Minitab Statistical Analysis Project
Jeremys
Example3DenmarkHealthCare.pptWhat Affects Health Care Costs in Denmark ?
Cecilie Nygaard - Pedersen
Statistics Project
STAT 4610
Why look at Health Care Costs?
- Health Care Costs are currently a hot topic in Danish politics because as the baby boomer generation is reaching retirement there is currently not enough young people to help pay the bill. The Danes are not having enough children. People are afraid that we will not be able to sustain our current welfare system.
- Currently there is also ambivalence towards strengthening health preventive measures. Therefore I am interested to see if there is a relationship between Total Health Care Cost and Health Prevention Cost.
- Most of my family is part of the Health Care System and therefore doing this product, will help me better understand the issues they are facing.
Where is Denmark?
This is where I live
Humlebæk, Denmark
Facts about Denmark
- The Capital: Copenhagen
- Other Major Cities: Aarhus, Odense & Aalborg
- Area: 42,915.7 Km2
- Population as of January 1st 2014: 5,627,235
- National Language: Danish
- Currency: Danish Kroner
- Exchange Rate: 1 dollar = 5,98 kr.
- GDP: $330.8 billion
Health Care in Denmark
Denmark is a Welfare State
Health Care is largely financed through local (regional & municipal) taxation
Denmark spends 11.2% of its GDP on Healthcare
Life Expectancy: Women 81.9 years ; Men 78.0 years
There is 1 doctor for every 294 people in Denmark
Total Health Care Cost in 2013: 14,199,570,000 DKK or $2,372,367,761.50
There is no copay when going to the doctor or hospital
Comparison to Other Countries
Chart1
| Denmark |
| USA |
| Germany |
| Norway |
| Sweden |
| Netherlands |
Sheet1
| Health Care Cost per Capita 2013 | |
| Denmark | $4,467 |
| USA | $8,745 |
| Germany | $4,342 |
| Norway | $5,391 |
| Sweden | $3,760 |
| Netherlands | $5,112 |
| To update the chart, enter data into this table. The data is automatically saved in the chart. |
Total Health Care Cost in Denmark 2006-2013
The Total Health Care Cost increased by 3,233,421,000 DKK or $540,218,030.54 from 2006 – 2013
Project Parameters
Q1: Is there a difference in Health Care Cost among Men and Women?
The dotplot indicates that there is a difference in Health Care Cost among Men and Women. A larger portion of the Health Care Costs from 2006 -2013 are spent on Women than Men
Q1: Is there a difference in Health Care Cost among Men and Women? Continued
Two Sample T - Test – Results & Summary
Gender N Mean StDev SE Mean
Female 8 7697861 754532 266767
Male 8 5315361 542905 191946
Difference = μ (Female) - μ (Male)
Estimate for difference: 2382500
95% CI for difference: (1666442, 3098557)
T-Test of difference = 0 (vs ≠): T-Value = 7.25
DF = 12
P-Value = 0.000
Based on the p – value of 0.000, and that the confidence interval does not contain 0, there is strong evidence to show that there is a statically significant difference in Health Care Cost among Men and Women. Based on the mean, women generate more Health Care Cost than men.
Q2: Are the Health Care Cost based on ages?
Hypothesis:
H0 = There is no difference in Health Care Cost between the age groups ( They are all the same)
Ha = There is some difference in the Health Care Cost between the age groups (They are not all the same)
Q2: Are the Health Care Cost based on ages? Continued
The Interval Plot indicates that there is some difference in Health Care Costs among different age groups. The 60-69 age group generate more Health Care Costs than any other age group.
