# ANOVA DISTRIBUTION/S QUESTION

#### joeb33050

##### Member
Anova is about Normal distribution/s with equal variance and differing means.
I can find only one kind of distribution where variance is constant as the mean varies; a distribution of random numbers between TOP and BOTTOM. This distribution has mean vary as top-bottom varies, yet s remains constant; s 9-0 = s 109-100; the distribution looks like a rectangle on the x axis with a rippled top, amplitude varies as n.
I'm looking for an example of a Normal distribution where variance is constant as mean varies.
EX 4 year old boys weigh 32 lbs, variance = 4 pounds///8 year old boys weigh 56 pounds, variance = 4 pounds.

#### obh

##### Active Member
Hi Joe,

You compare the average mark of 3 classes teacher by 3 teachers.
You assume that the standard deviation is similar but maybe the average is not the same.

#### joeb33050

##### Member
No, the requirement is that the variances are equal, then avg summed difference ratio = f, f critical = prob means differ.
Anyone have a distribution where variance is constant as mu varies?

#### obh

##### Active Member
I don't understand the question.
if for example:
class1 distributes N(μ1, σ)
class2 distributes N(μ2, σ)
class3 distributes N(μ3, σ)

What is your question, what is the distribution of all the students?

One distribution has only one mean, but if it is a mixture of 2 distributions in may has now mean but two peaks. (bimodal distribution)
and if it is a mixture of many distributions it will distribute normally.

#### joeb33050

##### Member
My example is incorrect, top-bottom = range, and range is an estimate of sigma.
Still looking for a distribution where sigma is constant as mu varies. ???

#### obh

##### Active Member
Please read what I wrote before ...
The mean of a distribution is constant!
To use ANOVA you don't need to have a special distribution, but only a normal population

#### joeb33050

##### Member
I don't understand the question.
if for example:
class1 distributes N(μ1, σ)
class2 distributes N(μ2, σ)
class3 distributes N(μ3, σ)

What is your question, what is the distribution of all the students?

One distribution has only one mean, but if it is a mixture of 2 distributions in may has now mean but two peaks. (bimodal distribution)
and if it is a mixture of many distributions it will distribute normally.
My problem with the words.
A distribution of student scores in the USA has mu and sigma.
Classified by state, these student scores have mu and sigma by state. 50 mu/sigma pairs.
These student scores have mu vary over the 50 states.
Does sigma vary by mu, by state?
I'm looking for the distribution/s that have sigma constant as mu varies.
The anova requirement.

OR
Anova requires sigmas be equal as mus vary, distributions be Normal.
What real world data is distributed thus?

#### joeb33050

##### Member
Please read what I wrote before ...
The mean of a distribution is constant!
To use ANOVA you don't need to have a special distribution, but only a normal population
Anova, 3 distributions, sigmas equal, mus not equal, Normal.
What is the measure? EX: Weight of 12 year old boys in Kansas, Florida, Oregon. But sigma varies!?
What distribution, 12 year old boys, when divided into 3 distributions, have sigma constant as 3 mus vary?
What measure is distributed thus?

#### obh

##### Active Member
You use the ANOVA test to check if the difference in the sample averages represent a difference in the population average.
If you know the population average you don't need to run a test.

Example of use
If you have sample data from 3 groups, obviously the average will not be exactly the same.
Now you want to understand if this is just random differences because we used sample data, or are the differences represent different means.

H0: μ1=μ2=μ3
H1: not(μ1=μ2=μ3)

If you reject H0, you prove that at least two groups have different distributions.

#### obh

##### Active Member
PS, if the mean (μ) of each country in your example is different the all population includes all countries,
may also distribute normally. with one mean (μ) : N(μ,σ)) (real about CLT)

#### joeb33050

##### Member
How about the question? What distribution, when divided into sets, has varied set mus and constant set sigmas?
The/an Anova requirement.

(Anova estimates the probability that a set of mus are equal, by estimating an f critical, a ratio of variances, estimated by differences squared, based on the notion that variances are EQUAL, and that differences squared vary as mu varies. Normal distributions. Thus my question.)

You use the ANOVA test to check if the difference in the sample averages represent a difference in the population average.
If you know the population average you don't need to run a test.

Example of use
If you have sample data from 3 groups, obviously the average will not be exactly the same.
Now you want to understand if this is just random differences because we used sample data, or are the differences represent different means.

H0: μ1=μ2=μ3
H1: not(μ1=μ2=μ3)

If you reject H0, you prove that at least two groups have different distributions.

#### obh

##### Active Member
How about the question? What distribution, when divided into sets, has varied set mus and constant set sigmas?
The/an Anova requirement.
Probably normal distribution

#### obh

##### Active Member
The normal distribution may be a mixture of many normal distributions so each "segment" like the state example may have different mean but together it is one normal distribution with one mean

#### joeb33050

##### Member
I find, with limited data, the suggestion that CV is sorta constant over families of sorta Normal data.
sigma/mu of weight of 13 year old boys is sorta constant, sigma varies as mu.
A Normal Monte Carlo simulation of distances suggests CV is constant over variations in mu.
I'm looking for a data family where CV varies as mu.