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0:00

Intro

8:22

Example

9:00

Results

10:03

ANOVA Calculation

13:02

Treatment Calculation

13:36

Rule of ANOVA

15:01

Sum of Squares

18:07

Sum of Squares Experimental Error

19:13

Degree of Freedom

20:50

Calculate MS

22:49

Calculate F

24:52

ANOVA Table

28:25

ANOVA Results

Le Grand Schtroumpf perd sa patience ! • Épisodes complets • Les Schtroumpfs

Le Grand Schtroumpf perd sa patience ! • Épisodes complets • Les Schtroumpfs

Channel: Les Schtroumpfs • Français

КИНО ОГОНЬ 7 ЛЕТ [ПРАЗДНИЧНЫЙ СТРИМ]

КИНО ОГОНЬ 7 ЛЕТ [ПРАЗДНИЧНЫЙ СТРИМ]

Channel: Кино Огонь

90 е Весело и громко | Серия 1

90 е Весело и громко | Серия 1

Channel: СТС

lecture

20

experimental

designs;

latin

square

design;

anova;

multi-factor

biostatistics

00:00:02

Latin squared design which is one of the

00:00:05

experimental designs and in the previous

00:00:08

lecture we had studied the basic

00:00:09

concepts of experimental designs that

00:00:11

what is meant by an experimental design

00:00:13

and what are the different components of

00:00:15

experimental design and what are the

00:00:18

principles of experimentation and we

00:00:20

also discussed that there are three

00:00:22

basic types of the experimental designs

00:00:24

that are used in field research the

00:00:26

first one is CRT which is the simplest

00:00:28

type of the experimental design in which

00:00:31

the only significant source of variation

00:00:34

is the treatment which is source of

00:00:36

variation of our interest and that one

00:00:38

is used under lab conditions mostly and

00:00:41

then we have discussed our CBD which is

00:00:44

randomized complete block design and our

00:00:47

CBD is that in which the significant

00:00:49

sources of variation are too and if we

00:00:53

have more than two significant sources

00:00:54

of variation then we are going to use

00:00:56

the Latin square design

00:01:07

so our CBD minimizes the contribution of

00:01:10

one source of variation other than

00:01:12

treatment as we discussed in the

00:01:14

previous lecture that if we have a

00:01:17

source of variation which is unavoidable

00:01:19

and that could have a significant effect

00:01:23

or that could have noticeable effect on

00:01:26

our response variable so we need to take

00:01:29

measures to control the effect of that

00:01:31

variable and we saw that how we can do

00:01:34

the blocking and how we can make blocks

00:01:36

to reduce the effect or to calculate the

00:01:39

effect of that source of variation and

00:01:43

these blocks are made in the direction

00:01:45

of the gradient of that source of

00:01:48

variation so our CBD is good in the

00:01:51

field research where mostly we have one

00:01:53

significant source of variation other

00:01:55

than the treatments so they let him

00:01:58

square design can handle two sources of

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variation that occur in a gradient so

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our CBD can handle only one source of

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variation other than treatment while the

00:02:08

letting square design can handle two

00:02:10

sources of variation that occur in a

00:02:12

gradient in the field and every

00:02:16

treatment occurs only once in each row

00:02:18

and column of the field which is

00:02:21

designed under a legend square design

00:02:23

for example we have a field in which

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there is a river on one side and there

00:02:29

is a road on another side so we are

00:02:32

going to see that if we have two

00:02:34

significant sources of variation then

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how we are going to handle those sources

00:02:40

of variation through the Latin square

00:02:41

design so here we are taking the example

00:02:44

of a field which has two sources of

00:02:47

variation other than treatment one is

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the river which is on one side and the

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other source of variation other than

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treatment is the road

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so both River and Road they may have

00:02:58

effect on the growth of the plants so

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therefore in order to control these

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sources of variation we need to design

00:03:06

our experiment in such a way that their

00:03:08

effect can be calculated in blocks so

00:03:11

that we can have a separate calculation

00:03:12

for their effect and their effect can be

00:03:15

controlled right

00:03:24

so let's see here we have our field so

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in the field you can see that there are

