Question

Section 2: Identity the error Each of the following statements have a significant error in statistical logic. Explain the error and correct the statement. (3 points each) A) As the number of individuals in a sample from a population increases, the standard deviation of the sample decreases. B) A likelihood-based estimate of a parameter is always less accurate than a Bayesian estimate that uses the same likelihood function. C) To achieve a global significance level of 0.05 (no more than a 5% chance of a false positive test in the entire experiment), an experiment that involves 50 independent statistical tests should use a p- value threshold of 0.01 for each test. D)If the correlation coefficient between two numerical variables is not significant, then the two variables should be considered independent. E) The likelihood of having a child with Down syndrome is much higher for women over 35 than for younger women, so we can conclude that a child who is diagnosed with Down syndrome probably born to a woman over 35. was

Answer 1

A) Standard deviation of the sample will be depend on the sample i have taken, which means if i take more sample from distant points (outlier points) of the population then variance will increase in spite of taking large sample. So the statement is false.

B) Bayesian estimate depends on the prior distribution. If my prior distribution is not good then Bayes estimate will be less accurate than likelihood-based estimate and it will totally leads to a wrong prediction. So the statement is false.

C) There is no need for the p-value of each of the independent test to be 0.01, you have to fix the p-values in such a way that the sum of 50 p-values will be 0.05. Moreover here 50*0.01=0.5(Not 0.05). So the statement is false.

D) Correlation between two numerical variables is not significant means there is almost no linear dependence between two variables, but there may be no-linear dependence. So the statement is false.

E) "The likelihood of having a child with Down syndrome is much higher for woman over 35 than younger women" means a woman's risk of conceiving a child with Down syndrome increases after 35 years of age. However, most children with Down syndrome are born to women under age 35 because younger women have far more babies. So the statement is false.