Question

Decisions about alpha level may be different, especially as it relates from hard sciences to social sciences. For example, a medical trial for cancer treatments conducts their statistical tests at .0001 – so for every 1 out of 10,000 patients, there may be issues, sickness or even death. For social science, we use alpha .05. We are comfortable with performing research, for example, on students. So we are satisfied with losing 5 out of 100 students or having our results being incorrect 5 out of 100 times. Do you agree with these alpha levels? Why or why not? What if your child’s education and the teacher assigned to him/her would be successful 95 out of 100 times?

Answer 1

H_0: ?_0??_a

H_1: not equal

t_est = (xbar-ybar)/S.E(xbar-ybar)

p = 2*p(t>t_test)

case1) sample size large approximately equal to population size.

the larger the sample size the smaller the standard error. The smaller the standard error, the smaller the p-value (as p-value is related to standard error). The smaller the p-value, the more significant the test result. That said, if you have sampled the entire population, or nearly so, there is no need for "drawing inferences" from "part to whole" or "sample to population" (i.e., no need for "inductive reasoning") .... you have actual, verifiable conclusions and not rely on hypothesized conclusions.

hence in a medical trial for cancer treatments alpha = 0.0001 setting having enough sample availability

2) sample size small )

the smaller the sample size the bigger the standard error. The bigger the standard error, the higher the p-value (as p-value is related to standard error). The higher the p-value, the no significant the test results.

conclusion:

I don't agree based on p values because I would use power analysis with the help of the alpha level of significance and population parameters to determine the sample size. because sample size plays the critical role in the testing of the hypothesis like confidence interval, p-value, t, or z test.

power = the probability of correctly rejecting a false null hypothesis = 1??.

n=?^2(t?/2+t?)^2/(?0??a)^2.