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0:02[Music]
0:17hello thanks for watching and welcome to
0:20the next video in my series on basic
0:22statistics now as usual a few things
0:25before we get started number one if
0:27you're watching this video because you
0:28are struggling in a class right now I
0:31want you to stay positive and keep your
0:33head up if you're watching this it means
0:35you've accomplished quite a bit already
0:37you're very smart and talented but you
0:39may have just hit a temporary rough
0:41patch now I know with the right amount
0:43of hard work practice and patience you
0:46can work through it I have faith in you
0:49many other people around you have faith
0:51in you so so should you number two
0:55please feel free to follow me here on
0:57YouTube on Twitter on Google+ or on
1:01LinkedIn that way when I upload a new
1:03video you know about it and it's always
1:06nice to connect with my viewers online
1:08I'll feel that life is much too short
1:10and the world is much too large for us
1:12to miss the chance to connect when we
1:14can number three if you like the video
1:17please give it a thumbs up share it with
1:20classmates or colleagues or put it on a
1:22playlist that does encourage me to keep
1:24making them for you on the flip side if
1:27you think there's something I can do
1:28better please leave a con instructive
1:30comment below the video and I will take
1:32those ideas into account when I make new
1:35ones and finally just keep in mind that
1:37these videos are meant for individuals
1:39who are relatively new to Stats so I'm
1:42just going over basic concepts and I
1:45will be doing so in a slow deliberate
1:48manner not only do I want you to know
1:51what is going on but also why and how to
1:55apply it so all that being said let's go
1:58ahead and get started so this video is
2:01part two of our larger video on the
2:04one-way analysis of variance or the
2:06oneway Innova now in part one we went
2:10over an example problem and really sort
2:12of took it apart and looked at how all
2:14the parts of the oneway and Nova fit
2:17together so in part two we're going to
2:20go into Microsoft Excel and do a quote
2:23hand calculation of the oneway Anova so
2:27if you're watching the video on YouTube
2:29you can go to the description deson
2:30below the video and there you'll find a
2:32link to the corresponding blog post for
2:35this problem on the blog post you can
2:37actually download a blank version of the
2:39Excel file we're going to use and you
2:41can follow along step by step so without
2:44further waiting let's go ahead and get
2:46started on part two of the one-way
2:49analysis of
2:51variance now what we're going to do in
2:54Excel is try to replicate the output in
2:58SPSS and again SPSS is the statistical
3:02software I use in my work so I went
3:04ahead and did our example problem in
3:07SPSS and this was the result so we're
3:10going to go into Excel and actually try
3:11to replicate this Anova chart doing hand
3:15calculations and of course I don't mean
3:17literally by hand we're going to use
3:19Excel formulas but in the end we want to
3:22have a chart that looks exactly like
3:26this now before we actually go into
3:28Excel we do have to go over a few
3:31formulas for the oneway Inova now I
3:34mentioned before that some textbooks and
3:36some professors and classes and
3:39everything else call the same things by
3:42different names so you may have to cross
3:45reference what we're going to learn here
3:46with how it's presented in your class so
3:49you may actually want to have your
3:50textbook open or your notes open as we
3:53go through it it's the same thing but
3:55again they go by different names
3:57depending on what text you're using or
3:58what Professor you have
4:01so before we do that I just want to
4:02point out what's going to come up um
4:04here in a second when you see the
4:06variable in or the large n that
4:09represents the total number of
4:11observations in our experiment or in our
4:14problem in this case it's 21 remember
4:18now C is the number of columns we have
4:22in our chart remember in this problem we
4:24had three because we had three years of
4:28students so let's talk about SSC
4:31remember that's sum of squares of the
4:33columns or sometimes What's called the
4:35treatments it's also the levels of our
4:38single Factor we're looking at remember
4:41I said they can go by different names
