# Multiple samples of different size and not normally distributed: how to compare/sort?

#### GretaGarbo

##### Human
Re: Multiple samples of different size and not normally distributed: how to compare/s

Oh, no! Take it easy now! Don’t throw out the child with the bathwater.

Thank you for you help.
I'm still trying to understand deeply the meaning of parameter estimations.
You were recently on this very elementary level. I hope you have found something on the net about fundamentals as parameters and samples and population.

If you understand how to interpret parameter estimates and the effect of factors it is time to continue.

However, can I somehow imply the "order" of factors? I.e. Can I assert what factor(s) or factor interaction(s) are most relevant?
The practical question would be: I'm using a given combination of A, B and C and I want to improve my performance. I can change only one factor level. Which one should I change to maximize the performance improvement?
This is what the estimation is about.

1) anova assumes the normality of residuals. SPSS outputs the results of the Levene's test, which was conducted on Error Variances. Its significance is 0.000, i.e. the hypothesis that variances are equal has to be rejected... does it make Anova results not useful?
Maybe you need to do a transformation, like taking the log or square root.

2) does anova really work with my boolean factors?
Yes it does.

Based on a long reflection, the entire study with ANOVA is completly wrong and inappropriate.
No, it is not. But you are at a very elementary level.

Besides, if you had spent two or three years, that could have been “long reflection”. Now you have spent an afternoon. Cool down!

I need to use Wilcoxon in place of t-test and Kruskal Wallis + Median test + Jonckheere-Terpstra Test. I need to start over, then.
This would be wrong route to go.

The only good thing of the entire study so far is that I understood ANOVA:
No, you don’t!

a cold comfort, but if you want things done correctly, you have to figure them out by yourself.
And don’t be bitter now. I have helped you much more than you could ever have hoped to.

And it is you who need to learn. You who need to figure it out. Although I have helped you very much.

Remenber, maybe you can’t put all your data in the same basket. That can make the distribution look strange.

Now, how does the histogram for the residuals look like, untransformed and after taking the square root transformation and the log transformation?

#### MManuel

##### New Member
Re: Multiple samples of different size and not normally distributed: how to compare/s

Dason, if you or anyone else try to change my posts again, I will sue you and this forum for calumny, because you are not authorized by law to pretend I said something that I didn't say.
In fact, I'm responsible for the content of any message I write; therefore if you edit them in my place, then I need to safeguard myself.

If you believe my posts are inappropriate, then remove them or put censorship on them and ban me.
In any case, you are not allowed to edit them according to your menstrual/hormonal opinion and feelings.

Last edited:

#### GretaGarbo

##### Human
Re: Multiple samples of different size and not normally distributed: how to compare/s

I would be happy if you provided me with any reliable reference showing:
Read any elementary book about analysis of variance and read the many posts on this forum on these issues. (But MManuel don’t seem very “happy” about the many suggestions I have made. Besides, who is “you”?)

1) how AnOVA works with boolean values
I take it that MManuel mean that the independent variable is Boolean. That is the case of t-test, and t-test is a special case of anova – comparing group0 with group1. Anova is all about comparing layouts with one or several factors, where each factor takes two or more levels.

If it would be the dependent variable that is dichotomous then run logit regression.

MManuel have not said much about the dependent variable.

There are many extensions to the normal distributed analysis of variance –many other distributions, but that is too difficult for MManuel right now. MManuel need to learn to walk before trying to run.

2) how robust AnOVA is with respect to unequal sample sizes
Anova will be more sensitive (i.e. increasing variance estimates) the more unbalanced the design is. But this is what MManuel have and MManuel need to do the best she/he can with it. MManuel haven’t told us about how unbalanced this layout is.

3) how I can infer level sorting from AnOVA results
I don’t know what MManuel mean by this, but if it is what I believe it will be shown by the parameter estimates.

- - -

Since MManuel only have the eight combinations MManuel can create two 2x2 cross tables, say with factor A vs. B with C at low level and an other table with A vs. B with C at high level.

Then in each of these eight cells, compute the number of observations, the mean, the median, possibly the mean of logged values and the standard deviation.

MManuel should just have one number in each cell so MManuel need many tables. Otherwise it will be to confusing reading the tables.

Then, look at the mean or median values and infer about the effect of each factor A, B and C.

If MManuel continue study the anova MManuel might realize the very clever way anova describes the effects of factors in parameters.

Still, maybe it is not appropriate to throw all the observations in one basket. Maybe this point is more sophisticated than Mmanuel realizes.

I've been asking to people who've been working in statistics for years

#### MManuel

##### New Member
Re: Multiple samples of different size and not normally distributed: how to compare/s

Staticians should first understand that the real world does not always need questions, but sometimes it needs answers. Then they should understand that the real world is different from their books, and that they should change the book accordingly, not try to change the world. Finally, they should understand that the real world professionals do not need staticians, but just Statistics. After that, they will be slightly useful to the rest of the world.

Goodbye forum.

#### Dason

Re: Multiple samples of different size and not normally distributed: how to compare/s

Staticians should first understand that the real world does not always need questions, but sometimes it needs answers. Then they should understand that the real world is different from their books, and that they should change the book accordingly, not try to change the world. Finally, they should understand that the real world professionals do not need staticians, but just Statistics. After that, they will be slightly useful to the rest of the world.

Goodbye forum.
Statisticians do understand some of that (and by some of that I mean the pieces that made sense). And if you were dealing with a paid consultant then they will just directly give you an answer. But we're here to help you learn and to understand. Removing all of the content from your posts is a very childish thing to do. You realize you're not paying anybody here to help you right? You realize that you've received quite a bit of help here don't you? I was very tempted to place a temporary ban on you but decided against it in case you want to come back and attempt to redeem yourself.

#### MManuel

##### New Member
Re: Multiple samples of different size and not normally distributed: how to compare/s

Dason, if you or anyone else try to change my posts again, I will sue you and this forum for calumny, because you are not authorized by law to pretend I said something that I didn't say.
In fact, I'm responsible for the content of any message I write; therefore if you edit them in my place, then I need to safeguard myself.

If you believe my posts are inappropriate, then remove them or put censorship on them and ban me.
In any case, you are not allowed to edit them according to your menstrual/hormonal opinion and feelings.