1. Tests
1.1. Tests of independance: H0 : A et B indép.
1.1.1. Chi-2
1.1.1.1. n>5
1.1.2. Fisher
1.1.3. ≠
1.2. "Goodness of "Fit tests
1.2.1. test d'ajustement d'une distribution observée avec une loi de distribution théorique.
1.2.2. Chi-2
1.2.2.1. loi binomiale , loi de poisson, loi normale
1.3. Regression tests
1.4. Comparison tests
1.5. Correlation tests
2. Concepts
2.1. exact test or "non paramectric"
2.2. Degrees of Freedom
2.2.1. refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample and are essential for assessing the importance and the validity of the null hypothesis.
2.3. contigency table
2.3.1. also "called crosstabs" or " two-way tables" def: used in statistics to summarize the relationship between several categorical variables. A contingency table is a special type of frequency distribution table, where two variables are shown simultaneously.
2.4. critical value
2.4.1. point (or points) on the scale of the test statistic beyond which we reject the null hypothesis, and, is derived from the level of significance α of the test.
2.4.2. Critical value can tell us, what is the probability of 2 sample means belonging to the same distribution. Higher, the critical value means lower the probability of 2 samples belonging to same distribution. The general critical value for a two-tailed test is 1.96, which is based on the fact that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean. If the test statistic is lower than the critical value, accept the hypothesis or else reject the hypothesis.
2.4.3. Critical values can be used to do hypothesis testing in following way 1. Calculate test statistic 2. Calculate critical values based on significance level alpha 3. Compare test statistic with critical values.
2.4.4. The determination of distribution type is necessary to determine the critical value and test to be chosen to validate any hypothesis
2.5. central limit theorem
2.5.1. n>30
3. sources
3.1. Statistical tests: which one should you use?
3.2. https://www.statisticssolutions.com/the-various-forms-of-anova/?__cf_chl_jschl_tk__=pmd_hvmtaXt6Q_OSGQjx3Xnx.bl6MLruDCzMnG3xcMEMyhs-1629260081-0-gqNtZGzNAfujcnBszQjR
3.3. Statistical Soup: ANOVA, ANCOVA, MANOVA, & MANCOVA — Stats Make Me Cry Consulting
4. Use of proper statistical techniques for research studies with small samples Charity J. Morgan
5. small dataset
5.1. comparison tests
5.1.1. Categorical data
5.1.1.1. n>5
5.1.1.1.1. Chi-2
5.1.1.2. n<5
5.1.1.2.1. Exact test of Fisher
5.1.2. Continuous data
5.1.2.1. to compare means of 2 or more groups
5.1.2.1.1. 2 samples t-test https://www.reneshbedre.com/blog/ttest.html unequal var ex --> https://www.theopeneducator.com/doe/hypothesis-Testing-Inferential-Statistics-Analysis-of-Variance-ANOVA/Two-Sample-T-Test-Unequal-Variance
5.1.2.1.2. ANOVA
6. non-parametric tests
7. count data
7.1. loi de Poisson
7.1.1. "it expresses the prob. of a number of events occuring in a fixed period of time if these events occur with a known average rate and are independent of the time since the last event"
7.1.2. "loi des évènements rares"
7.1.2.1. Data Analysis Examples
7.1.2.2. http://irma.math.unistra.fr/~delzant/coursproba4.pdf
7.1.3. "seule loi connue dont l'espérance = sa variance