4:42that's what I mean so in this case we
4:44had year one year 2 and year three those
4:47are our
4:49columns now the SSC also has a degrees
4:52of freedom actually all these have their
4:54own degrees of freedom in the SSC case
4:58the degrees of freedom of the columns is
5:02C
5:04minus1 now the
5:06MSC is the mean squared of the columns
5:11so mean square of the columns that's
5:15MSC and that is the SSC so the sum of
5:18squares of the columns divided by its
5:21own degrees of freedom again this is all
5:25very abstract until we do it so just
5:27hang with me so the SS e is the sum of
5:31the squares of the error or the within
5:34each column each individual column sum
5:37of squares so the SSC is a sum of
5:40squares between the columns the SS is a
5:43sum of squares within each
5:46column so degrees of freedom for SSC is
5:50n minus C and again we'll put numbers in
5:54all these here in a minute so the MSE is
5:58the mean squared error now the MSE is
6:02very important in many areas of
6:04Statistics so keep that in the back of
6:06your head as we proceed but msse is the
6:09mean squared of the error and that is
6:12the ssse divided by the degrees of
6:16freedom for the
6:17error and then we have SST which of
6:21course is the sum of squares of the
6:22total the total sum of squares the
6:25degrees of freedom for the SST is in -1
6:30so the total number of observations
6:34minus1 now in the end we will end up
6:37with an F statistic remember way back
6:40when in our f-stat video what the f
6:42statistic is it's a ratio the F ratio is
6:47a ratio of two variances so in our F
6:51ratio here in the numerator we're going
6:54to have the mean sum of squares for the
6:57columns which is the variant
7:00between the
7:01columns and then in the denominator
7:04we're going to have the mean squared
7:07error which is the variance of the sum
7:09of squares inside the columns so we have
7:13between the columns on top and within
7:17the columns in the denominator that's
7:19why you will often see this as an F
7:22ratio that is between divided by Within
7:27between the columns divided by the Vari
7:30of the data within the
7:34columns so let's go ahead and actually
7:36put some numbers in here let's find our
7:38degrees of freedom first so remember the
7:40degrees of freedom for SSC was C the
7:43number of columns minus one so in this
7:46case it's three because we have three
7:47columns minus one which equals 2 so the
7:52MSC equals the SSC divided by that
7:56degrees of freedom which is of course
7:58two
8:00now for the
8:01SSE the degrees of freedom for the ssse
8:04was n minus C so n is 21 that's number
8:09of overall observations minus 3 which is
8:12the number of columns so that is 18 so
8:16our msse equals the ssse divided by that
8:20degrees of freedom which is
8:2318 now the degrees of freedom total the
8:26SST is n minus one so our overall all
8:30number of observations minus 1 which of
8:32course is 21 - 1 = 20 now our F ratio
8:38Remains the Same it is still the msse
8:41divided by the
8:43MSE now let's go ahead and go into Excel
8:46and figure out the SSC and the SS which
8:51will allow us to find the MSC in the MSE
8:55that we need to do this
8:57problem so here we are in in Excel where
9:00we're going to do our hand calculation
9:02of this Anova problem but before I give
9:04you a tour of our spreadsheet here I
9:06want to draw your attention to the
9:07yellow box up here at the top now
9:10remember we're going to need the sum of
9:12squares however Excel does not have a
9:14sum of squares formula so what we're
9:17going to do is we're going to use the
9:18variance formulas and then alter them a
9:21bit so the Excel variance formulas which
9:23is var. S and var. P which is sample
9:28variance and population variance do the
9:30averaging step we don't want so the
9:33sample variance will divide by n minus
9:35one and the population variance will
9:37divide by n therefore we will have to
9:40sort of quote undo that step and make a
9:44couple of other adjustments to get the
9:45sum of squares we want so in the
9:48calculations we do in the formulas we
9:50use you will see multiplication added in
9:54that is the undoing of the variance
9:58averaging and other multiplication
10:00that's in the SST the SSC and the SS e
10:05so what I'm saying here is that some of
10:08this you're just going to have to take
10:10on faith and I hate saying something
