What is the relationship between a p-value for a one-sided test and the p-value
ID: 3226002 • Letter: W
Question
What is the relationship between a p-value for a one-sided test and the p-value for a two-sided test? What happens when a Type I error is made? What about a Type II error? What is the probability of making a Type I error? What is statistical power and how can it be increased? How does the sample size impact the p-value in a hypothesis test? What about the standard deviation? What are the sample mean in relation to the hypothesized mean? What are the different sources of variation in an ANOVA? What do they mean? How does increasing the standard deviation within each group in an ANOVA impact the p-value? What about increasing the sample size in each group? What happens to Fisher's LSD confidence intervals if the sample sizes taken from each group are the same? What does the correlation tell you in linear regression? What is the difference between an outlier and an influential point? What is a residual and how is it calculated? What are the different uses for simple liExplanation / Answer
Answers
l) p-value for a one-sided test = double the p-value for the two-sided test if the two-sided test is equally distributed over the left tail and right tail.
m) When a Type I error is made, we are rejecting a hypothesis when it is in reality true. Type II error occurs we accept a hypothesis when it is in reality not true, i.e., when alternative is true.
n) Probability of Type I error = P(hypothesis is rejected when it is true).
o) Statistical power of a test = 1 – P(Type II error). Power can be increased by opting for test which has a desired power.[Tests are derived by keeping the P(Type I error) at pre-fixed level, which is known as ‘level of significance’ and then mathematically (that is using Calculus) maximizing the power function.
p) There are mainly two ways by which sample size (n) impacts the p-value.
a) If n appears in the denominator of test statistic, as n increases/decreases, value of the test statistic decreases/increases and consequently p-value increases/decreases.If n appears in the numerator of test statistic, the impact will be reverse.
b) Majority of test statistics, barring the Z-test, follow distributions which are characterized by what is known as ‘degrees of freedom’ which in turn is always dependent on n. As a general rule, as n increases, degrees of freedom will also increase and consequently, p-value will also increase.
q) Different sources of variation in ANOVA depend on the ANOVA model and the design of the experiment. For example, in a one-way ANOVA which pertains to Completely Randomised Design, there is only one source of variation, namely ‘treatment’ whereas in a two-way ANOVA which pertains to Randomised Block Design, there are two sources of variation, namely one treatment which is represented along the rows and the other which is represented along the column.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.