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8 Data analysis
8.4 Analyze classes
experiment of this size, for populations that in reality have the same
mean. If the probability is small, you can conclude that the difference
is not likely to be caused by random sampling and assume instead that
the populations have different means.
CAUTION! You can display the desired statistical values for each
match in the Class Analysis Table. These values should be considered
as qualitative indications of the variations in protein expression
between two populations. To draw quantitative conclusions, you
must verify that the restrictive assumptions of the various tests are
met. In addition, one should always check the results by visual
inspection of the spots, since the conclusions may be erroneous due
to inaccuracies in detection or matching.
CAUTION! The given statistical values are useless when the samples
(classes) do not consist of more than two gels. Your objective should
always be to work with the largest possible sample sizes.
One-way ANOVA
Analysis of Variance (ANOVA) is one of the most important statistical
tests available for biologists. It is essentially an extension of the logic of
Student's t-tests to those situations where the comparison of the means
of several groups is required. Thus, when comparing two means,
ANOVA gives the same results as the t-test for independent samples.
One-way ANOVA tests the null hypothesis that all populations have
identical means. It generates a P value that answers this question: If the
null hypothesis is true, what is the probability that randomly selected
samples vary as much (or more) than actually occurred?
It is based on the same assumptions as the t-test:
•
The samples are randomly selected from, or at least representative
of, the larger populations.
•
The two samples are independent. There is no relationship
between the individuals in one sample as compared to the other.
•
The data are sampled from populations that approximate a
Gaussian distribution.
If you are not able to assume that your data are sampled from Gaussian
populations, then non-parametric tests like the Mann-Whitney or
Kolmogorov-Smirnov tests can provide a better analysis. Please note
that these test only allow you to compare two samples at the same
time.
Mann-Whitney or Wilcoxon test
The Mann-Whitney U test or rank sum test is the non-parametric
substitute for the two-sample t-test when the assumption of normality
(Gaussian bell-shaped distribution) is not valid. It is equivalent to the
Wilcoxon rank sum test. It should only be used for comparing two
unpaired samples. The assumptions of the Mann-Whitney U test are:
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Melanie User Manual Edition AC