Need reference for a dissertation

[Marta García-Granero]

Hi everybody

I've been searching thru all my collection of statistics book, but I
haven't been able to find a good reference for these sentences (which I
know to be true, but someone at the University doesn't want to
believe, giving a bad time to a client of mine who has to present his
dissertation very soon):

"Oneway ANOVA.

Assumptions concerning the data:

1. Observations come from independent random sampling (that is, only
   one observation for each subject who have been randomly assigned to
   groups)
2. The residuals of the model are normally distributed
3. The residuals have equal variances within each group (i.e.,
   homoskedasticity, the population sigma^2 is the same "unknown" value
   in each group)

Checking these Assumptions

The first assumption is generally met from the statistical design and the
process from which data are collected, namely, by randomly assigning
subjects to the independent groups and taking one observation per subject.
The design aspect is common to many types of analyses and will not be
covered in these pages.

The second assumption focuses on normality of the residuals and not the
observations themselves.

The third assumption implies equal "spread" of the residuals across the
groups as measured by the pooled variance (assuming an equal variance
model)...."

I found this excellent description in a Web page (unfortunately
without any reference attached).

The problem is that the man who is going to present his dissertation
used 5 groups of 7 rabbits for his research. I'm trying to fight the
extended error (at least among the researchers that will judge his
work) that with sample sizes under 10, you are condemned to use non
parametrics because you can't test the condition of normality inside
each treatment group. Therefore, I need a good reference for the fact
that normality is not very important, and, besides, it has to tested
on residuals, not observations themselves. It's one of those facts I
know, I remember I read time ago, but I can't pinpoint the source of
that knowledge. The refence needn't be in Spanish, it could also be in
English, French...

Thanks a lot in advance

Marta Garcia-Granero

[bdates]

Marta,

In one of my antique texts, Hays' Statistics for the Social Sciences, 2nd
Edition (1973), on page 467, there is a list of assumptions that will
confirm those in your message.

Brian

Brian G. Dates, Director of Quality Assurance
Southwest Counseling and Development Services
1700 Waterman
Detroit, Michigan  48209
Telephone: [phone]
FAX:  [phone]
email: [hidden email]

> -----Original Message-----
> From: Marta García-Granero [SMTP:[hidden email]]
> Sent: Thursday, March 15, 2007 12:28 PM
> To:   [hidden email]
> Subject:      Need reference for a dissertation
>
> Hi everybody
>
> I've been searching thru all my collection of statistics book, but I
> haven't been able to find a good reference for these sentences (which I
> know to be true, but someone at the University doesn't want to
> believe, giving a bad time to a client of mine who has to present his
> dissertation very soon):
>
> "Oneway ANOVA.
>
> Assumptions concerning the data:
>
> 1. Observations come from independent random sampling (that is, only
>    one observation for each subject who have been randomly assigned to
>    groups)
> 2. The residuals of the model are normally distributed
> 3. The residuals have equal variances within each group (i.e.,
>    homoskedasticity, the population sigma^2 is the same "unknown" value
>    in each group)
>
> Checking these Assumptions
>
> The first assumption is generally met from the statistical design and the
> process from which data are collected, namely, by randomly assigning
> subjects to the independent groups and taking one observation per subject.
> The design aspect is common to many types of analyses and will not be
> covered in these pages.
>
> The second assumption focuses on normality of the residuals and not the
> observations themselves.
>
> The third assumption implies equal "spread" of the residuals across the
> groups as measured by the pooled variance (assuming an equal variance
> model)...."
>
> I found this excellent description in a Web page (unfortunately
> without any reference attached).
>
> The problem is that the man who is going to present his dissertation
> used 5 groups of 7 rabbits for his research. I'm trying to fight the
> extended error (at least among the researchers that will judge his
> work) that with sample sizes under 10, you are condemned to use non
> parametrics because you can't test the condition of normality inside
> each treatment group. Therefore, I need a good reference for the fact
> that normality is not very important, and, besides, it has to tested
> on residuals, not observations themselves. It's one of those facts I
> know, I remember I read time ago, but I can't pinpoint the source of
> that knowledge. The refence needn't be in Spanish, it could also be in
> English, French...
>
> Thanks a lot in advance
>
> Marta Garcia-Granero
>
>

Confidentiality Notice for Email Transmissions: The information in this
message is confidential and may be legally privileged. It is intended solely
for the addressee.  Access to this message by anyone else is unauthorised.
If you are not the intended recipient, any disclosure, copying, or
distribution of the message, or any action or omission taken by you in
reliance on it, is prohibited and may be unlawful.  Please immediately
contact the sender if you have received this message in error. Thank you.

