The Kidd blood group in primates is inherited as a single gene with two codomina
ID: 32049 • Letter: T
Question
The Kidd blood group in primates is inherited as a single gene with two codominant alleles (Jka and Jkb). We would like to verify that this locus actually follows simple Mendelian inheritance with codominant alleles in gibbons. We have a pure breeding population of Type Jka and a pure breeding population of Type Jkb. We create an F2 population and test for the antigens.
Jka: 30
Jka Jkb: 63
Jkb: 35
Perform a chi square analysis on this data using the following hypothesis:
The mode of inheritance for the Kidd blood group in gibbons is simple Mendelian with codominant alleles.
Calculate the chi square value and place it in the space below. Round to three decimal places.
Explanation / Answer
Hi,
"chi-square" test, it's necessary to talk about the actual chi-square distribution. The chi-square distribution, itself, is based on a complicated mathematical formula. There are many other distributions used by statisticians (for example, F and t) that are also based on complicated mathematical formulas. Fortunately, this is not our problem. Plenty of people have already done the relevant calculations, and computers can do them very quickly today.
When we perform a statistical test using a test statistic, we make the assumption that the test statistic follows a known probability distribution. We somehow compare our observed and expected results, summarize these comparisons in a single test statistic, and compare the value of the test statistic to its supposed underlying distribution. Good test statistics are easy to calculate and closely follow a known distribution. The various chi-square tests (and the related G-tests) assume that the test statistic follows the chi-square distribution.
Let's say you do a test and calculate a test statistic value of 4.901. Let's also assume that the test statistic follows a chi-square distribution. Let's also assume that you have 2 degrees of freedom (we'll discuss this later). There is a separate chi-square distribution for each number of degrees of freedom. The value of chi-square can vary anywhere between 0 and positive infinity. 91.37% of the actual chi-square distribution for 2 d.f. is taken up by values below 4.901. Conversely, 8.63% of the distribution is taken up by values of 4.901 or greater.
We know that our test statistic may not follow the chi-square distribution perfectly. Hopefully, it follows it pretty well. We estimate our chance of calculating a test statistic value of 4.901 or greater as 8.63%, assuming that our hypothesis is correct and that any deviations from expectation are due to chance. By convention, if we use a test statistic to estimate the probability that our hypothesis is wrong, we reject the hypothesis if that probability is 95% or greater. To put it another way, we choose to reject the hypothesis if there is a 5% or less probability that we would be making a mistake doing so. This threshold is not hard and fast, but is probably the most commonly used threshold by people performing statistical tests.
When we perform a statistica l test, we refer to this probability of "mistakenly rejecting our hypothesis" as "alpha." Usually, we equate alpha with a p-value. Thus, using the numbers from before, we would say p=0.0863 for a chi-square value of 4.901 and 2 d.f. We would not reject our hypothesis, since p is greater than 0.05 (that is, p>0.05).
You should note that many statistical packages for computers can calculate exact p-values for chi-square distributed test statistics. However, it is common for people to simply refer to chi-square tables. Consider the table below:
The first column lists degrees of freedom. The top row shows the p-value in question. The cells of the table give the critical value of chi-square for a given p-value and a given number of degrees of freedom. Thus, the critical value of chi-square for p=0.05 with 2 d.f. is 5.991. Earlier, remember, we considered a value of 4.901. Notice that this is less than 5.991, and that critical values of chi-square increase as p-values decrease. Even without a computer, then, we could safely say that for a chi-square value of 4.901 with 2 d.f., 0.05<p<0.10. That's because, for the row corresponding to 2 d.f., 4.901 falls between 4.605 and 5.991 (the critical values for p=0.10 and p=0.05, respectively).
The Kidd antigen system (also known as Jk antigen) is present on the membranes of red blood cells and the kidney and helps determine a person's blood type. The Jk antigen is found on a protein responsible for urea transport in the red blood cells and the kidney. The gene encoding this protein is found on chromosome 18. Three Jk alleles are Jk(a), Jk(b)and Jk3. Jk (a) was discovered by Allen et al. in 1951 and is named after a patient (Mrs Kidd delivered a baby with a haemolytic disease of the newborn associated with an antibody directed against a new antigen Jka). Whereas Jk (b) was discovered by Plant et al. in 1953, individuals who lack the Jk antigen (Jk null) are unable to maximally concentrate their urine.
The Jk antigen is important in transfusion medicine. People with two Jk(a) antigens, for instance, may form antibodies against donated blood containing two Jk(b) antigens (and thus no Jk(a) antigens). This can lead to hemolytic anemia, in which the body destroys the transfused blood, leading to low red blood cell counts. Another disease associated with the Jk antigen is hemolytic disease of the newborn (HDN), in which a pregnant woman's body creates antibodies against the blood of her fetus, leading to destruction of the fetal blood cells. HDN associated with Jk antibodies is typically mild, though fatal cases have been reported.
d.f. p=0.9 p=0.5 p=0.1 p=0.05 p=0.01 1 0.016 0.455 2.706 3.841 6.635 2 0.211 1.386 4.605 5.991 9.210 3 0.584 2.366 6.251 7.815 11.345Related Questions
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