In statistics, does the odd ratio of the whole group for an outcome have to be within the odd ratios of subgroups for that outcome?
I would like to add to User-13728451172385841000’s great answer. It’s from Joe Blitzstein’s lecture on Simpson’s Paradox which you can watch in the video below. It’s around the 27:00 minute mark. He illustrates it with probabilities but it’s the same if you compute the odds ratios. (I modified it slightly to avoid division by zero).Imagine there are 2 doctors: Dr. Nick and Dr. Hibbert; and 2 procedures: heart surgery and bandaid removal.Suppose they each perform 100 operations, and there success/fail counts are as the following tables: Hibbert Nick Heart Bandaid Heart BandaidS 70 9 2 80F 20 1 8 10You can compute the odds ratio between Hibbert and Nick for each operation separately:Heart: [math]\frac{ \frac{70}{20} } { \frac{2}{8} } = 14[/math]Bandaid: [math]\frac{ \frac{9}{1} } { \frac{80}{10} } = \frac{9}{8}[/math]So for each type of surgery, the odds ratio is in favor of Dr. Hibbert.But OVERALL: [math]\frac{ \frac{79}{21} } { \frac{82}{18} } = \frac{237}{287}[/math] which favors Dr. Nick.
What is a control group in statistics?
A treatment group is a group where treatments are given. A control group is one in which no treatment is given.The more important question is why we use control groups?We use control groups (where no treatment or a placebo is given) as a baseline which we can use to compare against the treatment group.Control groups can represent a group in which the standard treatment is administered. This is used to assess if there is a statistically significant difference between the treatment group (new treatment) and the control (standard treatment).This can also be used to account for any psychological effects that are present. If you are comparing the effects of a certain drug, then the control group will not receive the actual drug but a blank pill (such as a sugar pill) and compare this with the treatment and no treatment group. For example, a patient who thinks that he/she is receiving the treatment may feel better although nothing real has been administered.
What statistical analysis should I use if I have 2 groups of subjects (high and low comprehenders) which are divided into 3 subgroups according to text genre (poetry, short story, drama) and subjected into three reading tests (pre-, post-intervention and post-intervention with text familiarity)?
OK, since you have measured the same people twice, you violate independence. You need to account for this. One way to do this is with a multilevel model, but these can have issues with only two time points (in fact, a two time point study is not the greatest when the variables are measured with error).Another possibility is too measure the change in number of correct answers as the dependent variable. Unless there are a very large number of questions, then this would be a count regression problem and the place to start is with Poisson or negative binomial regression. Then your independent variables would be group and genre and the interaction.
Statistics Math Homework help!?
I am working on my Stats homework for class tomorrow and I'm stumped on this problem. I'm probably just making a mistake that's making the answer wrong, but could someone help explain it? Thanks! According to the National Center for Health Statistics, there is a 23.4% probability that a randomly selected resident of the United States aged 25 years or older is a smoker. In addition, there is a 21.7% probability that a randomly selected resident of the United States aged 25 years or older is female, given that he or she smokes. What is the probability that a randomly selected resident of the United States aged 25 years or older is female and smokes? The back of the book says the answer is .051. Thanks for the help! (:
Can someone help me with this statistical significance question?
There have been arguments about the validity of identification based on DNA matching in criminal cases. One problem is that different subgroups may have different frequencies of "alleles," that is, variants of a gene. What is rare in one group may be common in another. Some empirical work has been done, to measure differences among subgroups. According to one geneticist, "Statistical significance is an objective, unambiguous, universally accepted standard of scientific proof. When differences in allele frequencies among ethnic groups are statistically significant, it means that they are real-the hypothesis that genetic differences among ethnic groups are negligible cannot be supported." Comment briefly on this interpretation of statistical significance.
How do you draw a subgroup / lattice diagram?
For a (finite?) group G, a subgroup diagram appears to be a graph with vertex set V = {H : H is a subgroup of G} and edge set E = {{H,K} : H, K in V, H is a proper subgroup of K }. A Y! search on "subgroup diagram" produced the source. Input a group, hit "generate group," "Subgroup Diagram," then "show diagram" (if necessary). Hope this helps. ♣ ♣
Question about normal subgroups of S4 of order 8.?