10:12like that in a math video but that's
10:14just the way it is I did not go over the
10:17individual SST SSC and ssse formulas
10:21because I thought your face would glaze
10:23over anymore than it already is and you
10:25can find those in your books however I
10:28will try to point out out what each
10:30component is when we put in the formulas
10:33okay so that's sort of my little caveat
10:35here now on the top left you will see
10:37our chart our data as we had it in the
10:39PowerPoint portion so we have our year
10:41one scores our year 2 scores and our
10:44year three scores nothing much surprise
10:47there and then we have a column summary
10:50so the mean for year 1 year 2 and year
10:53three and then we have the overall mean
10:55there in the middle now over on the
10:58right hand side I just put the formulas
11:00for the sample variance and the sum of
11:02squares we're going to be doing if
11:04you're really not interested in the
11:05formulas that much just ignore those two
11:08blue boxes up there in the right hand
11:11side now if you look below our data
11:13you'll see n and C well n remember is
11:16going to be the total number of
11:17observations we have which in this
11:19problem of course will be 21 C is the
11:22number of groups or columns or
11:24treatments we have so in this problem
11:27will be three over on the right you will
11:30see the SPSS output for this problem so
11:34what we're going to try to do is
11:35replicate that little chart over there
11:38on the left hand side where we have the
11:40green header and then the SSC SSC SST
11:43there in that chart so we're going to
11:45try to make that chart on the left look
11:48like the SPSS output over here on the
11:51right and of course we will actually do
11:53this problem in Excel using its Anova so
11:56we're going to have three versions or
11:58three out puts of the exact same thing
12:01to make them all match now everything
12:03else on here is pretty much a hint so we
12:05don't have to go back to PowerPoint to
12:07find these formulas So Below there on
12:10the left hand side you will see the MSC
12:13the msse and the F ratio and again those
12:17just come from our slides we already had
12:20now in the purple boxes on the lower
12:22right those the formulas we're going to
12:24use to actually find our sum of squares
12:27so I will explain those further when we
12:29get to that step but I just wanted to
12:31put them here sort of in a text format
12:33so you can copy and paste them into the
12:36proper cell so let's go ahead and do
12:39some actual calculations and put in some
12:41data so the first thing we're going to
12:43do is we're going to go over to the n
12:45and the c boxes over here on the left
12:48hand side so this is easy so our n in
12:51this case is 21 so we're going to go
12:53ahead and put 21
12:54there that's the number of observations
12:57we have and then C is the number of col
12:59which is
13:00three so we'll go ahead and do that now
13:04the next thing I want to do is find the
13:07column means so we'll go up to the year
13:10one mean box which is the bottom of the
13:12year one scores and then we'll use the
13:15average formula so we'll type equals
13:19average and I'm actually go ahead and
13:21begin filling that out now we'll just
13:24select all seven of those scores in the
13:27year one column close print
13:29parentheses and there we go so this is
13:3371.7 which is what we had in the
13:35PowerPoint now we need the mean for all
13:38three columns so we'll go ahead and do
13:39the same thing for year
13:45two and we'll go and do the same thing
13:47for year three in case you're wondering
13:49I don't drag across because it takes the
13:50color with it so they would all be blue
13:52if I dragged across okay so we have the
13:56column mean for each of the student
13:59years so 71.7 one for year 1 students
14:0375.2 n for year 2 students and 7657 for
14:07year three students now we want the
14:10overall mean which is in this gray box
14:12here below the yellow box so again
14:15equals
14:17average and then we'll select all 21
14:22scores in our data and hit enter so now
14:26we have our overall mean of 7
14:314.52 so again using Excel we did hand
14:34calculations of all three column means
14:37and the overall mean which of course we
14:38know we need to do this type of problem
14:41now let's go ahead and go down to our
14:45chart over here on the lower left let's
