additive model?

[Zdaniuk, Bozena-3]

hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
1. Sick and rural - 5.5
2. Healthy and rural - 7.5
3. Sick and urban - 8.5
4. Healthy and urban - 10.5

So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
Any reading tips on that?
thanks so much!
bozena

[Ryan]

Looks like you have an interaction. :-)

On Jan 14, 2013, at 4:54 PM, "Zdaniuk, Bozena" <[hidden email]> wrote:

hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
1. Sick and rural - 5.5
2. Healthy and rural - 7.5
3. Sick and urban - 8.5
4. Healthy and urban - 10.5

So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
Any reading tips on that?
thanks so much!
bozena

[Ryan]

Sorry. Read the email too quickly. Yes, looks like an additive effect, so exclude the interaction term. Two main effects without an interaction term seems appropriate. 

Sent from my iPhone

On Jan 14, 2013, at 5:13 PM, [hidden email] wrote:

Looks like you have an interaction. :-)

On Jan 14, 2013, at 4:54 PM, "Zdaniuk, Bozena" <[hidden email]> wrote:

hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
1. Sick and rural - 5.5
2. Healthy and rural - 7.5
3. Sick and urban - 8.5
4. Healthy and urban - 10.5

So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
Any reading tips on that?
thanks so much!
bozena

[Zdaniuk, Bozena-3]

yes, i know i have two main effects but just reporting those does not bring out the point i want to stress: the two main effects add up to make the sick-rural kids worse off than all other groups. This is why I was asking whether the One Way ANOVA is appropriate...
thanks!
bozena

---

From: [hidden email] [[hidden email]]
Sent: Monday, January 14, 2013 2:31 PM
To: Zdaniuk, Bozena
Cc: [hidden email]
Subject: Re: additive model?

Sorry. Read the email too quickly. Yes, looks like an additive effect, so exclude the interaction term. Two main effects without an interaction term seems appropriate. 

Sent from my iPhone

On Jan 14, 2013, at 5:13 PM, [hidden email] wrote:

Looks like you have an interaction. :-)

On Jan 14, 2013, at 4:54 PM, "Zdaniuk, Bozena" <[hidden email]> wrote:

hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
1. Sick and rural - 5.5
2. Healthy and rural - 7.5
3. Sick and urban - 8.5
4. Healthy and urban - 10.5

So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
Any reading tips on that?
thanks so much!
bozena

[Ryan]

There are a number of ways to do it. Okay. Going to simulate some data to show you a couple of ways. Just a few. -Ryan

On Mon, Jan 14, 2013 at 6:12 PM, Zdaniuk, Bozena <[hidden email]> wrote:

yes, i know i have two main effects but just reporting those does not bring out the point i want to stress: the two main effects add up to make the sick-rural kids worse off than all other groups. This is why I was asking whether the One Way ANOVA is appropriate...
thanks!
bozena

---

From: [hidden email] [[hidden email]]
Sent: Monday, January 14, 2013 2:31 PM
To: Zdaniuk, Bozena
Cc: [hidden email]
Subject: Re: additive model?

Sorry. Read the email too quickly. Yes, looks like an additive effect, so exclude the interaction term. Two main effects without an interaction term seems appropriate. 

Sent from my iPhone

On Jan 14, 2013, at 5:13 PM, [hidden email] wrote:

Looks like you have an interaction. :-)

On Jan 14, 2013, at 4:54 PM, "Zdaniuk, Bozena" <[hidden email]> wrote:

hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
1. Sick and rural - 5.5
2. Healthy and rural - 7.5
3. Sick and urban - 8.5
4. Healthy and urban - 10.5

So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
Any reading tips on that?
thanks so much!
bozena

[Rich Ulrich]

The original analysis is appropriate -- the test to show that both
effects are present.  You could also comment on the means, to say
that there is no hint of interaction, that the cells do fit the model well.

A one-way test on the four groups will mainly add to the narrative
if you put in post-hoc testing in order to make the point that this
one group differs from all (or almost all) of the others.

--
Rich Ulrich

---

Date: Mon, 14 Jan 2013 23:12:07 +0000
From: [hidden email]
Subject: Re: additive model?
To: [hidden email]

yes, i know i have two main effects but just reporting those does not bring out the point i want to stress: the two main effects add up to make the sick-rural kids worse off than all other groups. This is why I was asking whether the One Way ANOVA is appropriate...
thanks!
  ...

[Ryan]

I've been giving this some thought... Given the situation, I would be in favor of your approach of recoding the two factors into a single grouping variable, "Group" as follows:

IF  (FactorA=0 and FactorB=0) Group=1.
IF  (FactorA=1 and FactorB=0) Group=2.
IF  (FactorA=0 and FactorB=1) Group=3.
IF  (FactorA=1 and FactorB=1) Group=4.
EXECUTE.