00:03:30

different squares and let's see how

00:03:32

these squares are made so we have River

00:03:34

on one side and there is a river

00:03:37

gradient so the effect of River is

00:03:40

maximum in the in that side of the field

00:03:43

which is near the river and it decreases

00:03:45

away from the river so the effect of

00:03:48

River the effect of this source of

00:03:49

variation is present in the form of a

00:03:51

gradient so what we can do is as we

00:03:54

learned in RVs our CBD that we can make

00:03:57

the blocks so we can make the blocks

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according to this River gradient and

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here we can make these columns and you

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can see that the effect of the river is

00:04:07

maximum at column number one or the

00:04:09

block number one and then the effect of

00:04:11

the river is less and column number two

00:04:14

or block number two according to River

00:04:15

then one and then we can see that there

00:04:18

is a decrease in the effect of River as

00:04:21

we move to block number four according

00:04:25

to the River gradient so we have these

00:04:27

four columns or these four blocks and we

00:04:30

have divided the effect of River

00:04:32

gradient and these blocks so this is one

00:04:36

source of variation now let's see we

00:04:38

have another source of variation which

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is Road on one side and we can see that

00:04:43

the effect of this throat is also

00:04:45

present in the form of a gradient

00:04:46

because the effects of the road on the

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growth of the plants is going to be

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maximum in the plants growing near the

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road and as well decrease as we move

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away from the road so this road effect

00:04:58

this Road source of variation it is also

00:05:00

present in the form of a gradient so

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what we are going to do with that is we

00:05:04

are going to make blocks according to

00:05:06

the road gradient as well so we have

00:05:09

these four blocks the block number one

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has got the maximum effect of the road

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gradient and this is presented in row

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number one and then we have row number

00:05:18

two which is the block number two for

00:05:20

the road gradient then we have row

00:05:23

number three which is the block number

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three for for road gradient and then we

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have the block number four which is the

00:05:30

column number four for the road gradient

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and we can see that the effect of the

00:05:34

road gradient is minimum in this block

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so here we are going to make four blocks

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for the river gradient and four blocks

00:05:41

for the road gradient so this is how we

00:05:43

are going to have a square design and

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hence the name of this design is the

00:05:48

square design this is a Latin square

00:05:49

design because in this case the equal

00:05:52

number of blocks are made for both of

00:05:54

the gradients

00:06:05

so in the letting scare design we can

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have a maximum of only 16 plots right so

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it can have less than 16 but any number

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of squares like if we have if we make

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three blocks then this is going to be 3

00:06:19

into 3 9 so at maximum we can have only

00:06:23

16 plots so this is the limitation of

00:06:25

letting square design that you can have

00:06:27

only 16 plots in that so at maximum you

00:06:30

can have 4 types of the treatments

00:06:32

because each treatment appears only once

00:06:35

in row and once in column so each column

00:06:38

is going to have only one one copy of

00:06:43

each treatment so if you have four

00:06:45

treatments then each of the treatments

00:06:46

is present in a single copy in each of

00:06:48

the columns and if we have four

00:06:52

treatments then each of the treatments

00:06:53

is going to be repeated only once in

00:06:55

each row so here you can see that we

00:06:58

have a perfect square design with four

00:07:02

blocks for the River gradient and four

00:07:05

blocks for the road gradient and the

00:07:08

number of treatments are also four so in

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the first column as you can see that the

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first cell is D so the application of

