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Standard Error - YouTube
Channel: Bozeman Science
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hi it's mr. Andersen and in this video
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I'm going to talk about standard air
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standard air is one of my favorite
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statistics and the reason why is that it
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shows you how good your data is and let
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me show you what I'm talking about so
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let's say I collect two data sets so
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this is data set 1 and this is data set
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2 if you were to look at the data you
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would say well this one over here seems
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to show more precision it's going to
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have more data and it doesn't seem to be
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spread out as much but if I were to
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graph this data so of these two data
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sets if I were simply to create a graph
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showing the mean or the average of the
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data both of them would be 12 and so if
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I had a bar graph it would look like
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this for both data set 1 and data set 2
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and so you should never have a bar graph
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if you're using it to represent a lot of
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data unless it has error bars on it and
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so how do you figure out what the
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standard error is how do you make the
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standard error bars well let me show you
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so basically I'll work through data set
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two and then I'll ask you to work
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through data set one I'll put the answer
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down in the description down below and
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so to figure out standard error the
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equation is really ingenious basically
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all they do is they take the standard
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deviation and we divide it by the square
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root of the sample size why is that
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important well what a standard deviation
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measure standard deviation is going to
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measure the spread or how far the data
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is spread out and so if you have a lot
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of spread then you're going to have a
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large standard error and the other thing
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it uses is the sample size so the sample
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size is how much data are you collecting
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if you collect a lot of data and we're
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going to have a large number here then
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that's going to decrease my standard air
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likewise if I have not much data at all
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that's going to increase my standard
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error so let's get to standard deviation
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if you don't know how to calculate
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standard deviation or even what it is
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and how it measures spread you're going
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to want to go watch a video and so
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here's a little link I'll put to a video
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I made on standard deviation so you
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could simply click here or I'll put a
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link to the standard deviation in the
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video description down below but you
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want to figure out how to do standard
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deviation I show you how to do it by
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hand and then I'll show you how to use a
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spreadsheet to calculate standard
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deviation
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very very quickly and then what is
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sample size well sample size is going to
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be the number of trials that you do or
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the number of data points that you
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collect and so if we were to look at
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data set two there are 10 numbers over
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here and so that means I'm going to have
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a sample size of 10 and so keeping those
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in mind let me switch over to the
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spreadsheet and show you how I would
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figure this out so right here I'm in
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Excel this is going to be data set 2
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again I'm going to show you how to do
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that one and then here's data set 1 so
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what I'm going to do is since I've got
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this column right here I'm going to
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first of all calculate the average of
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that or the mean of that if you were to
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type equals MEA n for the mean nothing
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will show up and that's because
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spreadsheets don't use the word mean
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they're going to use the word average so
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you can see that that pops up I'm going
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to put a left first I hit an equal sign
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then I'm going to write an average and
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then parenthesis and now I'm going to
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tell Excel which kind of a data I want
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to figure out the average from I put it
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in parenthesis and it simply calculates
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for me that it's 12 now here's a quick
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little trick so I've done the average
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for this column if I select this average
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and then I move my cursor down here
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watch how it changes so it changes from
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that to that and so I can click it now
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and then just drag that over here and
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Excel is smart enough that it's going to
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figure out oh if you want the average of
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this now you want the average of this
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column so you can see that the average
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is going to be the same now let me show
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you how to do the standard deviation if
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you did that by hand it takes forever
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and so it's really important that you
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use either a calculator or a spreadsheet
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to do this I'm going to hit equals and
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then I'm going to start typing stdev
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it's going to be standard deviation I'm
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going to hit a parenthesis then I'm
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going to select the data and then I'm
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going to hit end parenthesis and there's
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my standard deviation now if we were to
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compare that to the standard deviation
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of data set 1 so again let me do that
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trick I'm going to select this move this
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over here you can see the data set 1 has
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a much larger standard deviation that
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means it's going to have a greater
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spread in the data but I'm going to
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figure out the standard error this first
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one so this is 0.8 to 5 and so how do
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I'm going to remember these numbers here
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and then switch back and figure it out
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so let me write down the things that I
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need to know so my X bar or my mean I
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said is going to
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12 the N or the sample size we set is
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going to be 10 in data set 2 because I
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have 10 values over here on the right
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and then the standard deviation that I
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just calculated is going to be 0.8 to 6
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and I did that in Excel so how do I
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figure out the standard DVR standard
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error
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so the standard error of the mean is
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simply going to be the standard
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deviation which is 0.8 to 6 and then I'm
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going to divide that by the square root
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of the sample size and the square root
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of the sample size is going to be 10 and
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so this is equal to 0.8 to 6 divided by
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the square root of 10 I'm going to need
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my calculator right here and that is
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going to be 3.6 and then I have to
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figure out so let me write that down
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so that's three point one six and then
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if I take point eight to six divided by
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three point one six I get point two six
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one so 0.26 one is my standard air or
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standard air of the meet so you can
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figure out the standard error of the
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data set one remember in data set one we
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simply had two values 9 and 15 and so if
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you want to figure out the standard
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error of those and so you make sure
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you're doing that right you could do
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that and I'll put the values down below
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but what does this all mean well let me
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show you why this is super important so
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if we go over here and look at our graph
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again so I just figured out the standard
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error of data set 2 and so what that
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means is data set to my mean is 12 and
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so the average is 12 but I could add an
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error bar on the top like that and then
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I could add an error on the bottom and
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my standard error is going to be we said
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point 2 6 1 in other words it goes from
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12 up to 12 point to 6 1 and then from
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12 down to 12 minus 0.26 1 so we're
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going to have an error bar on each side
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what you can do is go figure out set 1
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set 1 you're going to
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much larger standard deviation you're
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going to have a smaller sample size and
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so I would imagine you're going to have
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pretty big error bars and so what's neat
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about that is the bar graph now with the
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standard error bars is going to show me
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um kind of the story it's going to tell
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me about the data behind that mean or
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the data behind the average and so
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that's standard errors it's pretty
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straightforward it's simple you're
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probably going to need a spreadsheet to
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do it and I hope that was helpful
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