[Peck, Jon]

If you want an ancient and authoritative source, Kendall and Stuart, Advanced Theory of Statistics, Vol 3 has a fairly long discussion of robustness of ANOVA against a variety of assumptions.  It's section 37.22 through 37.25 in my edition (2nd ed).  37.24 is specifically about robustness to non-normality.

HTH,
Jon

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Marta García-Granero
Sent: Thursday, March 15, 2007 12:28 PM
To: [hidden email]
Subject: [SPSSX-L] Need reference for a dissertation

Hi everybody

I've been searching thru all my collection of statistics book, but I
haven't been able to find a good reference for these sentences (which I
know to be true, but someone at the University doesn't want to
believe, giving a bad time to a client of mine who has to present his
dissertation very soon):

"Oneway ANOVA.

Assumptions concerning the data:

1. Observations come from independent random sampling (that is, only
   one observation for each subject who have been randomly assigned to
   groups)
2. The residuals of the model are normally distributed
3. The residuals have equal variances within each group (i.e.,
   homoskedasticity, the population sigma^2 is the same "unknown" value
   in each group)

Checking these Assumptions

The first assumption is generally met from the statistical design and the
process from which data are collected, namely, by randomly assigning
subjects to the independent groups and taking one observation per subject.
The design aspect is common to many types of analyses and will not be
covered in these pages.

The second assumption focuses on normality of the residuals and not the
observations themselves.

The third assumption implies equal "spread" of the residuals across the
groups as measured by the pooled variance (assuming an equal variance
model)...."

I found this excellent description in a Web page (unfortunately
without any reference attached).

The problem is that the man who is going to present his dissertation
used 5 groups of 7 rabbits for his research. I'm trying to fight the
extended error (at least among the researchers that will judge his
work) that with sample sizes under 10, you are condemned to use non
parametrics because you can't test the condition of normality inside
each treatment group. Therefore, I need a good reference for the fact
that normality is not very important, and, besides, it has to tested
on residuals, not observations themselves. It's one of those facts I
know, I remember I read time ago, but I can't pinpoint the source of
that knowledge. The refence needn't be in Spanish, it could also be in
English, French...

Thanks a lot in advance

Marta Garcia-Granero

[Marta García-Granero]

Hi everybody

Thanks to all who replied, either to the list or directly to me.

I think that I have a bunch of good references (I'll try to track them
tomorrow morning at the University library) to bury under them those
stubborns blockheads that insist that the researcher must use
Kruskal-Wallis instead of ANOVA due to sample size issues.

Best regards,
Marta

(PS: If anybody needs a MACRO for Mann-Kendall test for time series
trend, just let me know, I'm just "polishing" it. It will be part of a
set of non-parametric miscellaneous routines I'm going to pack
together and send to Developer Central soon).

Thursday, March 15, 2007, 6:28:12 PM, I wrote:

MGG> Hi everybody

MGG> I've been searching thru all my collection of statistics book, but I
MGG> haven't been able to find a good reference for these sentences (which I
MGG> know to be true, but someone at the University doesn't want to
MGG> believe, giving a bad time to a client of mine who has to present his
MGG> dissertation very soon):

MGG> "Oneway ANOVA.

MGG> Assumptions concerning the data:

MGG> 1. Observations come from independent random sampling (that is, only
MGG>    one observation for each subject who have been randomly assigned to
MGG>    groups)
MGG> 2. The residuals of the model are normally distributed
MGG> 3. The residuals have equal variances within each group (i.e.,
MGG>    homoskedasticity, the population sigma^2 is the same "unknown" value
MGG>    in each group)

MGG> Checking these Assumptions

MGG> The first assumption is generally met from the statistical design and the
MGG> process from which data are collected, namely, by randomly assigning
MGG> subjects to the independent groups and taking one observation per subject.
MGG> The design aspect is common to many types of analyses and will not be
MGG> covered in these pages.

MGG> The second assumption focuses on normality of the residuals and not the
MGG> observations themselves.

MGG> The third assumption implies equal "spread" of the residuals across the
MGG> groups as measured by the pooled variance (assuming an equal variance
MGG> model)...."

MGG> I found this excellent description in a Web page (unfortunately
MGG> without any reference attached).