Q2: Are the Health Care Cost based on ages? Continued
One- Way ANOVA Test- Results
Factor = Age Levels = 10
Values = 0-9 years, 10-19 years, 20-29 years, 30-39 years, 40-49 years, 50-59 years, 60-69 years, 70-79 years, 80-89 years, 90 years +
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Age 9 2.53392E+13 2.81546E+12 112.62 0.000
Error 70 1.74995E+12 24999295594
Total 79 2.70891E+13
Model Summary
S R-sq R-sq(adj) R-sq(pred)
158112 93.54% 92.71% 91.56%
Q2: Are the Health Care Cost based on ages? Continued
One –Way ANOVA Test- Results
Means
Age N Mean StDev 95% CI
0-9 years 8 1002206 46666 (890716, 1113697)
10-19 years 8 757620 69210 (646129, 869111)
20-29 years 8 1182382 142544 (1070891, 1293872)
30-39 years 8 1536322 85911 (1424831, 1647813)
40-49 years 8 1759012 140248 (1647521, 1870503)
50-59 years 8 1866936 136991 (1755445, 1978426)
60-69 years 8 2138846 290293 (2027356, 2250337)
70-79 years 8 1640526 279147 (1529035, 1752017)
80-89 years 8 938179 116251 (826688, 1049670)
90 years + 8 189943 34386 (78452, 301434)
Pooled StDev = 158112
Q2: Are the Health Care Cost based on ages? Continued
One-Way ANOVA Test- Results
The Tukey Pairwise Comparisons:
Q2: Are the Health Care Cost based on ages? Continued
One-Way ANOVA Test- Results
The Tukey Pairwise Comparisons:
Age N Mean Grouping
60-69 years 8 2138846 A
50-59 years 8 1866936 B
40-49 years 8 1759012 B C
70-79 years 8 1640526 B C
30-39 years 8 1536322 C
20-29 years 8 1182382 D
0-9 years 8 1002206 D E
80-89 years 8 938179 D E
10-19 years 8 757620 E
90 years + 8 189943 F
Q2: Are the Health Care Cost based on ages? Continued
One-Way ANOVA Test- Results Summary
Step 1: Analysis of Variance
- A one-way ANOVA test was conducted to determine if Health Care Costs was different for groups with different ages.
- Based on the p-value of 0.000, which is lower than 10%, there is sufficient evidence to establish the alternative hypothesis and the null hypothesis can therefore be rejected.
Step 2: Tukey Pairwise Comparisons
- The means that do not share a letter are significantly different
Q3: Are the expenses based on
Regions?
Hypothesis:
H0 = There is no difference in Health Care Cost between the Regions ( They are all the same)
Ha = There is some difference in the Health Care Cost between the Regions (They are not all the same)
For this test I adjusted the Health Care from total to per capita, since each region in Denmark has very different population numbers, which would skew my results.
Q3: Are the expenses based on
Regions? Continued
The Interval Plot indicates that there is some difference in Health Care Costs among different Regions. The Region Hovedstaden generates more Health Care Cost per capita than any other region.
Q3: Are the expenses based on
Regions? Continued
One – Way ANOVA Test – Results
Factor = Region Levels = 5
Values = Region Hovedstaden, Region Midtjylland, Region Nordjylland, Region Sjælland, Region Syddanmark
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Region 4 728688 182172 10.86 0.000
Error 25 419501 16780
Total 29 1148189
Model Summary
S R-sq R-sq(adj) R-sq(pred)
129.538 63.46% 57.62% 47.39%
Means
Region N Mean StDev 95% CI
Region Hovedstaden 6 2861.6 129.0 (2752.7, 2970.5)
Region Midtjylland 6 2482.9 127.3 (2374.0, 2591.8)
Region Nordjylland 6 2451.2 128.5 (2342.3, 2560.2)
Region Sjælland 6 2523.5 120.8 (2414.6, 2632.4)
Region Syddanmark 6 2452.5 141.2 (2343.6, 2561.4)
Pooled StDev = 129.538
Q3: Are the expenses based on
Regions? Continued
One – Way ANOVA Test – Results
The Tukey Pairwise Comparisons:
Q3: Are the expenses based on
Regions? Continued
One – Way ANOVA Test – Results
The Tukey Pairwise Comparisons:
Region N Mean Grouping
Region Hovedstaden 6 2861.6 A
Region Sjælland 6 2523.5 B
Region Midtjylland 6 2482.9 B
Region Syddanmark 6 2452.5 B
Region Nordjylland 6 2451.2 B
Q3: Are the expenses based on
Regions? Continued
One-Way ANOVA Test- Results Summary
Step 1: Analysis of Variance
- A one-way ANOVA test was conducted to determine if Health Care Costs was different for different regions.
- Based on the p-value of 0.000, which is lower than 5%, there is sufficient evidence to establish the alternative hypothesis and the null hypothesis can therefore be rejected.
Step 2: Tukey Pairwise Comparisons
- The means that do not share a letter are significantly different
Q4: Is there a significant relationship between Health Care Costs & Physician Visits & Hospitalizations?
