n a study of the Gouldian finch, Griffith et al. (2011) looked at stress caused by having an incompatible mate. There are two genetically distinct types of Gouldian finches, one having a red face and the other having a black face. Previous experiments have shown that female finches have a strong preference for mating with males with the same face color as themselves and that when different face types of finch mate with one another, their offspring are less likely to survive than when both parents are the same type. Researchers paired females sequentially with males of both types in random order.In other words, each female bred twice once with a compatible male and once with an incompatible male. Each time, females produced a brood of young with the assigned male. For each pairing, the researchers measured the blood corticosterone concentration (in units of ng/ml) as an index of the amount of stress the females experienced. The corticosterone data for 43 females are given below: corticosterone_concentration_compatible corticosterone_concentration_incompatible 10 130 10 105 39 91 30 82 6 77 21 65 0 64 4 60 16 56 10 51 23 45 22 50 8 49 19 48 22 44 10 44 10 44 11 42 22 41 19 37 21 37 14 37 11 36 6 36 1 35 2 32 9 31 11 30 12 30 3 30 3 30 4 30 6 29 5 29 7 29 6 28 8 26 8 25 21 25 7 25 8 24 7 21 8 7 Plot the distribution of differences in stress levels between females with compatible and incompatible mates. What trend is suggested? If we wished to carry out a test of the difference between treatment means, would a paired t-test be appropriate for these data? Why or why not? Would a paired t-test be appropriate after a log transformation of the differences between treatments? Would a sign test be appropriate for these data? Why or why not? Test the hypothesis that stress levels are the same between females with compatible and incompatible mates. Use a sign test.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
In a study of the Gouldian finch, Griffith et al. (2011) looked at stress caused by having an incompatible mate. There are two genetically distinct types of Gouldian finches, one having a red face and the other having a black face. Previous experiments have shown that female finches have a strong preference for mating with males with the same face color as themselves and that when different face types of finch mate with one another, their offspring are less likely to survive than when both parents are the same type. Researchers paired females sequentially with males of both types in random order.In other words, each female bred twice once with a compatible male and once with an incompatible male. Each time, females produced a brood of young with the assigned male. For each pairing, the researchers measured the blood corticosterone concentration (in units of ng/ml) as an index of the amount of stress the females experienced. The corticosterone data for 43 females are given below:
|
corticosterone_concentration_compatible |
corticosterone_concentration_incompatible |
|
10 |
130 |
|
10 |
105 |
|
39 |
91 |
|
30 |
82 |
|
6 |
77 |
|
21 |
65 |
|
0 |
64 |
|
4 |
60 |
|
16 |
56 |
|
10 |
51 |
|
23 |
45 |
|
22 |
50 |
|
8 |
49 |
|
19 |
48 |
|
22 |
44 |
|
10 |
44 |
|
10 |
44 |
|
11 |
42 |
|
22 |
41 |
|
19 |
37 |
|
21 |
37 |
|
14 |
37 |
|
11 |
36 |
|
6 |
36 |
|
1 |
35 |
|
2 |
32 |
|
9 |
31 |
|
11 |
30 |
|
12 |
30 |
|
3 |
30 |
|
3 |
30 |
|
4 |
30 |
|
6 |
29 |
|
5 |
29 |
|
7 |
29 |
|
6 |
28 |
|
8 |
26 |
|
8 |
25 |
|
21 |
25 |
|
7 |
25 |
|
8 |
24 |
|
7 |
21 |
|
8 |
7 |
- Plot the distribution of differences in stress levels between females with compatible and incompatible mates. What trend is suggested?
- If we wished to carry out a test of the difference between treatment means, would a paired t-test be appropriate for these data? Why or why not?
- Would a paired t-test be appropriate after a log transformation of the differences between treatments?
- Would a sign test be appropriate for these data? Why or why not?
- Test the hypothesis that stress levels are the same between females with compatible and incompatible mates. Use a sign test.
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