MGG> The problem is that the man who is going to present his dissertation
MGG> used 5 groups of 7 rabbits for his research. I'm trying to fight the
MGG> extended error (at least among the researchers that will judge his
MGG> work) that with sample sizes under 10, you are condemned to use non
MGG> parametrics because you can't test the condition of normality inside
MGG> each treatment group. Therefore, I need a good reference for the fact
MGG> that normality is not very important, and, besides, it has to tested
MGG> on residuals, not observations themselves. It's one of those facts I
MGG> know, I remember I read time ago, but I can't pinpoint the source of
MGG> that knowledge. The refence needn't be in Spanish, it could also be in
MGG> English, French...

[Ornelas, Fermin]

Aren't you concerned with your reference and your statement (Granero):

Therefore, I need a good reference for the fact
that normality is not very important, and, besides, it has to tested
on residuals, not observations themselves.

AS we know the basic assumption for the error term is e~N(0,sigma^2) where the variance is assumed constant across the means.

The usual testing and verification of those assumptions requires evaluation of residual plots against the predictors and fitted Y to make sure that the assumption of constant variance is being met. Testing can be done using Levene's test.

Regarding normality a normal probability plot of the studentized residuals and Lilliefor's test could help you to decide whether normality is being maintained.

To deal with these problems you could transform the response variable and use the Box Cox transformation to decide an optimal transformation on the data. Equally important is the evaluation of outliers and there you could use Bonferroni's to decide whether a particular observation is an outlier.

If one of those assumptions is not satisfied the results of your research and data collection could be questioned.



Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
Tel: [phone]
E-mail: [hidden email]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Peck, Jon
Sent: Thursday, March 15, 2007 11:00 AM
To: [hidden email]
Subject: Re: Need reference for a dissertation

If you want an ancient and authoritative source, Kendall and Stuart, Advanced Theory of Statistics, Vol 3 has a fairly long discussion of robustness of ANOVA against a variety of assumptions.  It's section 37.22 through 37.25 in my edition (2nd ed).  37.24 is specifically about robustness to non-normality.

HTH,
Jon

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Marta García-Granero
Sent: Thursday, March 15, 2007 12:28 PM
To: [hidden email]
Subject: [SPSSX-L] Need reference for a dissertation

Hi everybody

I've been searching thru all my collection of statistics book, but I
haven't been able to find a good reference for these sentences (which I
know to be true, but someone at the University doesn't want to
believe, giving a bad time to a client of mine who has to present his
dissertation very soon):

"Oneway ANOVA.

Assumptions concerning the data:

1. Observations come from independent random sampling (that is, only
   one observation for each subject who have been randomly assigned to
   groups)
2. The residuals of the model are normally distributed
3. The residuals have equal variances within each group (i.e.,
   homoskedasticity, the population sigma^2 is the same "unknown" value
   in each group)

Checking these Assumptions

The first assumption is generally met from the statistical design and the
process from which data are collected, namely, by randomly assigning
subjects to the independent groups and taking one observation per subject.
The design aspect is common to many types of analyses and will not be
covered in these pages.

The second assumption focuses on normality of the residuals and not the
observations themselves.

The third assumption implies equal "spread" of the residuals across the
groups as measured by the pooled variance (assuming an equal variance
model)...."

I found this excellent description in a Web page (unfortunately
without any reference attached).

The problem is that the man who is going to present his dissertation
used 5 groups of 7 rabbits for his research. I'm trying to fight the
extended error (at least among the researchers that will judge his
work) that with sample sizes under 10, you are condemned to use non
parametrics because you can't test the condition of normality inside
each treatment group. Therefore, I need a good reference for the fact
that normality is not very important, and, besides, it has to tested
on residuals, not observations themselves. It's one of those facts I
know, I remember I read time ago, but I can't pinpoint the source of
that knowledge. The refence needn't be in Spanish, it could also be in
English, French...

Thanks a lot in advance

Marta Garcia-Granero

NOTICE: This e-mail (and any attachments) may contain PRIVILEGED OR CONFIDENTIAL information and is intended only for the use of the specific individual(s) to whom it is addressed.  It may contain information that is privileged and confidential under state and federal law.  This information may be used or disclosed only in accordance with law, and you may be subject to penalties under law for improper use or further disclosure of the information in this e-mail and its attachments. If you have received this e-mail in error, please immediately notify the person named above by reply e-mail, and then delete the original e-mail.  Thank you.