Hypothesis:
Ho = There is no significant relationship between Health Care Costs & Hospitalizations & Doctors Visits
Ha = There is a significant relationship between Health Care & Hospitalizations & Doctors Visits
Q4: Is there a significant relationship between Health Care Costs & Doctors Visits & Hospitalizations? Continued
As indicated by the Fitted Line Plot, there is a slight positive correlation between Health Care Cost and number of Hospitalizations.
Q4: Is there a significant relationship between Health Care Costs & Doctors Visits & Hospitalizations? Continued
Based on this Fitted Line Plot, there is also a positive correlation between Health Care Costs and Doctors Visits.
Q4: Is there a significant relationship between Health Care Costs & Doctor Visits & Hospitalizations ? Continued
Multiple Linear Regression – Results
Regression Analysis: Total Health Care Expense versus Hospitalization, Doctor Visits
Model Summary
S R-sq R-sq(adj) R-sq(pred)
442359 91.81% 88.53% 62.05%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -45697573 7960116 -5.74 0.002
Hospitalization 40.6 15.4 2.63 0.047 1.70
Doctors Visits 0.570 0.155 3.68 0.014 1.70
Regression Equation
Total Health Care Expense = -45697573 + 40.6 Hospitalization + 0.570 Doctors Visits
Fits and Diagnostics for Unusual Observations
Total Health Std
Obs Care Expense Fit Resid Resid
8 14199570 13401087 798483 2.07 R
Q4: Is there a significant relationship between Health Care Costs & Doctor Visits & Hospitalizations? Continued
Multiple Linear Regression – Results Summary
Based on the p-values of 0.047 and o.o14, there is strong evidence to show that Total Health Care Cost is strongly correlated with the number of Hospitalizations and Doctors Visits. Since Doctors Visits has a lower p-value than Hospitalizations, they are slightly more statistically significant.
This is captured by the high correlation coefficient (r-value) of 0.9582 (sqrt of the R2)
The coefficient of determination (R2) is 0.9181
Accordingly the regression model fits the data fairly well and the R2 suggests that about 91% the variability in Total Health Care Cost can be explained by the number of Hospitalization & Doctors Visits
Q4: Is there a significant relationship between Health Care Costs & Doctor Visits & Hospitalizations? Continued
Multiple Linear Regression – Using the model for prediction
- Given the low p-values obtained, there is an association/relationship between the output variable and the two input variables. Therefore the established regression model can be used for future predictions:
- Y= -45697573 + 40.6 X1 + 0.570 X2
- Y = Total Health Care Costs
- X1= Hospitalization
- X2= Doctors Visits
Q5: Are the Health Care Costs Based on Types of Benefits?
Hypothesis:
Ho = There is no difference in Health Care Cost between the Types of Benefits ( They are all the same)
Ha = There is some difference in the Health Care Cost between the Types of Benefits (They are not all the same)
Q5: Are the Health Care Costs Based on Types of Benefits? Continued
According to the Interval Plot, there are some differences in Total Health Care Cost among different Types of Benefits. Total General Medical Treatment generates more Health Care costs than any of the other Type of Benefits.
