Statistics and biostatistics are treated under a biological and practical issue, it is necessary to avoid the excess of theory and to make a practical approach supported by biological applications (including in the probability concept).
Statistics is a necessary tool for research, scientific publications, memories and theses.
It is to note that the purpose of this material is to know how to manipulate the statistical tests (chap. 9, 10, 11 and 12) and as a result to know how to apply them in biological problems.
Chapter 1: Population and characters
- Definition of statistics and descriptive statistics
- Population and sample
- Statistical variables: qualitative variable, discrete variable, continuous variable, census and sampling.
Chapter 2: Frequency distribution
- Arrange the data in a table
- Frequency and relative frequency
- Most used Graphs : line diagram and histogram
- Cumulative frequency, cumulative relative frequency and corresponding graphs
- Cumulative distribution function and ascending cumulative curve.
Chapter 3: Characteristics parameters of a frequency distribution
- First and third quartile
- Variance et standard deviation
Chapter 4: Correlation and linear regression
- graphic illustration of possible link which can exist between two quantitative variables
- Definition et interpretation of the covariance
- Determination of the linear regression line by the method of ordinary mean square error.
- Definition and properties of linear correlation coefficient.
Chapter 5: Elements of combinatory analysis
- Definitions and properties of the arrangement, permutation and combination.
Chapter 6: Probability
- Definitions et properties of the probability of an event
- Conditional probability
- Independent event, mutually exclusive events.
- BAYES’s theorem.
Chapter 7: Usually distribution and numerical tables
- Discrete random variable and continuous random variable.
- Binomial distribution
- Poisson distribution
- Normal distribution
- Special continuous distributions
- The Use of the numerical tables
Chapter 8: Estimation
- The need to estimate
- Student distribution
- Point estimation of percentage, mean and variance
- Confidence interval of percentage, mean and variance.
Chapter 9: χ2 (chi square) test
- conformity Test of
- contingency table
Chapter 10: parametric tests
- The risk criteria in a practical example.
- Comparison of two independent samples (small and large sample)
- Comparison of two variances (Fisher’s test)
- Comparison of two paired samples (small and large sample)
- Comparison of observed mean to a value of reference (small and large sample)
- Comparison of two proportions
- Comparison of observed proportion to a reference one
- Pearson’s correlation test
- the p-value criteria
- multiple regression
Chapter 11: Analysis of Variance (case of one factor – case of 2 factors without repetition)
- Comparison of many samples with a Normal distribution
Chapter 12: non parametric Tests
- The Mann Whitney ‘s Test for two independent samples
- The Wilcoxon ‘s Test for two paired samples
- The Kruskall- Wallis’s Test for many independent samples
- Spearman’s rank correlation Test.