Analysis of variance (ANOVA) can take care of this. The total sum of squares is partitioned into a between group sum of squares and a within group sum of squares . Their degrees of freedom are 1 and n-2 respectively where n is the total sample size (for both groups). Comparison of the groups may be done by the between group F and within group or error effect is measured by the corresponding F statistic.
Which statistical test should be used within same group and within two group in clinical study?
Comparison of units of an ensemble
- You will use tests for related samples, if You excute 2 experiments with the same objects. This is the TOTE scheme of programming: test - operation - test exit. Example: unit without exposition - same unit after exposition. The time course is in succession.
- And You will use tests for unrelated samples, if You choose two samples of the universe. This is a parallel loop with one switch on and one switch off. Example: unit with exposition and unit witout exposition. The time course is concurrent.
Decision making
MPW
You didn't mention about the type of data involved.
Continuous data:
If between 2 groups: Student's T test (normal distribution) and Mann Whitney U (skewed distribution).
More than 2 groups: ANOVA (normal distribution) and Kruskal Wallis H (skewed distribution).
Categorical data:
Pearson's chi-square test
Type of data for comparison of 2 samples
Thank You so much for Your hints about the clinical usual choice of preferred tests. This lightens practice.
"The assumptions underlying a t-test are that
- X follows a normal distribution with mean μ and variance σ2
- ps2 follows a χ2 distribution with p degrees of freedom under the null hypothesis, where p is a positive constant
- Z and s are independent."
Certainly the categorial nature of original data decides about the choice of appropriate tests. The 3 x 2- matrix above gives a comprehensible scheme for selecting tests with few assumptions. Perhaps this enlightens the knowledge seeker.
MPW
within group at 2 different times {assuming the DV is interval or ratio and normally distributed} you need to use paired sample ttest.
between 2 groups with the same assumptions for the variable above, you need to use Independent sample ttest.
if the assumptions violated, you have to use Wilcoxon rank sum test or Mann-Whitney Utest.
If the groups are Independent then
If between 2 groups: Student's T test (normal distribution) and Mann Whitney U (skewed distribution).
More than 2 groups: ANOVA (normal distribution) and Kruskal Wallis H (skewed distribution).
If the Groups are related
then for 2 groups : Paired t test (Normal distribution) and Wilcoxon Sign rank sum test ( Skewed distribution)
More than two groups : Repeated measures of Anova (Normal distribution)
The best test is worthless when you don't understand what the test actually does and what the result actually tells you.
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