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An estimate for the mean of a set of observations is just that - an estimate. Another set of observations will give a different estimates. These estimates for the mean will have a distribution which will have a standard error. If you have two sub-populations, the mean of each sub-population will have a standards error and the se of the difference between the means is a measure of the variability of the estimates of the difference.

A typical school work example: the heights of men and of women. There will be a mean height for men, Hm, with a se for men's heights and a mean height for women, Hw, with its own se. The difference in mean heights is Hm - Hw and which will have an estimated se.

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Q: What does the standard error of the difference between means mean?
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What the difference between err and error?

Err means to go astray in thought or belief, error means a deviation from accuracy or correctness.


What three elements are necessary to conduct a t-test in statistics and find a critical value and test for a scenario?

For the first part of your question: "http://wiki.answers.com/Q/What_three_elements_are_necessary_to_conduct_a_t-test_in_statistics_and_find_a_critical_value_and_test_for_a_scenario... This is a simple explanation, but a start. T-tests measure the difference between the means of 2 groups. The 2 groups should be of the same size. You take the difference between the means (a) and divide that by the Standard error of the difference between the means (b). a/b = t The Standard Error is the standard deviation divided by square root of the size of the population (n = number of things in the sample size). You need 2 standard errors because you have 2 populations. (To get the difference of the standard error, take the sum of the square of the standard deviation for each population, and divide the sum by n. Then take the square root of that calculation. That is the standard error of the difference of the mean. That goes into the denominator of the calculation from the 1st paragraph. FYI - variance = the square of the standard deviation.Once you've found t, you need to look it up in table. But you also need the degrees of freedom which is the sum of n for both groups, minus 2; and you need your confidence level, like at .05.


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Related questions

What is the difference between standard error of mean and standard deviation of means?

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What three elements are necessary to conduct a t-test in statistics and find a critical value and test for a scenario?

For the first part of your question: "http://wiki.answers.com/Q/What_three_elements_are_necessary_to_conduct_a_t-test_in_statistics_and_find_a_critical_value_and_test_for_a_scenario... This is a simple explanation, but a start. T-tests measure the difference between the means of 2 groups. The 2 groups should be of the same size. You take the difference between the means (a) and divide that by the Standard error of the difference between the means (b). a/b = t The Standard Error is the standard deviation divided by square root of the size of the population (n = number of things in the sample size). You need 2 standard errors because you have 2 populations. (To get the difference of the standard error, take the sum of the square of the standard deviation for each population, and divide the sum by n. Then take the square root of that calculation. That is the standard error of the difference of the mean. That goes into the denominator of the calculation from the 1st paragraph. FYI - variance = the square of the standard deviation.Once you've found t, you need to look it up in table. But you also need the degrees of freedom which is the sum of n for both groups, minus 2; and you need your confidence level, like at .05.


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What is the difference between standard error of sample mean and sample standard deviation?

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