Given the above, what is the relationship between Y11, p11, n11, etc? Essentiall

Question

Given the above, what is the relationship between Y11, p11, n11, etc? Essentially, my question is how did Y11 come from table 6.

4.2, Theoretical evaluation of G × E interaction The rice yield trait was measured in two different years (1998 and 1999). Three genotypes (AiAi, AiA2 and A2A2) of a locus (bin1005) were evaluated. So, we have two levels of E (E,-1998 and E,-1999) and three levels of G (Gi = AiAi, G,-A1A2 and G3-A2A2). The counts and frequencies of the 2x3 cells are given in Table 6 and the average yields of the six genotype and year combinations are given in Table 7. Table 6. Joint distribution (counts and frequencies) of three genotypes and two environments of the rice yield trait analysis Marginal Pn = 1 1.49% n21-66 12127 Pn = 24.33% 1122 = 146 ni3 -59 Pn = 1 1.30% n,, = 246 P. = 4713% n, = 276 E2 = 27.97% | p23- =12.26% = 123 = 12.64% | p22- IM. = 52.87% 21 Marginal n, -126 n,-273 n =522 P.1-24.14% l p,-52.3% p,-23.56% | P. = 100% Table 7. Average yield of rice for each of the six genotype and year combinations Conditional EG G ,,-43.6448 Y. -36.1015 ConditionalY, -39,6936 |y,= | Y, =43.2745 Yi3 -45.7171 Y3 43.1836 Y3-44.3988 Y-45.6151 ½ = 41.5381 Y 43.4595 E2 Y2 -44.7744

Explanation / Answer

Actually they have no relation whatsoever because n11 denotes count how many times a particular genotype occured in that particular year in total plantation of 522 plants which is just a number (say 60 plants of type A out of 522 plants) and p11 denotes the probability of occurence of such tupe in that year (say 11.49% of chance that it occured in year 1998). Finally is our yield Y11 which has unit of weight i.e. Kilo gram or gram which is used to identify the amount of rice produced. Since each genotype has different capacity for ex. if we plant 10 plnts of type A and type B and after harvest we see that type A produces 10 Kg whereas type B produces 10.05 Kg on average (actually this data is written in table 7).

So the table 6 and 7 datas are independent.

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