Second question first. A subgroup of S4 of order 3 is cyclic, and generated by a 3-cycle. Let's take a generic 3-cycle (a b c), so that a subgroup of order 3 is of the form H = {(1), (a b c), (a c b)}. Now a subgroup N of G is normal if and only if gNg^(-1) = N for all g in G. Here, (a d) = (a d)^(-1), and (a d)(a b c)(a d) = (b c d), which is not in H. Therefore, H is not normal in S4. _________ First question. A subgroup of order 8 must contain elements of orders 1, 2, 4, and 8. There isn't an element of order 8 in S4. Let us first see if we can get a subgroup of order 8 without a 4-cycle. Then generation of the subgroup requires 3 elements of order two. The elements of order 2 are (1 2), (1 3), (1 4), (2 3), (2 4), (3 4), (1 2)(3 4), (1 3)(2 4), (1 4)(2 3). There are 9 of them and we can only lose two. Observe that (a c)(a b) = (a b c), and (a b c) cannot appear in a subgroup of order 8, as it has order 3. Therefore, out of the two-cycles, we would have to eliminate in such a way so that the only 2-cycles left are disjoint. That requires the subtraction of four of them, and that is two too many. Therefore, we conclude that there is an element of order 4 (a 4-cycle) in the subgroup. Let that 4-cycle be (a b c d). Then (a b) (likewise (a d)) cannot be in the subgroup, as (a b)(a b c d) = (b c d), which cannot be in our subgroup. However, (a c) as the second generator will work. (a b c d) and (a c) generate the subgroup J = {(1), (a c), (b d), (a b)(c d), (a c)(b d), (a d)(b c), (a b c d), (a d c b)}. You should be able to show that J is not normal by trial and error from here. Good luck. ♣ ♣
In statistics, what's the difference between a subgroup, a moderator and 3rd variable?
I am not sure what you mean by "3rd variable" but I am guessing you mean "covariate". If so, the three things are quite different.A subgroup would be a group (or groups) that acts differently from others. If you wanted to analyze by subgroup then you would do stratified analysis. A covariate is a variable; the internals of the regression program will treat it the same as your main independent variable, the difference is in interpretation. Although there is no consistency in terminology, some people draw a useful distinction between "independent variable" and "covariate". An IV is the variable(s) you are primarily interested in. A covariate is a "noise" variable that you have to include. A moderator is a variable that affects the relationship between the dependent variable and the other independent variable. You analyze this by adding a term for the interaction to the model (usually just the product).Now, you said you weren't into examples, but I think one is needed; if not for you then for others who may read this.Suppose you were interested in the relationship between race/ethnicity and income. But you know that education is also important in determining income. (Actually, many variables enter into it, but I'll keep it simple; you'd probably also want to take log of income).In a subgroup analysis you would run separate regressions for (say) less than HS, HS Grad, some college, college grad, and higher degree.In a "third variable" analysis you would add education as a covariate.If you thought that education affected income differently for the different race/ethinicies (perhap you think that Black people get less beneftif from education, for example) you would enter the interactrion between education and race into the model.
Prove that a4 (+) z3 has no subgroups of order 18?
As mentioned before, you have to prove that the the A4 has no subgroup of order 6, since we already know A4 has no subgroup of order 18. This can be done by exhaustively listing the subgroups A4. There is no other way. But once you do this, the rest is book-keeping. The only subgroups of A4+Z3 are those of the form (S,0) or (S,Z3) where S is a subgroup of A4. We can rule out the former. Let S be a subgroup of A4 and assume set G={(s,z)|s∈S, and z∈Z3} be a subgroup with order 18 of A4. The group H=(1,Z3) can be considered a subgroup of this, and in fact it is a normal subgroup. This means that S/H can be identified with a subgroup of A4 of order 6 by identifying cosets with elements of A4. But A4 has no subgroup of order 6, contradicting the supposition. Thus A4+Z3 has no subgroup of order 18.