Hi. It's Mr. Andersen and in this video I'm going to talk about standard
error. Standard error is one of my favorite statistics and the reason why is that it shows
you how good your data is. And let me show you what I'm talking about. So let's say I
collect 2 data sets. So this is data set 1 and this is data set 2. If you were to look
at the data you would say well this one over here seems to show more precision. It's going
to have more data and it doesn't see to be spread out as much. But if I were to graph
this data, so these two data sets, if I were simply to create a graph showing the mean
or the average of the data, both of them would be 12. And so if I had a bar graph it would
look like this for both data set 1 and data set 2. And so you should never have a bar
graph if you're using it to represent a lot of data unless it has error bars on it. And
so how do you figure out what the standard error is? How do you make the standard error
bars? Well let me show you. So basically I'll work through data set 2 and then I'll ask
you to work through data set 1. I'll put the answer down in the description down below.
And so to figure out standard error, the equation is really ingenious. Basically all they do
is they take the standard deviation and we divide it by the square root of the sample
size. Why is that important? Well what does standard deviation measure? Standard deviation
is going to measure the spread or how far the data is spread out. And so if you have
a lot of spread then you're going to have a large standard error. And the other thing
it uses in the sample size. So the sample size is how much data are you collecting?
If you collect a lot of data and we're going to have a large number here and that's going
to decrease by standard error. Likewise, if I have not much data at all that's going to
increase my standard error. So let's get to standard deviation. If you don't know how
to calculate standard deviation or even what it is and how it measures spread you're going
to want to go watch a video. And so here's a little link I'll put to a video I made on
standard deviation. So you could simply click here or I'll put a link to the standard deviation
in the video description down below. But you want to figure out how to do standard deviation.
I show you how to do it by hand and then I'll show you how to use a spreadsheet to calculate
stand deviation very very quickly. And then what is sample size? Well sample size is going
to be the number of trials you do or the number of data points that you collect. And so if
we were to look at data set 2, there are 10 numbers over here and so that means I'm going
to have a sample size of 10. And so keeping those in mind let me switch over to the spreadsheet
and show you how to figure this out. So right here I'm in Excel. This is going to be data
set 2, again I'm going to show you how to do that one. And then here's data set 1. So
what I'm going to do since I have this column right here, I'm going to first of all calculate
the average of that or the mean of that. If you were to type =mean for the mean nothing
will show up. And that's because spreadsheets don't use the word mean. They're going to
use the word average. So you can see that that pops up. First I hit a = and then I'm
going to write in average and then parenthesis. And now I'm going to tell Excel which kind
of data I want to figure out the average from. I put an end parenthesis and it simply calculates
for me that it's 12. Now here's a quick little trick. So I've done the average for this column.
If I select this average and then I move my cursor down here, watch how it changes. So
it changes from that to that and so I can click it now and then just drag that over
here. And Excel is smart enough that it's going to figure out "Oh, if you want the average
of this, now you want the average of this column." So you can see that the average is
going to be the same. Now let me show you how to do the standard deviation. If you did
that by hand it takes forever. And so it's really important that you use a calculator
or a spread sheet to do this. I'm going to hit = and then I'm going to start typing stdev.
It's going to be standard deviation. I'm going to hit a parenthesis and I'm going to select
the data. Then I'm going to hit an end parenthesis and there's my standard deviation. Now if
we were to compare that to the standard deviation of data set 1. So again let me do that trick.
I'm going to select this, move this over here. You can see that data set 1 has a much larger
deviation. That means it's going to have a greater spread in the data. But I'm going
to figure out the standard error of this first one. So this is .825. I'm going to remember
these numbers here and then switch back and figure it out. So let me write down the things
that I need to know. So my x bar or my mean I said is going to be 12. The n or the sample
size we said is going to be 10 in data set 2 because I have 10 values over here on the
right. And then the standard deviation that I just calculated is going to be .826. And
I did that in Excel. So how do I figure out the standard error? So the standard error
of the mean is simply going to be the standard deviation which is .826. Then I'm going to
divide that by the square root of the sample size. And the square root of the sample size
is going to be 10. So this is equal to .826 divided by the square root of 10. I'm going
to need my calculator right here. And that is going to be 3.16 and then I have to figure
out, so let me write that down. So that's 3.16. And then if I take .826 divided by 3.16
I get .261. So .261 is my standard error or standard error of mean. So you could figure
out the standard error of the data set 1. Remember in data set 1, we simply had 2 values,
9 and 15. And so if you want to figure out the standard error of those and so you make
sure you're doing that right, you could do that. And I'll put the values down below.
But what does this all mean? Well let me show you why this is super important. So if we
go over here and look at our graph again. So I just figured out the standard error of
data set 2. And so what that means is data set 2 my mean is 12. And so the average is
12. But I could add an error bar on the top, like that. And then I could add an error on
the bottom. And my standard error is going to be we said .261. In other words it goes
from 12 up to 12.261 and then from 12 down to 12 minus .261. So we're going to have an
error bar on each side. What you could do is go figure out set 1. Set 1 you're going
to have a much larger standard deviation. Your'e going to have a smaller sample size
and so I would imagine you're going to have pretty big error bars. And so what's neat
about that is the bar graph now with those standard error bars is going to show me kind
of the story. It's going to tell me about the data behind that mean, or the data behind
the average. And so that's standard errors. It's pretty straight forward. It's simple.
You're probably going to need a spreadsheet to do it and I hope that was helpful.