Q5: Are the Health Care Costs Based on Types of Benefits? Continued
One – Way ANOVA Test – Results
Factor = Type of Benefit Levels = 9
Values = CHIROPODIST, CHIROPRACTOR, DENTIST/DENTAL HYGIENIST, GENERAL MEDICAL TREATMENT, TOTAL, LABORATORIES, OTHER, PHYSIOTHERAPIST, PSYCHOLOGIST, SPECIALIST TOTAL
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Type of Benefit 8 3.40087E+14 4.25109E+13 692.31 0.000
Error 63 3.86845E+12 61404028506
Total 71 3.43956E+14
Model Summary
S R-sq R-sq(adj) R-sq(pred)
247798 98.88% 98.73% 98.53%
Q5: Are the Health Care Costs Based on Types of Benefits? Continued
One – Way ANOVA Test – Results
Means
Type of Benefit N Mean StDev 95% CI
CHIROPODIST 8 36218 34027 (-138856, 211293)
CHIROPRACTOR 8 105851 8507 ( -69223, 280926)
DENTIST/DENTAL
HYGIENIST 8 1383767 87903 (1208692, 1558841)
GENERAL MEDICAL
TREATMENT, TOTAL 8 7085349 637825 (6910274, 7260423)
LABORATORIES 8 379401 49363 ( 204327, 554476)
OTHER 8 22236 9553 (-152838, 197311)
PHYSIOTHERAPIST 8 1047571 149539 ( 872496, 1222645)
PSYCHOLOGIST 8 173963 56543 ( -1111, 349038)
SPECIALIST, TOTAL 8 2853241 329805 (2678166, 3028315)
Pooled StDev = 247798
Q5: Are the Health Care Costs Based on Types of Benefits? Continued
One – Way ANOVA Test – Results
The Tukey Pairwise Comparison:
Q5: Are the Health Care Costs Based on Types of Benefits? Continued
One – Way ANOVA Test – Results
The Tukey Pairwise Comparison:
Type of Benefit N Mean Grouping
GENERAL MEDICAL TREATMENT, TOTAL 8 7085349 A
SPECIALIST, TOTAL 8 2853241 B
DENTIST/DENTAL HYGIENIST 8 1383767 C
PHYSIOTHERAPIST 8 1047571 C
LABORATORIES 8 379401 D
PSYCHOLOGIST 8 173963 D
CHIROPRACTOR 8 105851 D
CHIROPODIST 8 36218 D
OTHER 8 22236 D
Q5: Are the Health Care Costs Based on Types of Benefits? Continued
One – Way ANOVA Test – Results Summary
Step 1: Analysis of Variance
A one-way ANOVA test was conducted to determine if Health Care Costs was different for different Types of Health Benefits.
Based on the p-value of 0.000, which is lower than 10%, there is sufficient evidence to establish the alternative hypothesis and the null hypothesis can therefore be rejected.
Step 2: Tukey Pairwise Comparisons
The means that do not share a letter are significantly different
Q6: Are the Health Care Costs based on Socioeconomic Status?
Hypothesis:
Ho = There is no difference in Health Care Cost between the different Socioeconomic Statuses ( They are all the same)
Ha = There is some difference in the Health Care Cost between the different Socioeconomic Statuses (They are not all the same)
Q6: Are the Health Care Costs based on Socioeconomic Status? Continued
The Interval Plot shows that are some differences in Health Care Costs among Socioeconomic Statuses. The largest amount of Health Care Costs are generated among the Pensioner and Early Retirement group.
Q6: Are the Health Care Costs based on Socioeconomic Status? Continued
One –Way ANOVA Test – Results
Factor =Socioeconomic Status Levels= 11
Values = Assisting spouses, Employees higher level, Employees lowest level, Employees medium level, Other Employees, Pensioner and early retirement leave, Persons without any connection with labor market, Self-employed persons, Students, Top executives, Unemployed
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Socioeconomic Status 10 1.53597E+14 1.53597E+13 233.06 0.000
Error 77 5.07467E+12 65904851335
Total 87 1.58672E+14
Model Summary
S R-sq R-sq(adj) R-sq(pred)
256719 96.80% 96.39% 95.82%
Q6: Are the Health Care Costs based on Socioeconomic Status? Continued
One –Way ANOVA Test – Results
Means
Socioeconomic Status N Mean StDev 95% CI
Assisting spouses 8 14525 906 (-166209, 195259)
Employees higher level 8 937345 346949 (756611, 1118079)
Employees lowest level 8 2080015 155515 (1899281, 2260749)
Employees medium level 8 901018 219780 (720284, 1081752)
Other Employees 8 1057416 163344 (876682, 1238150)
Pensioner and early retirement
leave 8 4644461 622852 (4463726, 4825195)
Persons without any connection
with labor market 8 2386846 321433 (2206111, 2567580)
Self-employed persons 8 430296 55901 (249562, 611030)
Students 8 266527 88923 (85793, 447261)
Top executives 8 163149 35173 ( -17585, 343883)
Unemployed 8 184599 43311 (3864, 365333)
Q6: Are the Health Care Costs based on Socioeconomic Status? Continued
One –Way ANOVA Test – Results
The Tukey Pairwise Comparison
Socioeconomic Status N Mean Grouping
Pensioner and early retirement leave 8 4644461 A
Persons without any connection
with labor market 8 2386846 B
Employees lowest level 8 2080015 B
Other Employees 8 1057416 C
Employees higher level 8 937345 C
Employees medium level 8 901018 C
Self-employed persons 8 430296 D
Students 8 266527 D
Unemployed 8 184599 D
Top executives 8 163149 D
Assisting spouses 8 14525 D
Q6: Are the Health Care Costs based on Socioeconomic Status? Continued
One –Way ANOVA Test – Results - Summary
Step 1: Analysis of Variance
- A one-way ANOVA test was conducted to determine if Health Care Costs was different for among separate Socioeconomic Statuses.