14:47go ahead and find the degrees of freedom
14:50for each source of variance so remember
14:53we have column variance so between the
14:55columns we have within each column
14:57variance and then we have the the total
15:00sum of squares the total variance okay
15:02so remember that for the SSC we can see
15:05this sort of over here on the right hand
15:06side so degrees of freedom between which
15:09is the same thing as SSC is C minus one
15:13so we could say equals c which is this
15:16cell right here minus
15:19one and of course that is two now we
15:22need degrees of freedom for within so
15:25that is n minus C and you can see that
15:28little box on the right to help you sort
15:30of cheat a little so equals n which is
15:34that cell minus C which is that cell and
15:39that gives us 18 degrees of freedom now
15:41our total degrees of freedom is n minus
15:44one so this going to be equals in that
15:47cell minus
15:49one and that is 20 so that's very very
15:53easy now comes the hard part now we have
15:58to find the sum of
16:00squares now I went ahead and put
16:02placeholders in in our chart over here
16:04on the left hand side so we know where
16:06everything goes so you look in the SS
16:08column we have SSC SS and SST Su of
16:13squares column sum of squares erir and
16:15some of squares total now on the lower
16:18right you will see boxes outlined in
16:20sort of a purple color so those the
16:23actual formulas we're going to put in
16:26each one of those cells so let's take a
16:28look at each each one very briefly now
16:31there might be some multiplication in
16:32here you don't fully understand because
16:34I did not go over the actual formulas
16:37for SSC ssse and SST because they are
16:40mind- numbing you can find them in your
16:42book and the way we're doing it you
16:44really don't have to worry about it and
16:46that just sort of brings up my overall
16:48point the chances of you having to do an
16:50a Nova by hand are basically zero at
16:54least I hope not you're going to be
16:55using Excel or
16:57SPSS or many tab or whatever else it
17:00might be so we're doing all this by hand
17:02just so you can see how everything
17:03relates not because you'll have to do it
17:06that often and hopefully never so let's
17:08look at the top one first and that is
17:11SSC so in this one I'll go ahead and put
17:14my mouse in there you can see that we
17:16have SSC equals
17:20v.s that is the formula for sample
17:24variance and it's going to B sells A10
17:28to C10 let's go up here what is A10 and
17:32C10 well that is the column means so
17:37it's going to look at the variance of
17:39those three column
17:42means and then we multiply by two but
17:45where does the two come from in this
17:47case the two comes from the number of
17:48columns we have minus one so basically
17:52that's the same way of saying it's
17:53degrees of freedom so that's where that
17:55two comes from where does the seven come
17:57from well well that's how many
17:59observations we have in each column so
18:03v.s is the variance formula the sample
18:06variance formula for those three column
18:09means time 2 which is number of columns
18:12minus one so that's 2 time 7 which is
18:16the number of observations in each
18:19column so let's go ahead and go over
18:22here to our SSC box I'm going to take
18:24out the
18:25text then I'm going to go over here and
18:28copy
18:31our text in our box we'll go back over
18:33to the
18:34SS cell we'll paste it now I'm just
18:38going to take out the SSC part so delete
18:41delete delete hit
18:43enter and there we go so the sum of
18:46squares for the columns or the between
18:49sum of squares is
18:5188.6 67 repeating so let's go ahead and
18:55look at the SSE formula and it is
18:58admittedly much more involved if we take
19:00it apart we can see where everything
19:01comes from so we're using the v.s
19:04formula again so is the sample variance
19:08now the first one asks for cells A2
19:11through A8 well what are those well A2
19:15through
19:16A8 are the data points for column 1 or
19:21all the year one scores so we're asking
19:23for the sample variance of those seven
19:27scores
19:28now we're going to multiply by six well
19:31why are we multiplying by six well that
19:34goes up to the formulas up here at the
19:36top the sample variance is n minus one
19:38in the denominator well we do not want
19:40that we want to undo that so that's why
