Question

Explain Fishers Exact Test ?

Difference between BLUE and BLUP ? Different properties of BLUP

Answer 1

(1)Fishers Exact Test:Fishers Exact Test Fisher’s Exact Test of Independence is a statistical test used when you have two nominal variables and want to find out if proportions for one nominal variable are different among values of the other nominal variable.

For experiments with small numbers of participants (under around 1,000), Fisher’s is more accurate than the chi-square test or G-test.

Example:You are studying if certain treatments for skin cancer lead to good outcomes. The first nominal variable is the treatment: some patients are given drug X and others are given drug Y. The second nominal variable is the outcome: patients are cured of cancer, or they are not. When you complete the study of 50 patients, you find that the percentage of patients who were cured and took drug X is much higher than patients who took drug Y. Fisher’s Exact Test of Independence will tell you if your results are statistically significant.

Formula:

p= ( ( a + b ) ! ( c + d ) ! ( a + c ) ! ( b + d ) ! ) / a ! b ! c ! d ! N !

In this formula, the ‘a,’ ‘b,’ ‘c’ and ‘d’ are the individual frequencies of the 2X2 contingency table, and ‘N’ is the total frequency.

The Fisher Exact test uses this formula to obtain the probability of the combination of the frequencies that are actually obtained. It also involves the finding of the probability of every possible combination which indicates more evidence of association.

(2)Difference between BLUE and BLUP:

(i) Abstract

The use of best linear unbiased prediction/restricted maximum likelihood (BLUP/REML) in perennial crops and animal breeding enhances selection gain. However, its advantage with respect to annual crops is not clear. We compared the BLUP and best linear unbiased estimator selection efficiency in the breeding of various potato generations. This was done by simulating various selection intensities on clonal families (full sibs), and clones. The characters evaluated were tuber yield and tuber specific gravity. Two criteria were adopted for comparison: a) incidence of families or clones and b) selection gain. For tuber yield, BLUP/REML method was slightly more efficient for selecting families in the first clonal generation, if it were above 50%. Below this value, both methods were equivalent. However, they both presented equal behavior for family selection of tuber specific gravity. For clonal selection, BLUP/REML showed robust superiority from 10 to 90% selection intensities in both characters. Therefore, the adequate use of BLUP/REML in potato breeding can enhance the selection gain on the yield and specific gravity of tubers.

(ii)

In contrast to the case of best linear unbiased estimation, the "quantity to be estimated", {\displaystyle {\tilde {Y_{k}}}}, not only has a contribution from a random element but one of the observed quantities, specifically {\displaystyle Y_{k}} which contributes to {\displaystyle {\widehat {Y_{k}}}}, also has a contribution from this same random element.

In contrast to BLUE, BLUP takes into account known or estimated variances.^[2]