What is relationship between standard error and probability value? What should be value of standard error if probability value is small (significant)?
In two factor agricultural experiment:
1. The standard error value of Factor-A (Irrigation) is 7 or higher and P-value is small i.e 0.0000
2. The standard error value of Factor-B (Weed control practices) is small i.e 0.0127 and P-value is small i.e 0.0000
3. The standard error value of interaction Factor-A x Factor-B is also small i.e 0.0219 and P-value is small i.e 0.0068
The reviewer has asked question:
The P values are surprisingly small when you look at the SE. Any explanations?
The answer with suggesting solution is needed
With thanks and sincere regards
Dr. Muhammad Nawaz Kandhro
Providing standard errors makes sense only for estimates of single coefficients, not for "factors". If a factor in a linear model has two levels and the model includes an intercept term, then the factor will be represented by a single coeffiecient the model. In this case one may talk about the "standard error of the factor", although this would still not be correct.
So your question is interpretable/understandable only when we assume that each of your factors is a two-level factor, so that your design is a 2x2 design, and that your model has an intercept and 3 coefficients: Y(ai, bi) = β0 + β1·IA(ai) + β2·IB(bi) + β3·IA(ai)IB(bi) where i is an index of the observation, IA and IB are indicator functions that take the value 1 or 0, depending on their arguments, which are one of the two possible levels of the corresponding factors.
Let bk be the estimated value of the coefficient βk. For each bk, a standard error sk is estimated. The ratio of estimate and its standard error is known as the t-statistic
bk / sk = tk
And, under the null hypothesis (βk=0) this statistic has an approximate t-distribution with n-m degrees of freedom, where n is the total sample size and m is the number of coefficients in the model. The p-value is 2·Pr(|T|>|tk|), where T is a t(n-m)-distributed random variable. You can use this relationship to see how the p-value depends on the standard error or vice versa.
Hi,
In general, when the sample size is increased, then we estimate the parameters more accurately, i.e. standard error of our estimators deceases, and the p-value decreases so it results in the rejection of the null hypothesis, making it not meaningful in this specific situation.
See here,
https://stats.stackexchange.com/questions/134890/is-p-value-essentially-useless-and-dangerous-to-use
Good luck,
Hamid
- Badges
- Science topic