19:42we're multiplying by 7 - 1 which of
19:45course is six then we're going to add to
19:48that the variance of the next column so
19:51B2 through B8 same thing * 6 and then
19:55we're going to add that to the variance
19:584 three so C2 through C8 so that is all
20:02that is it's just the variance of each
20:05column added together so we'll go ahead
20:08and copy all that well first we'll go
20:11over to SSC and delete it make room now
20:14we'll go over copy all that contrl c on
20:18my PC contrl V to paste it now I'm going
20:22to go up and modify it by taking out the
20:25SS at the beginning delete now we hit
20:28enter
20:30and there we have a sum of squares
20:32within or an
20:34SS of 281
20:3712.57 so that is our sum of squares of
20:40the within and again that's within the
20:42columns we just add them all together
20:45now we'll go to SST sum of squares total
20:47so we'll delete
20:48that now if you look down here in our
20:51formula we have SS equal 20 * vs of A2
20:58through C8 well what is A2 through C8
21:02that's
21:03everything so A2 through C8 is our
21:07entire data set now we take the variance
21:10of that and we multiply it by 20 why
21:14well remember our variance is n minus
21:16one so we have 21 scores minus one we're
21:20going need to undo that put it in the
21:21top so that's what we multiply by 20 so
21:25we'll go ahead and select all
21:27that contrl C to copy we'll go over to
21:30our SS column here the SST contrl V to
21:34paste we'll take
21:36out the SST at the beginning hit enter
21:40and there we
21:41go now if you look close enough you will
21:43see that the
21:44SST is the sum of the SS and the SSC so
21:5188.6 667 plus 281 12.5 sish when you add
21:57those together you will get
22:0129123 so that goes back to the idea of
22:04partitioning the total variance so our
22:07total variance of SST is made up of two
22:09components the SS e and the SSC when you
22:13add those together you get the SST in
22:16return okay so a few more things to do
22:19now we need to find the
22:21MSC so that's up here under the MS
22:25column now if you look down here I have
22:27the little formula for the MSC or the
22:30mean square of the columns so we're
22:32going to delete the text and this is
22:34just the SSC divided by the degrees of
22:37freedom for columns and we have both of
22:39those so this is equal the SSC which we
22:43just found which is over here divided by
22:46the degrees of freedom for the SSC which
22:49is to the left of that so we go ahead
22:51and click that cell and hit enter now we
22:54have a mean Square for The Columns of 44
22:58. 3333 repeating now let's go ahead and
23:01do the
23:02msse so we'll delete the text in that
23:04cell so this is the SS divided by its
23:07degrees of freedom so we'll go to that
23:09cell we already have selected this is
23:12equal the SS the 281
23:1612.57 or whatever it was divided by its
23:20degrees of freedom which is to the left
23:21of it that's 18 and we'll go ahead and
23:24hit
23:25enter and that is 156
23:29257 so now we have our MSC and our MS e
23:36now what is f well f is merely division
23:40the MSC divided by the MSC of course we
23:42have both of those we just did them so
23:45the F here equals the
23:49MSC which is there to the left divided
23:52by the MSE e we found which is there hit
23:57enter and you'll notice we
24:00have 28 3726 Etc what was it in our SPS
24:05output look over here on the right our f
24:09is
24:11284 same thing so look at the SPSS
24:15output over here on the right and our
24:17chart we just did over here on the left
24:20what do you notice degrees of freedom
24:22for the between groups is two degrees of
24:25freedom for the within is 18 degrees of
24:27freedom to total is 20 the sum of
24:30squares for the between 88.6 67 it's in
24:34both the within sum of squares was 281
24:3812.57 same in both sum of squares total
24:432912 38 same in both so in Excel by hand
24:49we just replicated the output SPSS gave
24:52us so now you can see how everything
24:55works together now of course I do admit
24:58the only odd part of this are these
25:01formulas down here and again you're just
25:03going to have to look at them and figure
25:05out where everything is being uh pulled
25:08from but you're very smart and I know
25:09you can do that so let's do one more
25:12thing and let actually use excels built
25:14in an NOA to see if we get the same