00:07:17

the treatment is D so the treatment

00:07:20

applied in this cell is D and this lies

00:07:24

into the column number one and row

00:07:26

number one and then we have the other

00:07:30

one which is a so a is present in column

00:07:33

number one and sorry column number two

00:07:36

and row number one and this one has got

00:07:39

the treatment a and so on so in this you

00:07:43

can see that the treatments are repeated

00:07:46

only once in each row and only once in

00:07:49

each column so we have four blocks for

00:07:53

River gradient and for blocks for the

00:07:55

road gradient so we have the square

00:07:57

design of 16 plots and we have four

00:07:59

treatments so each treatment is repeated

00:08:02

four times but this is repeated only

00:08:04

once in each row and only once in each

00:08:06

column so this is how we are going to

00:08:09

make this design so this is the basic

00:08:11

design of the Latin square design

00:08:15

you

00:08:22

so we can take the example and the

00:08:24

example is effects of fertilizer dose on

00:08:27

the fresh rate of plants and the

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experimental design is the legend Square

00:08:32

design that we are going to use the

00:08:34

independent variable are the fertilizer

00:08:36

doses and the treatments are different

00:08:39

doses of fertilizer and in this example

00:08:41

we have four treatments a B C and D and

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the dependent variable is our response

00:08:46

variable which is the fresh rage of

00:08:48

plants so this is the experiment that

00:08:51

has been planned

00:09:00

so here we have the results of the

00:09:03

experiment and you can see that these

00:09:06

are the values of the fresh weight of

00:09:08

plants and the different doses of

00:09:11

fertilizer so here you can see that we

00:09:13

have 16 plants and we have 16

00:09:15

observations and these observations are

00:09:18

according to the plots according to the

00:09:21

blocks that are made according to the

00:09:23

river and the road gradient so these are

00:09:26

the observations we have so we are done

00:09:29

with the two phases remember what are

00:09:31

the phases or what are the components of

00:09:33

the experimental design we have to plan

00:09:36

an experiment to obtain an appropriate

00:09:37

data so we planned an experiment and the

00:09:40

experiment is executed and we have the

00:09:42

data

00:09:43

so now Tara is obtained so what is the

00:09:45

next step we have to draw inference out

00:09:47

of that data and for that purpose we

00:09:49

have to apply these statistical analysis

00:09:52

right so the next step is to do the

00:09:54

statistical analysis on this data

00:10:03

so the kind of statistical analysis we

00:10:05

are going to use for this data is ANOVA

00:10:08

and here we have the to' table for ANOVA

00:10:12

calculation and as you can see that this

00:10:15

table has got all those 16 observations

00:10:18

then we have the row totals and we have

00:10:21

the column totals so one two these row

00:10:24

totals and the column totals depict they

00:10:26

are according to the gradients so they

00:10:28

represent the gradients that row totals

00:10:31

they represent the road gradient and the

00:10:34

column totals they represent the river

00:10:36

gradient so the column number one which

00:10:39

has the sum of two eleven point four six

00:10:42

so that represents the result of column

00:10:45

number one which is the remember

00:10:47

gradient one and it has all the four

00:10:51

gradients of road and then we have the

00:10:54

column total which is chose you know

00:10:56

four point one four so this is the sum

00:10:58

of column number two which is our

00:11:00

gradient number two of the river and it

00:11:03

also has got all the four treatments and

00:11:05

all the four gradients of the road then

00:11:08

we have column number three witches our

00:11:11

gradient number three of the river this

00:11:14

value is one ninety four point seven

00:11:16

nine and it has got all the four

00:11:19

treatments and on the phone gradients of

00:11:21

the road and then we have one eighty

00:11:24

three point five nine which is the sum

00:11:26

of column number four which is the

00:11:28

fourth gradient fourth block of the

00:11:30

river gradient and it has got all the

00:11:33

four treatments and all the four

00:11:34

gradients of the road and then if we

