in this tutorial I'm going to introduce

the idea of a two-way ANOVA or factorial

analysis this video is part of a

playlist and in the playlist I describe

all the different aspects of a two-way

ANOVA from calculated by hand to

interpreting results SPSS and also

Microsoft Excel and you can find a link

to the playlist below right there

let's imagine I give an arithmetic test

to boys and girls of different age

groups 10 year olds 11 year olds and 12

year olds and now I have a list of test

scores and I want to determine what

impacts the variation is a gender is it

age group or is it both gender and age

group so I have two factors I have

gender and age and that's why it's

called a two-way ANOVA or factorial

analysis have two factors if I was going

to analyze the same data with a one-way

ANOVA and let's say I just looked at

test scores variation by age so I have

ten-year-old group I have my 11 year old

group and also I have my 12 year old

group

I would take the average of the

ten-year-old group their average test

scores and the average of the

eleven-year-old group and also the

average of the 12 drill group that

compare these back and forth of course

I'd also look at the group as one big

large group and I would take the sum

average of the total average of the

entire group which is equal to nine by

the way

and in the end I would take all these

averages and then build a little table

of just averages let me organize this

let me move this around a little bit so

I end up with one row and it's all

averages in the end I just have a row of

data all averages by H now in a two-way

anova it's different it's more

complicated so let's imagine I want to

analyze my data by age and gender so

I'll put everything back let me put my

test scores back in for the 10 year olds

11 year olds and 12 year olds now I have

everything the way I like it so I have

above the first group of data I'm going

to label is boys and the bottom group is

girls I take the average data or average

scores for each age group for the boys

then I take the total average for all

boys which is 7.7 now I do the same

exact thing for the girls I take the

average for each age group and then the

total average for all the girls and

their average score is ten point three

now let me put this all back into a

single table I'm going to call that the

mean table and I'm going to end up with

two I'm sorry with three rows of data

boys girls and the average row and also

have four columns of data the

ten-year-old data the 11 year old data

12 year old data and also the average

there in this table I end up with

averages for all the boys by age group

in total also averages for all the girls

by age group in total

I have ten year old data broken down by

gender and total average eleven year old

data broken down and twelve year old

data broken down having data organized

in a table like this makes it easier to

calculate degrees of freedom to

understand the factors and also to make

any of the other calculations I have to

make my first factor is I'm going to

call that gender first factors my gender

my second factor is age and it doesn't

make a difference what I call my first

factor or my second factor I could swap

those if I wanted to a two way ANOVA is

a lot more complicated than a one way

ANOVA in fact if I put that one-way

ANOVA table back in you'll see that the

average for the two way is the entire

table for the one-way ANOVA and a

one-way ANOVA I'm going to work with

four different averages and in a two way

ANOVA I'm going to have twelve averages

having data organized into this nice

table makes a lot easier to work with

and a lot easier to understand in

essence what we're doing is a two-way

anova is we're taking our data and i'm

going to reorganize it in a variety of

different ways and analyze it i'm going

to organize it based upon age group and

it would calculate summer squares of my

first factor which is age then I'll

reorganize the data and this time I'll

organize it by gender and this time I

have a thing called summer squares

factor again but of gender this is my

second factor so I'm going to analyze it

based upon gender and finally I'm going

to take all the data and treat it as one

big chunk and this is called my total

summer squares your summer squares of

the total and I'll take the mean and

I'll analyze it this way as well

and then I have summer squares of the

first factor which is gender summer

squares of the second factor which is

age sum of squares of both factors age

and gender interaction summer scores

within the error and if I add all these

up hi good summer squares of the total

or total sum of squares both the same

thing

in the next video I'm going to show you

how to make all these calculations by

hand

and subsequent videos I'm going to show

you how to calculate the F ratio and

also how to calculate degrees of freedom

I'm also going to show you how to

interpret the results how to come up

with a rejection region the F ratio is

in the red area we reject the null

hypothesis if it's in the green area we

fail to reject the null hypothesis the

first hypothesis we're going to test is

gender we'll have no significant effect

on student score

the second hypothesis is age will have

no significant effect on student score

the final hypothesis is gender and age

and our action will have no significant

effect on students 4 so up next I'm

going to show you how to make a lot of

calculations by hand if you must

and again the playlist is right below

and recommend you go through the videos

using the playlist as always share the

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