...and then fitting a one-way ANOVA and performing post-hoc contrasts demonstrating that the "sick and rural" level of the grouping variable is(perhaps) significantly different than the others separately (EMMEANS sub-command) and perhaps together (LMATRIX sub-command). I would also be in favor of plotting the means of each group (PLOT sub-command) because there may be a meaningful story in the trend.

 

For example,

UNIANOVA y BY Group
  /METHOD=SSTYPE(3)
  /INTERCEPT=INCLUDE
  /PLOT=PROFILE(Group)
  /CRITERIA=ALPHA(0.05)
  /DESIGN=Group
  /EMMEANS=TABLES(Group) COMPARE ADJ(LSD)
  /LMATRIX = 'Group 1 vs Group 2,3,4' Group 1 -1/3 -1/3 -1/3.

Best,

 

Ryan

On Mon, Jan 14, 2013 at 6:12 PM, Zdaniuk, Bozena <[hidden email]> wrote:

yes, i know i have two main effects but just reporting those does not bring out the point i want to stress: the two main effects add up to make the sick-rural kids worse off than all other groups. This is why I was asking whether the One Way ANOVA is appropriate...
thanks!
bozena

---

From: [hidden email] [[hidden email]]
Sent: Monday, January 14, 2013 2:31 PM
To: Zdaniuk, Bozena
Cc: [hidden email]
Subject: Re: additive model?

Sorry. Read the email too quickly. Yes, looks like an additive effect, so exclude the interaction term. Two main effects without an interaction term seems appropriate. 

Sent from my iPhone

On Jan 14, 2013, at 5:13 PM, [hidden email] wrote:

Looks like you have an interaction. :-)

On Jan 14, 2013, at 4:54 PM, "Zdaniuk, Bozena" <[hidden email]> wrote:

hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
1. Sick and rural - 5.5
2. Healthy and rural - 7.5
3. Sick and urban - 8.5
4. Healthy and urban - 10.5

So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
Any reading tips on that?
thanks so much!
bozena

[Ian Martin-2]

Bozena,

It looks as though there would be no interaction (lines don't cross), but how can you "believe" there is no interaction unless you first do the 2-way and test for interaction significance?

If that is confirmed then you will have the results for the 2-way main effects, and you might choose to set up a dummy categorical variable to compare your 4 groups via 1-way and post-hoc.

regards,

Ian D. Martin, Ph.D.

Tsuji Laboratory
University of Waterloo
Dept. of Environment & Resource Studies


On Jan 14, 2013, at 4:54 PM, Zdaniuk, Bozena wrote:

> hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
> 1. Sick and rural - 5.5
> 2. Healthy and rural - 7.5
> 3. Sick and urban - 8.5
> 4. Healthy and urban - 10.5
>
> So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
> Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
> Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
> Any reading tips on that?
> thanks so much!
> bozena

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[Bruce Weaver]

Two comments:

1) Lines do not have to cross for there to be an interaction.

2) Look at the simple main effects:

> 1. Sick and rural - 5.5
> 2. Healthy and rural - 7.5
> 3. Sick and urban - 8.5
> 4. Healthy and urban - 10.5

Simple main effects of Sick/Health:  7.5 - 5.5 = 2.0; 10.5 - 8.5 = 2.0
Simple main effects of Rural/Urban:  8.5 - 5.5 = 3.0; 10.5 - 7.5 = 3.0

Because the simple main effects of one variable are exactly the same at both levels of the other variable, there is no possibility of an interaction.  The null hypothesis for the interaction term is that the simple main effects are exactly equal, as they are here.

Ian Martin-2 wrote

Bozena,

It looks as though there would be no interaction (lines don't cross), but how can you "believe" there is no interaction unless you first do the 2-way and test for interaction significance?

If that is confirmed then you will have the results for the 2-way main effects, and you might choose to set up a dummy categorical variable to compare your 4 groups via 1-way and post-hoc.

regards,

Ian D. Martin, Ph.D.

Tsuji Laboratory
University of Waterloo
Dept. of Environment & Resource Studies


On Jan 14, 2013, at 4:54 PM, Zdaniuk, Bozena wrote:

> hello, I have trouble figuring out an analytical strategy for that seemingly simple model. I have two factors that I believe do not interact but have an additive impact on the outcome variable. Let's call them health (sick vs healthy) and location (rural vs urban). The mean educational outcomes are as follows:
> 1. Sick and rural - 5.5
> 2. Healthy and rural - 7.5
> 3. Sick and urban - 8.5
> 4. Healthy and urban - 10.5
>
> So, two main effects: rural worse than urban, and sick worse than healthy. No interaction, as can be seen.
> Clearly there is a "double-whammy" effect for rural and sick kids doing worse on educ outcomes.
> Can I test it with a One-way - four group ANOVA, showing that the sick-rural group is worse off than any other three groups, or is there some obviously more appropriate way to test it that escapes me?
> Any reading tips on that?
> thanks so much!
> bozena

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

[John F Hall]

How can you be sure that your two predictors are statistically independent?
How about starting with some simple crosstabs of (dichotomised?) educational
outcome by health status and urbanicity (and health by urbanicity) then a
three way crosstab, using percentages (and chi-square and related measures)?