00:11:38

move on to the roads so that total of

00:11:40

first row is two hundred point seven six

00:11:43

so this first row belongs to the first

00:11:46

gradient of the road and you can see

00:11:49

that it has got all the treatments and

00:11:51

it has got all the gradients of the

00:11:53

river then we have the next row which is

00:11:56

one ninety nine point two seven so this

00:11:59

is the total of the second row and the

00:12:01

second row is the second gradient of the

00:12:03

road and it has got all the four

00:12:05

treatments and all the four gradients of

00:12:07

river then we have one ninety six point

00:12:10

zero five so this is the total of row

00:12:12

number three and row number three is our

00:12:14

gradient number three of the

00:12:16

Road and it has got all the four

00:12:19

treatments and all the four gradients of

00:12:21

the river and then we have my 97.9 and

00:12:25

this is the total of row number four and

00:12:28

the row number four is the gradient

00:12:29

number four of the road and it also has

00:12:32

got all the four treatments and all the

00:12:34

four gradients of the river so this is

00:12:37

how we have obtained our values and then

00:12:41

we have the total value of Z summation X

00:12:44

total and the summation X square total

00:12:46

but you can see that we don't have any

00:12:49

totals for the treatments which are in

00:12:52

fact are a main source of interest right

00:13:02

so what do we do for the treatments the

00:13:05

treatment observations are listed

00:13:07

separately and here you can see we have

00:13:10

the totals for different treatments

00:13:12

treatment a the total is 250 point one

00:13:16

treatment B the total is 218 point zero

00:13:18

six the treatment C the total is two

00:13:21

zero four point eight nine and the

00:13:23

treatment D the total is 120 point nine

00:13:26

three so here we have the values for the

00:13:29

treatments

00:13:36

now remember that what is the rule of

00:13:40

ANOVA that we have to figure out that

00:13:43

what are the components that contribute

00:13:45

to total variability so in this case

00:13:47

total variability is because of the

00:13:49

variability due to treatment of course

00:13:51

and it is due to variability due to

00:13:53

gradient a which is our road gradient

00:13:56

and it is the case of the gradient V

00:13:58

which is our River gradient and it is

00:14:02

due to the experimental error so for the

00:14:04

sake of simplicity we can designate

00:14:06

total by capital t small o treatment by

00:14:10

small t gradient a by capital a gradient

00:14:13

B by capital B an experimental error by

00:14:16

small e and the gradient a is our road

00:14:18

gradient which is presented in rows and

00:14:20

gradient B is our River gradient which

00:14:22

is presented and columns now we have to

00:14:26

calculate the correction term as we move

00:14:27

on to the ANOVA so this is the formula

00:14:31

for correction term summation XTO whole

00:14:34

square divided by the total number of

00:14:36

observations so what is the total sum of

00:14:39

observations this is 793 0.98 we take

00:14:42

the square and divided by 16 so we get

00:14:45

the correction term as very 9400 point 2

00:14:49

6 5 so this is the value of our

00:14:52

correction term

00:15:01

now we have to calculate the total sum

00:15:05

of squares so the total sum of squares

00:15:07

is equal to the summation XT total

00:15:10

square minus CT so remember what is this

00:15:14

term the summation x squared for total

00:15:16

so this is the square of all the

00:15:19

individual 16 observations and then we

00:15:21

take their sum so this is equal to 40

00:15:25

1800 2.6 1 so we subtracted from the

00:15:29

correction term which is 39 thousand

00:15:31

four hundred point two six five and we

00:15:33

get the value of our total sum of

00:15:36

squares which is two thousand four

00:15:37

hundred two point three four five so

00:15:41

this is the value for our total sum of

00:15:43

squares now we have to calculate the sum

00:15:48

of squares for treatment and this is the

00:15:51

formula for the calculation of sum of

00:15:54

squares of treatment so we have four

00:15:56

treatments so we calculate the summation

00:15:58

X whole square divided by the number of

00:16:00

observations for each of the four

00:16:02

treatments and then we take their sum

00:16:05

and subtract it from correction term so

00:16:09