25:18thing so we're going to go ahead and go
25:20up to data here at the top of the ribbon
25:24go all the way over to the right and
25:25you'll see data analysis so we'll click
25:28on that that now remember we are doing
25:31the Anova single Factor so we go and
25:34click
25:35okay now this wants the input range so
25:39we'll select the little icon on the
25:40right and then we'll select all of our
25:43data actually I'm going to select the
25:45column headings to right we'll go back
25:49it's grouped by columns we have labels
25:52in the first row our Alpha is 05 we're
25:55going to stick with that and we'll leave
25:57it to new worksheet ply those will give
25:59us all of our results on a new worksheet
26:02we go a and click
26:04okay and here we go so I'm going to go
26:06ahead and spread some of these columns
26:13out okay now a few things to look
26:16at actually a lot to look at so you can
26:19see that we have a summary of each score
26:22group so year one students year two
26:24students and year three students so it
26:25gives us our count the sum of all those
26:28the average and the variance in each
26:31column so we go down to the bottom
26:34that's our actual Anova table so you can
26:36see our between group sum of squares
26:3888.6 667 same thing within groups sum of
26:43squares 28 12.57 same thing total sum of
26:47squares 29.2 4 same thing degrees of
26:51freedom 2 18 and 20 good our mean
26:54squares for the with between or the
26:57columns for 4 4.33 good are within mean
27:01Square
27:02156.25 very good divide those we have an
27:07F of 2837 Etc same thing we had before
27:11now this gives us a few more bits of
27:13information which are helpful now
27:15remember that when we're doing this sort
27:17of problem we're going to test our F
27:19value of
27:212837 against an F critical value in the
27:24F distribution based on our degrees of
27:26freedom in the numerator of two
27:28and a degrees of freedom of 18 in the
27:31denominator with an alpha of 05 we
27:34learned how to do that a long time ago
27:37so our F critical is
27:4135545 so is our F statistic of
27:452837 larger or Beyond
27:493554 well no so we would fail to reject
27:53or null hypothesis that these three
27:55means are different so let's go back to
27:58our original and you can see that all
28:01this is the same now so our SPSS output
28:05we set out to replicate we did by hand
28:08over here on the left and we did it in
28:11Excel using its built-in formula now of
28:14course that's the whole point we will
28:16not do this by hand we will either use
28:17Excel or we'll use some other
28:19statistical package but I wanted to show
28:21you where all this information comes
28:23from so you can understand the
28:25foundation sort of the guts the working
28:28the gears of the Innova process so let's
28:32go ahead and go back into PowerPoint and
28:35finish everything
28:37up let's go ahead and put in our numbers
28:40from Excel so remember in Excel we found
28:43that the SSC or the sum of squares and
28:46the columns was 88.6 7 then we divide
28:51that by our degrees of freedom which is
28:53two and we end up with an MSC of 44
28:5933 now the MSE e is the
29:03SS ided 18 so that was
29:0828125 7 ided 18 and that comes out to an
29:13MSE of
29:16156.25
29:18so remember our F ratio here is the msse
29:22divided by the
29:23MSE so the mean square of the columns
29:27divided by thean mean square of the
29:29error or you can think of it as the mean
29:31Square between divided by the mean
29:34Square within so that is 44.3 3 divid
29:39156.25 and we end up with an F statistic
29:43of
29:450.28 and that is exactly what SPSS gave
29:48us and what excel's own builtin and Nova
29:52calculator gave us as well so we know we
29:54did it
29:56correctly now how do we we ultimately
29:58interpret this so our F ratio is the MSC
30:02the MSC that's what we just did now in
30:06the numerator we have a degrees of
30:07freedom of Two And in the denominator we
30:10have a degrees of freedom of 18 so
30:13remember when we look up a critical
30:15value in the F distribution we have a
30:18numerator degrees of freedom and a
30:20denominator degrees of freedom and in
30:22this case those two degrees of freedoms
30:25come from our formulas for the MSC
30:28and the m
30:30e so we can write this F statistic we
30:33got to find like this so we have an
30:36alpha level say
30:3805 then we have degrees of freedom of C
