Metainformation
| Tag | Value |
|---|---|
| file | Inferential_Statistics_vufsw-onewayanova-0255-en_vufsw-onewayanova-0255-en |
| name | vufsw-onewayanova-0255-en |
| section | inferential statistics/parametric techniques/anova/oneway anova |
| type | num |
| solution | 0.5 |
| tolerance | 0 |
| Type | calculation |
| Program | calculator |
| Language | English |
| Level | statistical thinking |
Question
In the Netherlands, municipalities are partly allowed to determine the distribution of their health care expenses.
Two municipalities (‘gemeente A’ and ‘gemeente B’) wondered how satisfied residents are with the care they receive from the municipality (on a scale of 1, very dissatisfied to 10, very satisfied) and put this question to a number of respondents. Below are the results of the survey.
The null hypothesis is that there is no difference in satisfaction between the two municipalities and perform an ANOVA for this.
Calculate the Sum of Squares Model (SSM) based on the above data. Round to one decimal place
Solution
gemeente A score tevredenheid (schaal van 0 tot 10)
respondent 1 7 0,75 0,5625
respondent 2 6 -0,25 0,0625
respondent 3 5 -1,25 1,5625
respondent 4 7 0,75 0,5625
gemeente B
respondent 5 6 0,25 0,0625
respondent 6 4 -1,75 3,0625
respondent 7 5 -0,75 0,5625
respondent 8 8 2,25 5,0625
totaal gemiddelde= 6
Total sum of squares= Σ(Y-Ῡ)²
Model sum of squares=Σnk*(Ῡk-Ῡ)²
Residual sum of
squares=Σ(Y-Ῡk)²=(4-5)²+(5-5)²+(6-5)²+(6-6)²+(3-6)²+(9-6)²=20
Mean square model= MSS/dfm
Mean square residual= RSS/dfr=20/4=5
F=MSM/MSR
gemeente A 6,25 SSm 0,5
gemeente B 5,75 SSr 11,5
MSM 0,5/1=0,5
RSS 11,5/6=1,916667
F= 0,5/1,916667=0,261 a very small F so probably not
significant