Cancer Survival

Step 1: Graphs
Graph > Boxplot > with Groups, Graph variable=Survival, Categorical variable=Cancer

This graph uses alphabetic ordering of the cancers. Better might be to use an ordering based on "size", say based on the median survival times. Use Stat > Basic Statistics > Display Descriptive Statistics, Variable=Survival, By variables=cancer to find the ordering Stomach, Bronchus, Colon, Ovary and Breast. Click on C2-T, choose Editor > Column > Value Order, User-specified order. Draw the boxplot again to get

Graph > Boxplot > with Groups, Graph variable=Survival, Categorical variable=Cancer

There are a number of outliers, so maybe we should try a transformation. Calc > Calculator, Store in Sqrt(Survival), Expression: SQRT('Survival'). Again draw the boxplot:
Graph > Boxplot > with Groups, Graph variable=Sqrt(Survival), Categorical variable=Cancer

which looks much better. (Try the log transform, it does not give a better result)
So now we use Sqrt(Survival) for the rest of the analysis.

Step 2: Summary Statistics
Stat > Basic Statistics > Display Descriptive Statistics, Variable=Survival, By variables=cancer, Statistics > check IQR
Because we used a transformation we can use one of two tables:
1) Mean and STD of transformed data
SQRT(Survival)
Groups n Mean std
Bronchus 17 13.21 6.29
Stomach 13 14.39 9.25
Colon 17 19.63 8.75
Ovary 6 25.58 16.62
Breast 11 33.20 17.98

2) Median and iqr/1.35 of original data
Survival
Groups n Median IQR/1.35
Stomach 13 124 266
Bronchus 17 155 131
Colon 17 372 255
Ovary 6 406 1107
Breast 11 1166 804


Stat > ANOVA > Oneway, Response=Sqrt(Survival), Factor=Cancer, Graphs > Residual vs. Fits Plot and Normal Plot


both plots look ok, no problems with the assumptions, the transformations have worked

 

Step 3: Hypothesis Test

1) α=0.05
2) H0: α1 = .. = α5=0 (no difference in the mean survival times of different cancers)
3) Ha: αi≠0 for some i (some differences in the mean survival times of different cancers)
4) p-value=0.000 < α
5) We reject H0, there are some differences in the mean survival times of different cancers

Step 4: Multiple Comparison
Stat > ANOVA > Oneway, Response=Sqrt(Survival), Factor=Cancer, Comparisons > check Tukey

Bronchus Stomach Colon Ovary Breast
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      ____________

Interpretation: There is a stat. signif. difference between the mean survival times of Breast cancer and Stomach, Bronchus and Colon cancers. Other differences are not stat. signif., at least not at these sample sizes.