30:42of the columns and a degrees of freedom
30:44for the error E so that is the degrees
30:47of freedom in the numerator and the
30:49degrees of freedom in the denominator so
30:51we could write it like this so we need
30:53to find the critical value of f with an
30:55alpha of
30:5605 a numor gra of freedom of Two and a
31:00denominator gra of freedom of 18 and we
31:02already learned how to do that in a
31:04previous video now the easiest way is to
31:06go into Excel and use the
31:10f.v. RT function that's the F
31:13distribution the inverse right tailed
31:15that's what all that stands for and we
31:17put in those three parameters so an
31:20alpha of 05 a numerator degrees of
31:23freedom of Two and a denominator degrees
31:25of freedom of 18 so when we put that
31:28into an Excel cell we will get an F
31:31critical value of
31:363.55 so we have to ask oursel is the F
31:39statistic in our Anova table larger than
31:42our F critical value well no so remember
31:47what our no hypothesis said we talked
31:48about this in the first Anova video and
31:51these type of problems our no hypothesis
31:53is that the means are equal to each
31:56other or that's another way of saying
31:58that the means the three means come from
32:00a common
32:01population so since our F statistic is
32:04so low and does not exceed the
32:06f-critical value we fail to reject our
32:10null
32:11hypothesis so we found no significant
32:14difference in mean test score by year of
32:17student so the means of the firste
32:20students the seconde students and the
32:22third year students on their study
32:24skills exam did not differ significantly
32:27and that's
32:29it so remember up to this point we could
32:33only do comparisons involving two
32:35populations independent samples T Test
32:37and match sample T Test limiting
32:40ourselves to those two comparisons is of
32:42course limiting what if we wanted to
32:45compare the means of more than two
32:46populations like we did in this problem
32:49what if we wanted to compare the
32:50populations each containing several
32:52levels or subgroups so this get hints at
32:55the two-way Inova so imagine this
32:57scenario where we have year one students
33:01year two students and year three
33:04students but on the other axis we divide
33:07them into male and
33:09female now we have two factors so our
33:13first factor is the year of the student
33:15and our second factor is their
33:17biological sex that would be a two-way
33:20Anova and we can do that of course using
33:22this technique so the analysis of
33:25variance is the tool we use to do those
33:28more complex
33:31analyses okay so that wraps up part two
33:34of our video on the oneway Anova or the
33:36one-way analysis of variance now I know
33:39it was a lot to digest but I really
33:42wanted to take you from the very basic
33:43conceptual foundations up through an
33:46example problem so you can see how all
33:47the data is related to each other learn
33:49how to do the sum of squares and then
33:51eventually find a relationship between
33:54those sum of squares because that is the
33:55foundation of how we conduct
33:58the Inova so I have no doubt that you
34:00may need to go back and watch parts of
34:01the video to really grasp it but
34:03hopefully after watching it you have a
34:05really good solid understanding of what
34:08an NOA is so a few reminders and then
34:11we're done if you're watching the video
34:12CU you're struggling in a class stay
34:15positive and keep your head up you're an
34:17amazing smart talented person never let
34:20anyone tell you any differently
34:22including yourself if you like the video
34:25please give it a thumbs up share it with
34:27class mates or colleagues or put it on
34:29the playlist feel free to follow me here
34:31on YouTube on Twitter on Google+ or on
34:35LinkedIn it's always nice hearing from
34:38you and finally just keep in mind that
34:40the fact that you're on here trying to
34:41learn committing yourself to improving
34:44as a student or as a business person
34:47that is what really matters I firmly
34:50believe if you have the right learning
34:52process in place the results will take
34:55care of themselves so thank you very
34:57much for watching
34:58I wish you the best of luck in your
34:59studies and in your work and I look
35:01forward to seeing you again next time
35:05[Music]

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