# Statistical Analysis

EMBC+ MODULE 2: Toolbox for investigating marine Biodiversity
semester:
1
ects:
6

The course consists of three modules:
Module 1: Introduction to Statistics,
Module 2: Using R for basic statistics,
Module 3: Design and Analysis of Experiments).

Students must choose two out of three modules only.

Module 1 - Introduction to statistics
Basic statistical concepts, sampling distributions, point estimation, confidence intervals, tests of hypotheses and simple linear regression.
Module 2 – Using R for basic statistics
Basics of working with R : Introduction to the R environment. Simple manipulations, numbers, vectors, matrices and data frames.
Graphical procedures: the plot function, high-level graphics functions.
Univariate distributions using R: Binomial, Poisson, Normal, t-Student, Chi-Square, F distribution.
Hypothesis testing using R:
-Parametric tests: one sample t-test, two samples t-test, paired t-test, comparing variances.
-Non-parametric tests: Wilcoxon tests, Chi-square tests, Fisher exact test, Kruskal-Wallis Test.
Performing ANOVA using R: the ANOVA table, pairwise comparations.
Regression analysis using R: correlation test, fitting the regression model, testing the regression model.
Module 3 - Design and Analysis of Experiments
Analysis of Variance: Analysis of the Fixed Effects Model; Model Adequacy Checking; Practical Interpretation of Results; Determining Sample Size; The Random Effects Model; Nonparametric Methods in the Analysis of Variance: The Kruskal-Wallis Test.
Experiments with Blocking Factors: The Randomized Complete Block Design; Model Adequacy checking; The Latin Square Design; The Graeco-Latin Square Design.
Factorial Experiments: Basic Definitions and Principles; The Advantage of Factorials; The Two-Factor Factorial Design; Statistical Analysis of the Fixed Effects Model; Model Adequacy Checking; Estimation Model Parameters; Choice of Sample Size; The Assumption of No-Interaction in a Two factor Model; One Observation per cell.
Regression Modeling: Linear Regression Models; Estimation of the Parameters in Linear Regression Models; Hypothesis Testing in Multiple Regression; Confidence Intervals in Multiple Regression; Prediction of New Response Observations; Regression Model Diagnostics.
Other topics: Nested Design and Repeated Measures

keywords:
Statistical infernence R Design and Analyis of Experiments
initial:

Module 1: For students with knowledge of elementary calculus.
Module 2: For students who have had an introductory statistics course.
Module 3: For students who have completed a first course in statistical methods: descriptive statistics, standard sampling distributions, and basic concepts of confidence intervals and hypothesis testing for means and variances.
For students who have completed a first course in statistical methods: descriptive statistics, standard sampling distributions, and basic concepts of confidence intervals and hypothesis testing for means and variances.

final:

Module 1: The student will be able to apply the main statistical inference methods for drawing conclusions from a data set.
Module 2: The student will be able to use R for graphical exploration of data, and to carry out statistical tests.
Module 3: The student will be able to design and analyse experiments in life sciences. The emphasis is on understanding some of the most important statistical methods rather than surveying many techniques in a superficial manner. The student will be able to use statistic software to carry out the analyse.