here we have put all those four values

00:16:11

and we subtracted from correction term

00:16:15

and we get the treatment sum of squares

00:16:18

as two thousand two hundred seventy five

00:16:20

point seven seven so this is the value

00:16:23

for our treatment sum of squares

00:16:33

ABCD efg now we calculate the sum of

00:16:38

squares for the road gradient which is

00:16:41

presented in rows so this is gradient a

00:16:43

and this is the formula so we had four

00:16:46

blocks according to this gradient of

00:16:49

rows which were four rows so we put in

00:16:52

the values for each of these rows take

00:16:53

their sum and subtracted from correction

00:16:56

term so here we input the values for

00:17:00

these four blocks for these four

00:17:03

gradients of the road and we subtracted

00:17:06

from the correction term and we get the

00:17:08

value for the sum of squares a which is

00:17:10

the sum of squares due to the road

00:17:13

gradient and this is three point zero

00:17:15

two now we have to do that for the River

00:17:20

gradient and this River gradient was

00:17:23

presented in columns so we take the

00:17:25

totals of these columns take their

00:17:27

square divided by a number of

00:17:28

observations in each of the column they

00:17:30

take their sum and then we subtracted

00:17:32

from the correction term so we input

00:17:35

these values and we get the value of one

00:17:38

zero eight point nine six so this is the

00:17:41

sum of squares of the River gradient

00:17:43

which was present in columns and this is

00:17:46

I think designated here as B so now we

00:17:50

have calculated the sum of squares total

00:17:54

the sum of squares treatment these sum

00:17:57

of squares for road and sum of squares

00:17:59

for river and now we have to calculate

00:18:02

the sum of squares for error for the

00:18:05

experimental error so here is the

00:18:10

calculation for sum of squares

00:18:12

experimental error and for that purpose

00:18:14

we are going to make use of this basic

00:18:17

principle of the ANOVA in this case

00:18:19

which means that the sum of squares

00:18:22

total is equal to the sum of squares

00:18:24

treatment plus sum of squares due to

00:18:25

gradient is a most curious to the

00:18:27

gradient B and sum squares experimental

00:18:31

error so because we have calculated the

00:18:34

sum of squares for total sum of squares

00:18:37

for treatment sum of squares for a sum

00:18:39

of squares for B so we can work out the

00:18:41

value of sum of squares

00:18:42

E

00:18:44

so some skewers here or the sound scares

00:18:46

experimental error is equal to the sum

00:18:49

of squares total minus the sum of sum of

00:18:52

squares treatment sum of squares a and

00:18:54

sum of squares B so here we have these

00:18:59

values and we get the value for our sum

00:19:02

of squares experimental error and this

00:19:04

value is fourteen point five nine five

00:19:13

and now we calculate the degree of

00:19:16

freedom and we are done with the

00:19:19

calculation of the sum of squares for

00:19:20

total sum of squares for treatment sum

00:19:22

of squares for River gradient sum of

00:19:25

squares for road gradient and the

00:19:26

experimental error sum of squares so now

00:19:29

we have to calculate their degrees of

00:19:31

freedom and first of all the total

00:19:34

degree of freedom which is and total

00:19:36

which is the total number of

00:19:37

observations which is 16 in this case of

00:19:40

16 minus 1 we have 15 degree of freedom

00:19:42

for total then we have to calculate the

00:19:45

treatment degree of freedom so the

00:19:46

number of treatments were 4 so 4 minus 1

00:19:48

is equal to 3 and then the gradient a

00:19:52

and the blocks number of blocks in the

00:19:55

gradient over 4 so 4 minus 1 is 3 and

00:19:58

then the gradient B so the number of

00:20:00

blocks and the gradient number B were

00:20:04

also 4 so the degree of freedom for this

00:20:06

one is also 3 and then we have the

00:20:10

degree of freedom and for that purpose

00:20:12

we have to multiply n minus 1 and n

00:20:16

minus 2 so what is n here and is the

00:20:19

number of columns which is equal to the

00:20:20

number of rows because this is the

00:20:22

square design that we have so in the

00:20:24

square design we have we are going to

00:20:26

have the same number of columns and the

00:20:28

same number of rows so they which is 4

00:20:31

in this case so 4 minus 1 and 4 minus 2

