

19

11

20C

38

40

35

42

15

17

13

12

20

24

26

29

20

12

19

15

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

5) The amount of natural sunlight a person is exposed to throughout the day is thought to be linked to several mental disorders, such as attention span. A researcher attached a photometer to students to record the time spent outdoors, an estimate of their exposure to sunlight. After the wearing the meter, the students then participated in a test to measure their attention span. The results are shown in the table below.

Sunlight exposure (minutes)

Attention span (minutes)

98

60

143

81

20

18

64

29

75

38

50

21

68

27

42

16

87

76

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

6) The same researcher then performed an experiment using mice. The mice were exposed to different interval times of sunlight, and then tested on how quickly they complete a maze. The data from this experiment is shown below.

Sunlight exposure (hours)

Time to complete maze (s)

1

78

2

65

3

56

4

43

5

33

6

24

7

16

8

9

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

7) A neurologist is studying the effect of different migraine medications on males and females. She tests medication A, B, and C on a group of males and females, and records the time until the patient feels pain relief. Is there a difference in pain relief patterns between sex and medication?

Medication

Male

Female

A

12

21

15

19

16

18

14

24

17

25

B

14

21

17

20

19

23

20

27

17

25

C

25

37

27

34

29

36

24

26

22

29

a) What statistical test will you use?

b) If needed, does your data have equal variance? Put NA is not needed.

Do you need to transform your data?

If yes, does transformed data have equal variance?

c) H_o: statistical and explanatory

H_A: statistical and explanatory

d) p-value(s)?

Accept or reject null hypothesis?

Discuss results of your data that are applicable to this statistical test (e.g. exp-obs, patterns, pvalue, post-hoc test, etc):

Conceptual Questions:

1)Match the data descriptions to the corresponding data analysis

a.X squared Goodness of Fit

b.X squared Independence

c.X squared homogeneity

d.One-factor ANOVA

e.Two-factor ANOVA

f.Regression

g.Correlation

___ Two factors/categories, one dependent or continuous variable

___ Frequency (count) data that fit a given distribution

___ Two randomly measured continuous variables

___ One factor/category, one dependent or continuous variable

___ Frequency (count) data with one trait and two groups

___ One controlled continuous variable and one dependent continuous variable

___ Frequency (count) data with one group and two traits

2)State the assumptions for each of the tests above if they have any.

3)State the differences between regression and correlation.

4)How are a p-value, critical value and calc value all related?

5)What does it mean when a 2-Factor ANOVA has a significant interaction between factor 1 and factor 2?

6)How does a regression/correlation calculate the p-value?

7)What are all of the sums of squared being compared in an ANOVA? Describe what each one is calculating.

8)In R, if you are running an ANOVA and you have a factor that is represented by a number (1,2,3 days or treatment 1,2,3 etc.) how do you ensure R treats it as a factor and not a number?