1) Missing specifications and hidden assumptions in Medical Statistical hypotheses tests.
In this paper, we analyse the implicit hypotheses used in Medical Statistical Hypotheses Tests, that are not usually experimentally tested and we bring them to the surface. We suggest new formulations and specifications for many familiar tests.We speculate on the development of methods that could be classified as non-parametric forecasting, non-parametric regression, and non-parametric disciminant analysis. The next table gives some examples:
|
Name of The test |
Used for |
Distribution used |
Assumptions not tested, |
Additional test required |
Vague specifications |
New formulae or specifications required witch is
not the size of the sample for the power or significance level |
|
Z-test, variance known |
Comparison of means |
Normal |
Normal Population |
Test for the Normality of
Population Test for the equality of variance in the two samples version |
"Large sample" |
Minimum size of the sample
according to the accuracy level of normality |
|
Z-test, Variance unknown |
Comparison of means |
Normal |
Normal Population |
Test for theNormality of Population Test for the equality of variance in the two samples version |
"Small Sample" |
Minimum size of the sample
according to the accuracy level of normality |
|
T-tests |
Comparison of means |
Student |
Normal Population |
Test for the Normality of Population Test for the equality of variance if it is assumed in the two samples version |
"Small Sample" |
Minimum size of the sample
according to the accuracy level of normality |
|
Yate's corrected X^2 independence test |
Comparison of proportions |
X^2 |
Normal Approximation |
|
"Sufficient large sample to apply normal approximation" |
Minimum size of the sample
so as to have no error up to the accuracy level of normality approximation |
|
Signed rank (Wilcoxon) Test |
Comparison of medians |
Non-parametric |
|
|
"Sufficient Large sample to make use of the normal approximation in the central limit theorem" "Small sample", "Large sample" |
Minimum size of the sample
according to the accuracy level for the central limit theorem to apply
without error |
|
McNeamars Test |
Comparison of proportions |
X^2 |
Normal Approximation |
|
"Sufficient large sample to apply normal approximation" |
Minimum size of the sample
according to the accuracy level of normality approximation |
|
Woolf's test |
Comparison of proportions |
X^2 |
Normal Approximation |
|
"Sufficient large sample to apply normal approximation" |
Minimum size of the sample
according to the accuracy level of normality approximation |
|
Log-rank test |
Comparison of proportions |
X^2 |
Normal Approximation |
|
"Sufficient large sample to apply normal approximation" |
Minimum size of the sample
according to the accuracy level of normality approximation |
|
Sign-test |
Comparison of proportions |
Non-parametric |
|
Test for the equality of
distributions in the two samples version |
"Sufficient Large sample to make use of the normal approximation in the central limit theorem" "Small sample", "Large sample" |
Minimum size of the sample
according to the accuracy level for the central limit theorem to apply
without error |
|
Anova's F-test |
Comparison of means |
F |
Normal Population, equality of variances |
Test for the Normality of the Population. Test fo the equality of
variances |
|
Minimum size of the sample according to the accuracy level of normality |
|
|
|
|
|
|
|
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