00:20:36

we multiply them and we get 6 so this is

00:20:39

the degree of freedom for error so now

00:20:42

we have calculated the degrees of

00:20:43

freedom

00:20:51

now we calculate the MS which is the

00:20:54

mean sum of squares or variance and this

00:20:57

is the variance or Ms for treatment and

00:21:00

this is going to be calculated by

00:21:03

dividing the sum of squares treatment by

00:21:05

a degrees of freedom treatment so we

00:21:07

have two thousand two hundred seventy

00:21:09

five point seven seven divided by three

00:21:11

and we have seven fifty eight point five

00:21:14

nine as the variance or mean sum of

00:21:16

squares for treatment then we calculate

00:21:21

the variance or the mean sum of squares

00:21:23

for our first gradient which is a

00:21:26

gradient and this is the raw wrote

00:21:29

gradient so this is the sum of squares

00:21:32

for a gradient divided by a degrees of

00:21:34

freedom of the a gradient so this is

00:21:36

three point zero two divided by three

00:21:38

and our variance is one point zero zero

00:21:42

seven in this case then we are going to

00:21:45

calculate the variance or mean sum of

00:21:47

squares for our gradient B and for that

00:21:50

purpose we are going to divide the sum

00:21:52

of squares for gradient P by degrees of

00:21:54

freedom for gradient B so one zero eight

00:21:57

point nine six divided by three we get

00:22:00

thirty six point three two which is the

00:22:04

variance or the mean sum of squares due

00:22:07

to gradient B and now finally we are

00:22:11

going to calculate the variance due to

00:22:14

experimental error so this is our error

00:22:16

or within variance and this is equal to

00:22:18

the sum of squares for error divided by

00:22:21

the degree of freedom for error so we

00:22:23

have fourteen point five nine five

00:22:25

divided by 6 and we get the value to

00:22:28

point 4 three 3 which is the MS value or

00:22:32

the variance for experimental error so

00:22:35

now we have calculated the MS values so

00:22:38

what is going to be our next step we are

00:22:41

going to compare these MS values

00:22:49

and how do we compare these variance

00:22:54

values may calculate the F values so

00:22:57

here we are going to calculate the F

00:22:59

value for the treatment which is our

00:23:01

source of radiation of interest so for

00:23:03

that purpose the variance of treatment

00:23:06

is going to be divided by variance of

00:23:08

experimental error so 758 point five

00:23:11

nine divided by two point four three

00:23:13

three and we have three eleven point

00:23:16

seven nine so this is our F value for

00:23:20

the treatments and we can see that this

00:23:23

value is quite high it is actually quite

00:23:25

quite higher than one so we will see

00:23:29

that how much significant this value is

00:23:33

now we calculate the effect of the

00:23:36

gradient a witches are Road gradient so

00:23:39

for that purpose the MS a the variance a

00:23:42

is going to be divided it by variance

00:23:44

error so we have one point zero zero

00:23:47

three divided by two point four three

00:23:48

three and we have the F value which is

00:23:52

less than one so this is probably going

00:23:54

to be non significant right because this

00:23:57

is less than one then we are going to

00:24:01

calculate the effect of second gradient

00:24:05

which is our River gradient and in this

00:24:08

case we are going to divide the variance

00:24:10

of gradient B by the variance of

00:24:12

experimental error so this is 36.3 two

00:24:15

divided by two point four three three

00:24:17

and we get fourteen point nine two eight

00:24:20

so we can see that this F value is also

00:24:23

greater than one and now we have to see

00:24:26

that whether it is a significantly

00:24:27

greater than one or no so now we are

00:24:30

done with the calculations of ANOVA and

00:24:32

the next step is to make the ANOVA table

00:24:35

and compare these calculated F values

00:24:38

with the tables or the critical values

00:24:40

to find out that which one of these are

00:24:43

significant and which one are non

00:24:45

significant

00:24:52

and here is our ANOVA table and you can

00:24:56

see that we have the source of variation

00:24:58

in the first column and the sources of

00:25:00

variation were treatment and gradient a

00:25:04

gradient be error and total so the

00:25:08

degrees of freedom for the treatment and

00:25:10

