One Way ANOVA query

[Mark Webb-5]

Factors = Company Divisions [8 of these]
Dep Var = Overall satisfaction [A score from 0-100]
Post Hoc - Equal variance assumed & Bonferroni

The ANOVA table suggests that the means between the divisions differ
[p=0.011]

BUT in the multiple comparisons table I get no individual comparisons
that are significantly different.
No p values near 0.05.

Can someone explain this to me - if the ANOVA table suggests difference
why is this not reflected in the multiple comparison table ?

[I do have low sample sizes for some of the divisions. Should I not be
assuming equality of variance i.e. should I test for this ?]

--
Mark Webb

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[Mike]

You have one grouping factor with 8 levels (company divisions).
It would be helpful if you provided a table of means, SD, and,
perhaps more importantly, sample sizes.  A significant ANOVA F-value
suggest three possible conditions:

(1) a Type I error has been committed, that is, the probability
of your F-value is less than .05 only because of chance factors.

(2) You have not committed a Type I error, you have systematic
differences, but the systematic difference is not between *pairs*
of means but *combinations* of means, for example, the the
combined first three means versus the combined last five means
is significant. A significant F-value only guarantees, in general, that
one orthogonal comparison among means will be significant, it does
not guarantee that pairwise differences will be significant.

(3)  You have not committed a Type I error with F test and there is
a significant difference between some pair of means but the Bonferroni
correction lacks statistical power to detect these differences because
of how it controls the overall Type I error rate for comparisons.
Re-run the analyses but use the LSD post hoc test.  This is the most
powerful post hoc test but at the cost of not controlling the overall Type I
error rate for the multiple comparisons.  The LSD may detect pairwise
differences that disappear when the Bonferroni test is used.  This
suggests that you need more cases (i.e., increase statistical power) in
order to detect the difference by Bonferroni test or use a multiple
comparison procedure between the LSD and Bonferroni that
(a) controls the Type I error rate at, say, .05, and
(b) has more power than the Bonferroni.  If the LSD results provides
no significant pairwise differences, then (2) and (1) above increase in
likelihood.

-Mike Palij
New York University
[hidden email]





----- Original Message -----
From: "Mark Webb" <[hidden email]>
To: <[hidden email]>
Sent: Wednesday, February 17, 2010 12:53 AM
Subject: One Way ANOVA query

> Factors = Company Divisions [8 of these]
> Dep Var = Overall satisfaction [A score from 0-100]
> Post Hoc - Equal variance assumed & Bonferroni
>
> The ANOVA table suggests that the means between the divisions differ
> [p=0.011]
>
> BUT in the multiple comparisons table I get no individual comparisons
> that are significantly different.
> No p values near 0.05.
>
> Can someone explain this to me - if the ANOVA table suggests difference
> why is this not reflected in the multiple comparison table ?
>
> [I do have low sample sizes for some of the divisions. Should I not be
> assuming equality of variance i.e. should I test for this ?]
>
> --
> Mark Webb
>
> Line [phone]
> Cell [phone]
> Fax to email [phone]
> Skype  webbmark
> Email  [hidden email]
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

=====================
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