- Based on the p-value of 0.000, which is lower than 10%, there is sufficient evidence to establish the alternative hypothesis and the null hypothesis can therefore be rejected.
Step 2: Tukey Pairwise Comparisons
- The means that do not share a letter are significantly different
Q7: Is there a significant relationship between Health Care Costs & Health Promotion Costs?
Hypothesis:
H0 = Health Promotion cost does not affect overall health expenses
Ha = Health Promotion costs decrease overall health expenses
Q7: Is there a significant relationship between Health Care Costs & Health Promotion Costs? Continued
The Fitted Line Plot indicates that there is a positive correlation between Health Care Costs and Health Promotion Cots.
Q7: Is there a significant relationship between Health Care Costs & Health Promotion Costs? Continued
Simple Linear Regression – Results
Regression Analysis: Total Health Care Expense_1 versus Total Promotion Costs
Model Summary
S R-sq R-sq(adj) R-sq(pred)
255255 91.65% 88.86% 84.55%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 8761073 852274 10.28 0.002
Total Promotion Costs 11.02 1.92 5.74 0.011 1.00
Regression Equation
Total Health Care Expense_1 = 8761073 + 11.02 Total Promotion Costs
Q7: Is there a significant relationship between Health Care Costs & Health Promotion Costs? Continued
Simple Linear Regression – Results Summary
- Based on the p-value of o.o11, there is strong evidence to show that Total Health Care Costs is strongly correlated with Health Promotion Costs in a positive relationship.
- This is captured by the high correlation coefficient (r-value) of 0.9573 (sqrt of the R2)
- The coefficient of determination (R2) is 0.9165
- Accordingly the regression model fits the data fairly well and the R2 suggests that about 91% the variability in Total Health Care Cost can be explained by Health Promotion Costs.
Q7: Is there a significant relationship between Health Care Costs & Health Promotion Costs? Continued
Simple Linear Regression – Using the model for prediction
Given the low p-value, which is less than 5%, an association/relationship between Health Care Cost and Health promotion costs has been established. Therefore the regression model can be used for future predictions.
Y = 8761073 + 11.02x
Y = Health Care Cost
X =Health Promotion Cost
Conclusion
Outcome of my tests:
Based on my two sample t-test there is evidence that there is a difference in Health Care Costs among men and women. Women cost more, which may be a result of them having a longer life expectancy and generating costs associated with childbirth. This may skew the Women’s cost compared to men.
My One-Way ANOVA tests revealed that there is statically significant evidence to show that there is some differences in Health Care Costs among different age groups, regions, types of benefits and socioeconomic statuses.
The 60-69 age group generates more Health Care Costs than any other age group, which may be a result of that the baby boomer generation has reached this age group.
The Region Hovedstaden, which is where the capital is located, generates more Health Care Costs per capita. This may be a result of the fact that this is where the University Hospital is located.
The Type of Benefit that generates more Health Care Costs is General Medical Treatment, which was not surprising given that that it contains all general medical visits.
The Pensioner and Early Retirement group was the socioeconomic group that generated most Health Care Costs, which makes sense since they belong to the 60-69 age group.
Conclusion – Continued
- The multiple and simple linear regression I ran illustrate that there is a relationship between Health Care Cost and Hospitalizations and Doctors Visits as well as between Health Care Costs and Health Promotion Costs.
Application of Results:
- Statistics play a fundamental role in showing trends such as the ones discussed in this project which are used to inform policy decisions regarding health care costs.
Sources
The main source for my project is the Dansk Statistics Bank:
http://www.dst.dk/en.aspx
http://www.statistikbanken.dk/statbank5a/default.asp?w=1280
Other Sources:
http://denmark.dk/en/quick-facts/facts/
http://pgpf.org/Chart-Archive/0006_health-care-oecd
http://www.expatindenmark.com/livingindenmark/pages/health-care.aspx
