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Denote: ai = contrast and ni = sample size for each level
Estimate of contrast:
sum( ai ybari )
note: sum is written as Sigma
Standard Error of contrast:
sqrt( sum( sigma2 ai2 / ni ) )
note: sum is written as Sigma, and lowercase sigma is usually estimated with MSE
Sums of Squares of contrast:
( sum( ai ybari ) )2 / ( sum( ai2 / ni ) )
note: sum is written as Sigma
Usually when one uses estimate divided by SE, the test statistic follows a t-distribution (unless he/she didn't estimate lowercase sigma). When one uses SS(contrast) divided by MSE, the test statistic follows a F-distribution. The formulas are similar because there's a strong relationship between the t-distribution and the F-distribution.
Hopes this helps and sorry I don't know how to write math equations here.
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What is the relationship of the standard error of the mean to the standard error of the difference?
It would help to know the standard error of the difference between what elements.
What is the fractional error formula?
What is the formula for percent fractional error? (Physics)
Why is standard deviation of a statistic called standard error?
The standard error is the standard deviation divided by the square root of the sample size.
Will the standard error always be lower than the standard deviation?
No.
Can standard deviation equal standard error?
If n = 1.
What is the standard error if the population standard deviation is 100 and the sample size is 25?
Formula for standard error (SEM) is standard deviation divided by the square root of the sample size, or s/sqrt(n). SEM = 100/sqrt25 = 100/5 = 20.
Difference between standard error and sampling error?
Standard error is random error, represented by a standard deviation. Sampling error is systematic error, represented by a bias in the mean.
What is the relationship of the standard error of the mean to the standard error of the difference?
It would help to know the standard error of the difference between what elements.
A common formula error?
There are two common formula errors. One error is that the formula is read wrong. The other error is that the formula is written down incorrectly.
What is the fractional error formula?
What is the formula for percent fractional error? (Physics)
Is accuracy or precision related to standard error?
Standard error is a measure of precision.
Why is standard deviation of a statistic called standard error?
The standard error is the standard deviation divided by the square root of the sample size.
What is the T-Test formula?
t= absolute value of ( sample 1 - sample two) THEN DIVIDED by the (standard error of sample one - standard error of sample 2) standard error = the standard deviation divided by (square root of the pop. sample number) You have to work in steps to get all info 1. mean ( REPRESENTED BY 'Xbar') 2. sum of squares ('SS') 3. Sample variance ('s^2') 4. standard deviation ('s') 5. standard error ('s subscript x') 6. pooled measure ('s^2p') 7. Standard error between means (s subscript mean one-mean two) 8. t test In other word finding the mean and having ht esample info leads you to each formula with the end formular being the t-test have fun, its easy but dumb
What happens to the standard error of the mean if the sample size is decreased?
The standard error increases.
The purpose and function of standard error of measurement?
the purpose and function of standard error of mean
How does sample size affect the size of your standard error?
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
What is the standard error of the sampling distribution equal to when you do not know the population standard deviation?
You calculate the standard error using the data.