John F Hall (Mr)
[retired academic survey researcher]

Email:    [hidden email]
Website: www.surveyresearch.weebly.com





-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Ian
Martin
Sent: 15 January 2013 16:04
To: [hidden email]
Subject: Re: additive model?

Bozena,

It looks as though there would be no interaction (lines don't cross), but
how can you "believe" there is no interaction unless you first do the 2-way
and test for interaction significance?

If that is confirmed then you will have the results for the 2-way main
effects, and you might choose to set up a dummy categorical variable to
compare your 4 groups via 1-way and post-hoc.

regards,

Ian D. Martin, Ph.D.

Tsuji Laboratory
University of Waterloo
Dept. of Environment & Resource Studies


On Jan 14, 2013, at 4:54 PM, Zdaniuk, Bozena wrote:

> hello, I have trouble figuring out an analytical strategy for that
seemingly simple model. I have two factors that I believe do not interact
but have an additive impact on the outcome variable. Let's call them health
(sick vs healthy) and location (rural vs urban). The mean educational
outcomes are as follows:
> 1. Sick and rural - 5.5
> 2. Healthy and rural - 7.5
> 3. Sick and urban - 8.5
> 4. Healthy and urban - 10.5
>
> So, two main effects: rural worse than urban, and sick worse than healthy.
No interaction, as can be seen.
> Clearly there is a "double-whammy" effect for rural and sick kids doing
worse on educ outcomes.
> Can I test it with a One-way - four group ANOVA, showing that the
sick-rural group is worse off than any other three groups, or is there some
obviously more appropriate way to test it that escapes me?
> Any reading tips on that?
> thanks so much!
> bozena

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

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
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For a list of commands to manage subscriptions, send the command
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[David Marso]

"How can you be sure that your two predictors are statistically independent?"
---
Please enlighten me as to why this is any concern.
ANOVA is merely a form of regression (predictors are rarely orthogonal) but that is not a show stopper.

"How about starting with some simple crosstabs of (dichotomised?) educational
outcome by health status and urbanicity (and health by urbanicity) then a
three way crosstab, using percentages (and chi-square and related measures)?"
---
And this is supposed to shed light on what?

John F Hall wrote

How can you be sure that your two predictors are statistically independent?
How about starting with some simple crosstabs of (dichotomised?) educational
outcome by health status and urbanicity (and health by urbanicity) then a
three way crosstab, using percentages (and chi-square and related measures)?


John F Hall (Mr)
[retired academic survey researcher]

Email:    [hidden email]
Website: www.surveyresearch.weebly.com





-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Ian
Martin
Sent: 15 January 2013 16:04
To: [hidden email]
Subject: Re: additive model?

Bozena,

It looks as though there would be no interaction (lines don't cross), but
how can you "believe" there is no interaction unless you first do the 2-way
and test for interaction significance?

If that is confirmed then you will have the results for the 2-way main
effects, and you might choose to set up a dummy categorical variable to
compare your 4 groups via 1-way and post-hoc.

regards,

Ian D. Martin, Ph.D.

Tsuji Laboratory
University of Waterloo
Dept. of Environment & Resource Studies


On Jan 14, 2013, at 4:54 PM, Zdaniuk, Bozena wrote:

> hello, I have trouble figuring out an analytical strategy for that
seemingly simple model. I have two factors that I believe do not interact
but have an additive impact on the outcome variable. Let's call them health
(sick vs healthy) and location (rural vs urban). The mean educational
outcomes are as follows:
> 1. Sick and rural - 5.5
> 2. Healthy and rural - 7.5
> 3. Sick and urban - 8.5
> 4. Healthy and urban - 10.5
>
> So, two main effects: rural worse than urban, and sick worse than healthy.
No interaction, as can be seen.
> Clearly there is a "double-whammy" effect for rural and sick kids doing
worse on educ outcomes.
> Can I test it with a One-way - four group ANOVA, showing that the
sick-rural group is worse off than any other three groups, or is there some
obviously more appropriate way to test it that escapes me?
> Any reading tips on that?
> thanks so much!
> bozena

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

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