## ANOVA and Normally distributed random variables

## ANOVA and Normally distributed random variables

(OP)

Hello,

I am carrying out two-ways ANOVA analysis on different random variables and I need your comments please to make sure that I am (being not statistician or probability guy) not doing an error

1- Should these random variables be normally distributed in order for ANOVA analysis and the following regression analysis applied on these variables to be valid

2- I have a random variable (water depth below the ground) with Mean value of 1 m and Minimum value of 0 and maximum value of 2.5 m . Since I don't have sufficient data on the variability of this variable(other than the minimum and max values) I am trying to represent this variable ( with above mean and min and max values ) by a normally distributed function. Is that assumption valid,,?

If yes how can I calculate the standard deviation of this variable

Thanks

I am carrying out two-ways ANOVA analysis on different random variables and I need your comments please to make sure that I am (being not statistician or probability guy) not doing an error

1- Should these random variables be normally distributed in order for ANOVA analysis and the following regression analysis applied on these variables to be valid

2- I have a random variable (water depth below the ground) with Mean value of 1 m and Minimum value of 0 and maximum value of 2.5 m . Since I don't have sufficient data on the variability of this variable(other than the minimum and max values) I am trying to represent this variable ( with above mean and min and max values ) by a normally distributed function. Is that assumption valid,,?

If yes how can I calculate the standard deviation of this variable

Thanks

## RE: ANOVA and Normally distributed random variables

Diving into some weird statistical analysis on the basis of just 3 numbers is just bad statistics.

How could anybody establish a mean without knowing more than the two limits? Go and find the data that was used for the mean and plot it as a histogram.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: ANOVA and Normally distributed random variables

-Actually the variable is natural variable. Also the values given are the mean (the most likely value of this variable based on some annual observation) and the minimum and maximum values that are physically possible for this variable.

but my question is , theoretically can a normal distribution function of this variable be defined for given mean , min , and max value.

- Also, any comment on my first question above...

Thx

## RE: ANOVA and Normally distributed random variables

-Actually the variable is natural variable. Also the values given are the mean (the most likely value of this variable based on some annual observation) and the minimum and maximum values that are physically possible for this variable.

but my question is , theoretically can a normal distribution function of this variable be defined for given mean , min , and max value.

- Also, any comment on my first question above...

Thx

## RE: ANOVA and Normally distributed random variables

This should be chapter 1 in any stats manual, first plot the data.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: ANOVA and Normally distributed random variables

Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: ANOVA and Normally distributed random variables

Now, how are you going to fit a symmetric distribution like a normal curve to your assymetric limits? how many standard deviations is that?

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: ANOVA and Normally distributed random variables

TTFN

FAQ731-376: Eng-Tips.com Forum Policies

Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers

## RE: ANOVA and Normally distributed random variables

Well that is really the question of the day for me. I have reviewed quite a lot of materials on this. (As I said this is a hypothetical case and this statistics issue is just a small part related to a deterministic problem I am investigating, but I have to cover it unfortunately).

For the Mean, Max, Min values I can't find an answer to your question above.

But if for the Min and Max values given, the use of the normally distributed curve is not theoretically possible, I will be willing to adopt any other distribution for this variable as long as the ANOVA and Least Square Regression approach ( which was used for optimizing the dependent response function of that variable) are not violated.

Background on my problem:

I am just carrying out MCS on an optimized equation which has many variables one of which is a variable with no data (with specified mean , max , min). I came up with that optimized function after carrying out 2ways-Factorial and ANOVA analysis( I did sampling at mean, min , and max values) and Least Square regression analysis. If these ANOVA and Regression do not imply that the analyzed variables have to be normally distributed, I am open to use any suitable distribution function fitting my concerning variable for my MCS. But the point is that I don't want to have discrepancy. I continue to search and review the related statistics. Thx a lot for help

## RE: ANOVA and Normally distributed random variables

Selecting the number of standard deviations to fit this data will obviously have some effect, so try SD=range/6, and SD=range/10, and repeat the analysis. in both cases you will have some extremes where the waterline is abobve ground level but that is the sort of thing that you get with made up data.

A final check would be to run the analysis with a uniform distribution as well, and see if it makes much difference.

Greg Locock

## RE: ANOVA and Normally distributed random variables

I don't know if it is crazy to try various standard deviations and specify the given minimum and maximum by truncating the normally distributed function till fitting the mean, min, and max I have . I check if i can do that with the software I have:@Risk

By the way does using uniform distribution (or say any other function different from normally distributed one) for this variable in the MCS violates the assumptions impeded in the ANOVA and least Square optimization (the normal distribution of the residuals and their homoscedastic variance) which are used to obtain the optimized Polynomial that is function to that variable.

Maybe at the end of the day I will end up using generalized spline shape function ( which is closer representative to the random nature of the variable than the uniform function, is not it..?)

## RE: ANOVA and Normally distributed random variables

the data points must be independent from each other

the distributions must be normal (though small departures can be accommodated)

the variances of the samples are not different (though some departures are accommodated)

all individuals must be selected at random from the population

all individuals must have equal chance of being selected

sample sizes should be as equal as possible but some differences are allowed

Greg Locock

## RE: ANOVA and Normally distributed random variables

Any notes on this is welcome