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Created: Oct 21, 2017
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Week 9- Depression Scores
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This study was a long term research study of individuals 65 years and older. Sociologists and physicians investigated the relationship between geographic location, health status, and depression.

Statistical Methods:

Samples of 20 healthy participants were chosen from 3 geographical areas: Florida, New York, and North Carolina. Each participant was given a test to measure depression levels. Similarly, samples of 20 individuals with one or more comorbidities were taken from the 3 geographic locations. They were also given the same test to measure depression levels. Depression scores will be treated as interval data for this study.

Statistical Analysis:

First we need to check our assumptions. 

 The QQ Plot and The Scatter Plot below do not indicate any straying from normality or constant variability. 


Now we will examine the Two-Way Anova. 


We will check for interaction. At a p-value of 0.262 we have no evidence of an interaction. 

Now we must consider main effects: The location does not show evidence of a difference in regards to depression scores. (F=3.04 p-value=0.052) where the health of the patient shows a significant difference in regards to depression scores (F= 200.45 p-value=

Since no interaction was evident we will not use the interaction plot graph. With the P values and the plot we are able to say that we have differences. We will use the Tukey pairwise comparisons to tell use what type of differences we have. 

Tukey HSD results (95% level) for Location:
Florida subtracted from

New York 1.6 0.018211142 3.1817889 0.0468
North Carolina 0.475 -1.1067889 2.0567889 0.7563

New York subtracted from

North Carolina -1.125 -2.7067889 0.45678886 0.2138


Tukey reults (95% level) show no evidence of differences in regards to location between North Carolina and Florida and then new york and north carolina. There may have been a difference of 3.18 difference between Florida and New York. 


Tukey HSD results (95% level) for Health:
CMB subtracted from

Healthy -7.7 -8.777393 -6.622607 <0.0001

 Tukey HSD results (95% level) People with comorbidities average 6.62 to 8.78 higher depression scores than healthy people do. 

Tukey HSD results (95% level) for Location*Health:
Florida,CMB subtracted from

Florida,Healthy -8.95 -11.680654 -6.2193455 <0.0001
New York,CMB 0.75 -1.9806545 3.4806545 0.9676
New York,Healthy -6.5 -9.2306545 -3.7693455 <0.0001
North Carolina,CMB -0.55 -3.2806545 2.1806545 0.9919
North Carolina,Healthy -7.45 -10.180654 -4.7193455 <0.0001

Tukey (95% level) for location. A sickly person from Florida has scores 6.22 to 11.69 higher than a healthy person from florida. A sickly person from Floriday has scores 3.78 to 9.23 higher than a healthy new york person. A sickly florida person has scores 4.72 to 10.18 higher than a healthy person from north carolina. 

Florida,Healthy subtracted from

New York,CMB 9.7 6.9693455 12.430654 <0.0001
New York,Healthy 2.45 -0.28065447 5.1806545 0.1054
North Carolina,CMB 8.4 5.6693455 11.130654 <0.0001
North Carolina,Healthy 1.5 -1.2306545 4.2306545 0.6053

A sickly person in New york may have scores 6.97 to 12.43 higher than a healthy florida person. A sickly north carolina persn may have scores 5.67 to 11.13 higher than a healthy florida person. There was no difference in the locations in regards to healthy people. 

New York,CMB subtracted from

New York,Healthy -7.25 -9.9806545 -4.5193455 <0.0001
North Carolina,CMB -1.3 -4.0306545 1.4306545 0.7389
North Carolina,Healthy -8.2 -10.930654 -5.4693455 <0.0001

The average scores for a sickly person in New York may have been 5.47 to 10.93 higher than a healthy person in North Carolina. The average scores for a sickly person in new york may have been 4.52 to 9.99 higher than a healthy person in new york.  

New York,Healthy subtracted from

North Carolina,CMB 5.95 3.2193455 8.6806545 <0.0001
North Carolina,Healthy -0.95 -3.6806545 1.7806545 0.9143

North Carolina,CMB subtracted from

North Carolina,Healthy -6.9 -9.6306545 -4.1693455 <0.0001

A person from North Carolina who is sickly may have scores 3.22 to 8.68 higher than a healthy person from new york. A sickly person from North Carolina may have scores 4.17 to 9.63 higher than a healthy north carolina person. 
Future Studies:

In summary, we are able to conclude that location really does not have an impact on depression scores. We are able to say that health status does have a significant impact on the scores. I would reccomend that future studies be done with more regard to any medications that the person is already on. That can affect depression levels. I also think that seasons should be looked at. This can affect depression levels as well. 

I do think that the level of healthy or sick a person is classified as does have a huge impact on their happiness. I think that this study gave us all the results we were looking for.  


Result 1: QQ Plot Residuals (Week 9)   [Info]
Right click to copy

Result 2: Scatter Plot Week 9   [Info]
Right click to copy

Result 3: Two Way ANOVA Week 9   [Info]
Two Way Analysis of Variance results:
Responses: Score
Row factor: Location
Column factor: Health

ANOVA table

Fitted values stored in new column: Fit
Residuals stored in new column: Residuals

HTML link:
<A href="">Week 9- Depression Scores </A>

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By nku.katie.waters
Oct 24, 2017

Hi Candace,
This is a good start! A few comments:
1. In your introduction, you should also explain why we might care about the topic. (I'm suggesting this in order to help prepare you for the next CUA.)

2. Since there is no evidence of interaction between location and health as it relates to average depression scores (F=1.35, p-value = 0.262), then we should interpret the factors separately. This means that you should NOT interpret the interaction level comparisons. Please review the solutions on how to interpret the main effect p-values and CIs.

3. Don't forget the word "average" in your interpretations. We are talking about average depression scores.

4. You should include an interaction plot and interpret it along with the ANOVA results. From the interaction plot we can see that the relatively large difference between healthy and comorbidity is represented by the distance between the lines. The lack of evidence of interaction is represented by the fact that the lines are nearly parallel. The lack of evidence of location effect is represented by the fact that all of the comorbidity averages are near to one another, as are the healthy averages also near to one another.

5. Our overall conclusion should address how comorbidity clearly makes the largest difference - increasing average depression score substantially.

Please review the solutions and let me know if you have any questions.
By evva.allen
Oct 23, 2017

Your analysis was very in depth and I appreciate your explanation of the confidence intervals found using the Tukey test. I find it interesting, yet understandable, that people who live in a sunnier, warmer location and those who do not have comorbidities had lower depression scores.

I noticed in the introduction that you stated the data would be interpreted as interval/ratio data. However, were the depression scores used calculated with a type of Likert scale? I am sure Dr. Nolan could provide more insight about if we are able to perform ANOVA tests with Likert scale items and scoring?

Great job!
By colleen.pfister28
Oct 22, 2017

Good job on your report. I agree that seasons can definitely have an effect on people's depression and find it interesting that location did not. I appreciated how your report was broken down and each table was able to be analyzed right next to it. makes it easier to read and interpret. I am curious about the interaction p-value being 0.252 and wouldn't that indicate there was no interaction? You did;t provide interaction tables which is correct but can we still interpret CI's without a p-value less than 0.05? Still trying to grasp the ANOVA process!
Oct 21, 2017

Great job on your analysis. I think this is a complicated study because depression does not always have an explanation. There are numerous factors, excluding health, that can lead to depression. Of course, comorbidities could certainly add to people's depression, but it is not always the reason. I agree with your findings that location did not have an effect on depression. I think that depression could be found among all different genders, races and religions. Therefore, location would likely not have an impact on the data gathered for this study.
-Barrett Green

Always Learning