My Math Forum What is the Standard Error Significance?

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 November 6th, 2017, 03:29 AM #1 Newbie   Joined: Nov 2017 From: Stockholm Posts: 8 Thanks: 0 What is the Standard Error Significance? Hi, I'm having a hard time really understanding what Standard Error is, why it's important and perhaps more importantly how to interpret the result. Or "Ok I have the result, what is it telling me about the data?"
 November 6th, 2017, 08:10 AM #2 Senior Member   Joined: Jun 2015 From: England Posts: 853 Thanks: 258 OK, so you understand that a sample and the actual population do not have the the same mean and variance or standard deviation? That is if we have a population with a true mean X and standard deviation s (sorry not greek letters) and we take a series of samples from it, each sample will have its own mean (X1_, X2_ X3_...) and standard deviation about that mean (s1_, s2_, s3_....). The standard deviation of the collection of sample means is called the standard error. The significance is that if the standard error is large the chances are that the mean of a given sample will not be close to the true population mean.
November 6th, 2017, 08:38 AM   #3
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Quote:
 Originally Posted by studiot OK, so you understand that a sample and the actual population do not have the the same mean and variance or standard deviation?
I know that there is a difference in regards to if we have the actual population or just a sample. The sample mean and variance is of course depending on our sample.

In regards to the variance it is a measure of the data spread around the mean. Ex. if it is large the mean is less representative value of the data and a small variance is more representative if I am not mistaken?

Quote:
 That is if we have a population with a true mean X and standard deviation s (sorry not greek letters) and we take a series of samples from it, each sample will have its own mean (X1_, X2_ X3_...) and standard deviation about that mean (s1_, s2_, s3_....).
No worries about the greek letters etc. Understanding this without them helps me understand better.

Quote:
 The standard deviation of the collection of sample means is called the standard error. The significance is that if the standard error is large the chances are that the mean of a given sample will not be close to the true population mean.
Ok so the Standard Error is like a confidence factor. Ie how much we can trust it to actually represent a true population mean. So a Standard Error of 0.00 means that we have found the true population mean and can be counted as such?

I guess a "Large" standard error differes depending on your actual data set or are there some praxises regarding ranges. like a 0.75 would mean large?

 November 6th, 2017, 11:38 AM #4 Senior Member   Joined: Jun 2015 From: England Posts: 853 Thanks: 258 Let us say you were testing the consistency (homogeny) of some cake mix. So you took samples from the left , right , front, back top and bottom of the bowl. Say the % fat is supposed to be 15 % and your samples indicated (the first 4 are the top and the second 4 the bottom) { 12, 15, 14, 14, 18, 21, 10, 12} which has a mean of 14.5. What does the above tell you about the mixing?
 November 6th, 2017, 12:22 PM #5 Global Moderator   Joined: May 2007 Posts: 6,582 Thanks: 610 For a random variable chosen from a normal distribution, the value will be within one standard deviation from the mean approximately 65% of the time. This is typically applied for measurement samples which usually have normal distributions.
November 6th, 2017, 10:03 PM   #6
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Quote:
 Originally Posted by studiot Let us say you were testing the consistency (homogeny) of some cake mix. So you took samples from the left , right , front, back top and bottom of the bowl. Say the % fat is supposed to be 15 % and your samples indicated (the first 4 are the top and the second 4 the bottom) { 12, 15, 14, 14, 18, 21, 10, 12} which has a mean of 14.5. What does the above tell you about the mixing?
Thank you for this way of visualising this (to me, abstract topic).

From what you describe above it tells me that the fat % at the top and bottom is 0.5% short.

So either we would need to add the 0.5% of fat or stir the bowl since the last remaining 0.5% might be found in the middle?

November 6th, 2017, 10:14 PM   #7
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Quote:
 Originally Posted by studiot OK, so you understand that a sample and the actual population do not have the the same mean and variance or standard deviation? That is if we have a population with a true mean X and standard deviation s (sorry not greek letters) and we take a series of samples from it, each sample will have its own mean (X1_, X2_ X3_...) and standard deviation about that mean (s1_, s2_, s3_....). The standard deviation of the collection of sample means is called the standard error. The significance is that if the standard error is large the chances are that the mean of a given sample will not be close to the true population mean.
Quote:
 Originally Posted by mathman For a random variable chosen from a normal distribution, the value will be within one standard deviation from the mean approximately 65% of the time. This is typically applied for measurement samples which usually have normal distributions.
In regards to what the "Standard Error" is.

So the Standard Error is, at it's core, just a "label" for

The standard deviation of the collection of sample means.

It's context

To put this into some type of context to see if I got this correct.

Let's say I am working on finding out salary levels at a company based on the employees voluenteering information. The company is very large and have several departments. From each departments I would get a sample information since getting a 100% answer rate isn't allowed in this example.

Each department would get it's own sample mean since they also naturally can differ in total number of employees.

In order to be able to compare their respective means or put them in context to eachother the Standard Deviation of these Collected Means is called the Standard Error of the total of this sample data?

Have I understood what the standard error is and it's contextual use?

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