Analysis Of Variances - ANOVA

  

Categories: Tech, Metrics

While ANOVA seems like it should be the name of some Star Trek supercomputer, it's actually used to determine if there are statistically significant (i.e. actually legitimate) differences between three or more independent groups.

In plain(er) English, you've just implemented new workplace perks (liked mandatory mini-golf at lunch) for your employees at all levels. You want to see if there's a difference in employee satisfaction among entry-level, middle management, and/or upper level management due to the perks. Running an ANOVA will let you know if there are differences in productivity among those three groups.

ANOVA comes in two flavors. There's the one-way ANOVA which limits you to measure the effect of only one independent variable on one dependent variable across the three or more individual groups. The two-way ANOVA is much more powerful and allows for two independent variables to be measured against a dependent variable across three or more individual groups.

Related or Semi-related Video

Finance: What is co-variance?8 Views

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Finance allah shmoop what is co variance while co variance

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is a way to tell if two investments will both

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head to millionaire acres together or to the poor house

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together or if one is headed to millionaire acres while

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the other is headed Teo you know the poor house

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three choices there that's where co variance comes in and

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it basically comes in these three flavors Positive co variance

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which means the investments both either grow in value or

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both lose value typically in a linear fashion that's positive

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co variance They're like tied together Negative cove arians means

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that as one investment grows well the other loses like

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loses value also typically in a linear fashion you know

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kind of graphically linear and then you have zero co

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variance which means well we're just sure that whatever their

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relationship is it almost certainly isn't a linear one They're

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just not really varying together They may both grow together

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but in a non linear kind of curvy almost random

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fashion they may head opposite directions but they probably won't

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do it in a straight line of kind of way

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right Well co variances used to help investors make sure

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their portfolios are adequately diversified after all if our when

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one or more markets do crash again it'd be nice

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if our net worth wasn't also completely totally changed right

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Kind of kind of want to hedge your bets there

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a little bit So let's pretend we have a portfolio

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in which all the investments are in companies that make

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different kinds of hand held tech like smartphones and tablets

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and smart watches and you know adult aides of different

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flavors and forms So these investments in our portfolio will

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almost all certainly have a positive co variance with each

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other like they all kind of have the same buyers

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and sellers and appetites and market swings And then the

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surgeon general one day determines that the radiation from handheld

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tech causes monster ism The value of our portfolio will

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hit rock bottom fast stirred on an album of spoken

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word poetry by vladimir putin if instead we had paid

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attention to all that positive co variance data and try

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to get some investments with negative co variance is well

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we might not be looking through the want ads and

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selling plasma every day to pay for food a portfolio

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With a number of pairs of investments with negative co

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variances would mean that while some of our tech stocks

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might have plummetted our monster defense stocks might have skyrocketed

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All right So how do we calculate co variance Well

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they're two ways First we can use the co variance

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formula which has us take one investments returns subtract the

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mean return from each of those returns And repeat that

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for the other investments multiplying all the pairs together to

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sum up those values Wait can we just do this

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step by step All right let's do that that way

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Yeah There we go So let's take the returns from

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two different investments Read from the same time period We'll

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need to find the means The averages of investment one

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and investment to well to get that for investment one

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an average Well we'll add up the returns of five

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point one five point three five hundred francs having and

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if i had a total of twenty seven point two

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by five giving us an average there Five point four

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for for investment too We had three point three of

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your own and these are like percent returns on bonds

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Or something like that That's A kind of think about

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a total seventeen point nine five by five and we

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get three point five eight Right now we subtract the

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mean from each individual return So for investment one that

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means subtracting the mean of five point four four from

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each data point you get five point one five point

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three five point four five seven five seven Not to

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be mean But that means we also need to subtract

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the mean of investment to which was that three point

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five eight from each of those data points and so

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on And get what we mean here that's How it

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should look so next up multiply the matched pairs of

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points like negative zero point three four times negative zero

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point two eight and then negative point one four times

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Negative point one eight and so on All right time

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to some All those values to get point o nine

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five two plus point two five two plus uh negative

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went for a a aa plus Pulling on three One

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two and five seven two gives us point two oh

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four There we go What We finish up dividing that

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Some by one last the number of hairs of data

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points So we'll divide by point two Oh four There

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that thing will divide that by four Which gives us

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a cove Arians finally of point Oh five one What

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the hell does that mean Well that positive cove arians

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means that in general as investment one gains value in

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general so too does investment to or that in general

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as investment one loses value so too does investment to

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meaning they're pretty correlated So it's not a huge issue

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to have some investments with positive co variances but the

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entire portfolio i probably shouldn't be made up of positive

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cove Arians pairs of investments maybe kick in a few

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investments to the curb in favor of some that produced

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negative co variances Good idea no matter how attached you

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are to a particular investment or sector of the economy

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Well now that we've used the actual co variance formula

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what are other ways we can do A ploy to

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find co variance Well we can calculate the correlation coefficient

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a k a the r value r r squared value

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of the data points And then multiply that value by

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both the standard deviation of the ecs data and the

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standard deviation of the wide data Okay well the individual

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standard deviations and our values can be quickly calculated using

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technology like a graphing calculator website er's frenchie or something

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like that using a graphing calculator on those same returns

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from investments one into from before while we found our

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to be point nine o two one exit standard deviation

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to be point two six eight and wise standard deviation

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be point two one six eights is just different Pairs

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of investments Like a bond portfolio How correlated worthy Well

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when we multiply point nine o two one by point

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two six away and then by point two one six

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eight we get a co variance love wait for it

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point oh five one yeah we've seen that number before

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And we're not in the matrix Alright again a positive

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cove Arians means that the two investments will probably either

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both grow in value over same time period or probably

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lose value together over the same time period They may

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grow or lose value of different race but whatever direction

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one goes in well the other follows Think about him

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Like penguins were kind of you know sniffing each other

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well A negative co variance will mean that is one

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investment gains value than the everyone loses value and that's

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Good Sometimes people call that ej that's kind of a

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good thing to have stabilized Report Follow at least in

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the short term a well diversified portfolio should have enough

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pairs of investments or combinations of investments that have negative

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co variances so that they protect you in the really

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ugly scenarios Right now we just have to figure out

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who's going to clean up the office before the boss 00:06:41.797 --> [endTime] gets back

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