for gradient a and for gradient we are

00:25:12

three each and for error it is six and

00:25:15

the sum of squares for treatment is two

00:25:18

thousand two hundred seventy five point

00:25:20

seven seven then the sum of squares for

00:25:22

gradient a is quite low this is three

00:25:24

point zero two and he Samos cares for

00:25:27

gradient ps10 eight point nine six and

00:25:30

sum of squares for error is fourteen

00:25:33

point five nine five and the sum of

00:25:35

squares total of all these four sum of

00:25:38

squares is 2400 two point three five

00:25:42

then in the next column we have the

00:25:44

variances or the mean sum of squares so

00:25:46

for the treatment we have seven fifty

00:25:48

eight point five nine for the gradient a

00:25:51

we have one point zero zero three for

00:25:53

the gradient B we have thirty six point

00:25:55

three two and for the gradient F for the

00:25:58

error we have two point four three three

00:26:01

now we have to compare their F values

00:26:04

sorry if there are these mean sum of

00:26:07

squares and variances and we get the F

00:26:08

values and the F values are documented

00:26:10

in next column so we have three eleven

00:26:13

point seven nine for the treatments and

00:26:16

point four one two for the gradient a

00:26:18

fourteen point nine two eight for the

00:26:20

gradient B and as expected we can see

00:26:23

that this three eleven point seven nine

00:26:25

is much much greater than event one

00:26:30

because the table value is four point

00:26:34

seven six at probability of 0.05 and the

00:26:38

degree of freedom of three and six so we

00:26:42

can see that our calculated F value of

00:26:45

three eleven point seven nine at is

00:26:47

greater then the critical value of four

00:26:49

point seven six as well as the critical

00:26:51

value of nine point seven and eight and

00:26:53

the critical value of twenty three point

00:26:55

seven at probability point zero zero one

00:26:57

so our probability is less than point

00:27:00

zero zero one and this means very highly

00:27:04

significant

00:27:06

it's a very highly significant effect of

00:27:08

treatments on the response variable then

00:27:11

we see the gradient a and the gradient a

00:27:14

is less than 1 and we can see that this

00:27:18

is non significant against the critical

00:27:20

value for the degree of freedom three

00:27:22

and six is four point seven six that

00:27:24

probability of point zero five so

00:27:26

therefore this is going to be non

00:27:28

significant and then we have the

00:27:31

gradient B and let's see the effect of

00:27:32

gradient P fourteen point nine to eight

00:27:35

is also higher than the critical value

00:27:37

at point zero five which is four point

00:27:40

seven six so this is also significant

00:27:42

and at C at point zero one the critical

00:27:45

value at point zero one is nine point

00:27:47

seven eight and our calculated F value

00:27:51

for gradient P is fourteen point nine

00:27:53

two eight which is higher than this one

00:27:55

so this is highly significant let's see

00:27:58

for the next level so at probability of

00:28:00

point zero zero one the critical value

00:28:02

is twenty three point seven and we can

00:28:04

see that the value of our gradient P is

00:28:07

not higher than this one so our gradient

00:28:09

B is also exerting a significant effect

00:28:12

but this effect is highly significant it

00:28:14

is not very highly significant so here

00:28:18

we have the ANOVA table

00:28:25

now it is time to report the result and

00:28:29

a result for our the source of variation

00:28:32

of interest which is our independent

00:28:33

variable so there is very highly

00:28:35

significant effect of fertilizer on the

00:28:38

fresh weight of plants so the F value at

00:28:41

degrees of freedom three and six is

00:28:43

three eleven point seven nine and the

00:28:45

probability is less than point zero zero

00:28:47

one then we have the result for our

00:28:52

gradient a which is the road gradient

00:28:55

and the effect of Road on the fresh

00:28:57

weight of plants is non significant so

00:29:00

the F degrees of freedom three and six

00:29:02

is point four one two and the

00:29:04

probability is greater than point zero

00:29:06

five then we have the result for our

00:29:10

gradient B which is our River gradient

00:29:13

and we can see that there is highly

00:29:16

significant effect of River on the fresh

