Question

Below, there are 3 different biological studies. The corresponding datasets are located in the end of the text:

1. Name the independent variable(s) and state their type (categorical/nominal, categorical/ordinal, numerical/discrete or numerical/continuous). If relevant, state whether the variable(s) are fixed or random.

2. Name the dependent variable and state its type (categorical/nominal, categorical/ordinal, numerical/discrete or numerical/continuous).

3. State your null and alternate hypotheses in the form of statements about population
parameters.

4. Name a parametric test you might use to analyze the data and list the assumptions of the test. If there is no parametric test appropriate for this kind of situation, simply enter NA
5. Name a nonparametric test you might use to analyze the data and list the assumptions of the test. If there is no nonparametric test appropriate for this kind of situation, simply enter NA.

6. Assess whether or not your data satisfy the assumptions of the test(s) listed in question 4 and 5 above. In particular, produce and paste into a Word document at least one figure to help you visually assess whether or not your data meet these assumptions. Interpret this figure in your figure caption. If you transform your variables, note the transformation that you use, create a new figure and paste it into your answer sheet, and interpret this figure in your figure caption. If you choose to run statistical test(s) to assess your data (or your transformed data, if you decide to transform) for these assumptions, report the results of the test(s) (test statistic, df, P-value), make a decision regarding the null hypothesis, and interpret these results in terms of whether or not your data satisfy the assumptions.

7. Name the test you ultimately chose to analyze the data, and briefly explain why you chose it. Report the results of your test, including the test statistic, degrees of freedom, and p-value. Interpret the results. First, note whether you reject or fail to reject your null hypothesis. Second, interpret the results with respect to the original biological question.

Seals:
Individual Dive.Type Oxygen.use
1 Nonfeeding 42.2
2 Nonfeeding 51.7
3 Nonfeeding 59.8
4 Nonfeeding 66.5
5 Nonfeeding 81.9
6 Nonfeeding 82
7 Nonfeeding 81.3
8 Nonfeeding 81.3
9 Nonfeeding 96
10 Nonfeeding 104.1
1 Feeding 71
2 Feeding 77.3
3 Feeding 82.6
4 Feeding 96.1
5 Feeding 106.6
6 Feeding 112.8
7 Feeding 121.2
8 Feeding 126.4
9 Feeding 127.5
10 Feeding 143.1


Finches:
preference
23
27
57
15
15
54
34
37
-65
12


Lupus
Treatment Autoimmune.reactivity
sham 57
sham 260
sham 137
sham 373
sham 172
sham 507
sham 76
sham 105
sham 284
sham 96
control 260
control 137
control 373
control 172
control 456
control 76
control 105
control 284
control 96
enhancement 137
enhancement 60
enhancement 146
enhancement 78
enhancement 22
enhancement 122
enhancement 55
enhancement 69

Solution Preview

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1. The independent variable is Dive.Type which is categorical/nominal and fixed because there are only two types: Nonfeeding and Feeding.
2. The dependent variable is Oxygen.use which is numerical/continuous.
3. The null hypothesis H0 is that the mean of oxygen consumption for the feeding dive µFeeding is equal to a mean of oxgen consumption of nonfeeding dive µNonfeeding. The alternative hypothesis H1 is that µFeeding > µNonfeeding.
4. Paired t-test. Because the sample size is small (10), we have to be able to assume that the distribution of difference between Oxygen.use for two dive types is normally distributed as well as each pair is chosen randomly and independently.
5. Wilcoxon signed-rank test. There are a few assumptions. It tests the null hypothesis that two matched samples were drawn either from identical populations or from symmetric populations with the same mean. It has only very general assumptions: each pair is chosen randomly and independently. It does not have to assume the distribution of the difference of response is normal....

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