00:29:18

wage of plants so F value at degrees of

00:29:21

freedom three and six is fourteen point

00:29:23

nine two eight and probability is less

00:29:26

than point zero one so this is how we do

00:29:31

the calculations for letting square

00:29:33

design so this is our letting square design and

00:29:36

the letting square design handles with

00:29:38

two additional sources of variation then

00:29:41

treatment so treatment is our obviously

00:29:43

our main source of variation our source

00:29:46

of variation of interest but if we are

00:29:48

doing experiment in the field and we

00:29:50

encounter two other sources of variation

00:29:53

that cannot be controlled so by the by

00:29:57

changing the experimental conditions so

00:30:00

what we have to do for that is we have

00:30:02

to calculate their individual effects

00:30:06

and we can do that through making the

00:30:08

blocks according to the gradients of

00:30:10

those two sources of variation so we are

00:30:13

going to have a scared design and this

00:30:16

square design can have a maximum of four

00:30:18

treatments four blocks of gradient a and

00:30:21

four blocks of the gradient B so it can

00:30:24

have a maximum of 16 plots or 16

00:30:27

experimental units and we saw the

00:30:31

results of that of a hypothetical

00:30:34

experiment and then we can

00:30:36

related the effects of these sources of

00:30:39

radiation through ANOVA and we found out

00:30:43

that the effect of our independent

00:30:44

variable which is the fertilizer dose on

00:30:46

our response variable which is the fresh

00:30:49

weight of plants is very highly

00:30:51

significant and the effect of the road

00:30:53

weather which was the other source of

00:30:55

variation and is non significant and the

00:30:58

effect of the river which once the other

00:30:59

source of variation is highly

00:31:01

significant so this is how we will be

00:31:04

able to differentiate between the

00:31:06

effects of these sources of variation on

00:31:08

the growth of plants and letting Square

00:31:12

design is our third type of the

00:31:14

experimental design so we have three

00:31:16

basic types of the experimental designs

00:31:17

are CBD and RC in are CBD there is only

00:31:22

one major source of variation which is

00:31:24

treatment so in total we have two

00:31:26

sources variation treatment and the

00:31:28

experimental error then in our CBD which

00:31:31

is the most widely used design in the

00:31:32

field research we have three sources of

00:31:35

variation the treatment which is the

00:31:37

source of variation of our interest

00:31:38

experimental error which is due to the

00:31:40

extraneous factors which are unavoidable

00:31:42

and we have an additional source of

00:31:44

variation which is known as the source

00:31:47

of variation due to the environmental

00:31:51

conditions that we have over there which

00:31:53

cannot be avoided and we calculate the

00:31:57

effect of those that source of variation

00:31:59

from making blocks so we have three

00:32:02

sources of variation in our CBD

00:32:03

variation due to treatment variation due

00:32:05

to blocks and variation due to

00:32:06

experimental error then we have the

00:32:09

letting square design and letting square

00:32:11

design can handle two sources of

00:32:13

variation other than treatment so in

00:32:15

this design we are going to have four

00:32:17

sources of variation treatment which is

00:32:20

the source of variation of our interest

00:32:21

and then we are going to have the source

00:32:24

of variation due to some other factor

00:32:27

which is present in the field which is

00:32:28

not of our interest but it is present in

00:32:31

the field so we make the blocks for

00:32:33

calculating the effect of that gradient

00:32:35

and then that source of variation

00:32:38

according to its gradients and then we

00:32:41

have another source of variation and we

00:32:44

are going to have this calculated

00:32:47

through making the gradients or blocks

00:32:48

for that source of

00:32:50

and then we have the fourth source of

00:32:52

variation which is the experimental

00:32:53

error so in Latin secure design we have

00:32:56

four sources of variation and we are

00:32:58

able to calculate their effect through

00:33:00

ANOVA so this is all about the

00:33:04

experimental designs introduction to

00:33:06

experimental designs

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