Statistical Analysis

Code:

CN32003

Acronym:

ANEST

Keywords
Classification	Keyword
OFICIAL	Physical Sciences

Instance: 2017/2018 - 2S

Active?	Yes
Course/CS Responsible:	Nutrition Sciences

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
CNUP	80	Plano oficial	3	-	4	42	108

Teaching language

Portuguese

Objectives

In the end of the semester, the students should be aware of the importance of statistics in the scientific investigation and should be able to build hypothesis and to apply the adequate statistical tests.
The course has the objective of motivating the students to make a critical analysis of the statistical tools used in studies made by them or by others.
For such, the students should be able to use different point estimators and interval estimators.
The students should be able to formulate the null hypothesis and the alternative hypothesis, according to the analysis they intend to do. Furthermore, the students should be able to do the appropriate hypothesis testing.
The students should be able to compute and interpret simple and multiple linear regressions and do the same in the case of logistic regressions.

Learning outcomes and competences

Awareness of the importance of statistics in the scientific investigation;

Ability to build hypothesis and to apply the adequate statistical tests;

Ability of critical analysis of the statistical tools used in studies made by them or by others;

Ability to use different point estimators and interval estimators;

Ability to formulate the null hypothesis and the alternative hypothesis, according to the intended analysis;

Ability of appropriate hypothesis testing;

Ability to compute and interpret simple and multiple linear regressions and logistic regressions.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Students should possess the competences of Biostatistics from the 1st year of the First Degree in Nutrition Sciences.

Program

1 Revision of concepts about the study of samples:
a) Notion of statistic and sampling distribution;
b) Distribution of the sampling mean and variance.
2 Estimators:
a) Notions and properties;
b) Point estimators for the mean and variance;
c) Interval estimators - confidence interval for normally distributed populations:
(i) For the mean - application of the standardized Normal distribution and the t-Student distribution; 
(ii) For the difference of means (between two paired samples and between two independent samples) - application of the standardized Normal and the t-Student distributions;
(iii) For the variance - application of the chi-square distribution.
d) Interval estimators - confidence interval for non normally distributed populations:
(i) Continuity correction;
(ii) Application of the Central Limit Theorem (for large samples);
(iii) Application of the Chebyshev inequality (for small samples);
(iv) Application of the Hypergeometric, Binomial and Poisson distributions and their approximations.
3 Bilateral hypothesis testing:
a) Null hypothesis and alternative hypothesis;
b) Error of type I and error of type II;
c) Significance level, power of the test;
d) Rejection region and acceptance region;
e) Test statistic and its distribution.
4 Application of some statistical tests:
a) Kolmogorov-Smirnov and Shapiro-Wilk for the Normality of a distribution;
b) z for the mean of one sample, for two paired samples and for two independent samples;
c) t-Student for the mean of one sample, for two paired samples and for two independent samples;
d) Chi-square for the variance;
e) F-Snedecor for the ratio of variances;
f) ANOVA for the means of three or more independent samples;
g) Wilcoxon for the mean ranks of two paired samples;
h) Friedman for the mean ranks of three or more paired samples;
i) Mann-Whitney for the mean ranks of two independent samples;
j) Kruskal-Wallis for the mean ranks of three or more independent samples;
k) Chi-square tests for homogeneity and for independence.
5 Linear regression analysis and logistic regression analysis.

Mandatory literature

Daniel Wayne W.; Biostatistics. ISBN: 0-471-16386-4
Guimarães Rui Campos; Estatística. ISBN: 972-8298-45-5

Complementary Bibliography

Clegg Frances; Estatística para todos. ISBN: 972-662-411-8

Teaching methods and learning activities

Theoretic classes (1h00/week): expository and interrogative method.
Theoretic-practical classes (1h00/week): interrogative and demonstrative method, with the resolution of exercises.
Laboratory classes: (1h00/week): interrogative and demonstrative method, with the resolution of exercises in a computer.

Software

R (software de estatística)
Excel
SPSS

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Statistics > Medical statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Participação presencial	10,00
Trabalho prático ou de projeto	20,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	33,00
Frequência das aulas	42,00
Trabalho de investigação	33,00
Total:	108,00

Eligibility for exams

For a student (in the ordinary regimen) to be eligible for exam at Bioestatistics, he/she must not have more than the legal limit of missed classes (without proper justification) nor he/she may have a presencial grade below 9.5 points (out of 20). To pass at this chair, he/she must obtain at least 8.0 points (out of 20) in the group work and in each test or in the the final exam), and a final grade of at least 9.5 points (out of 20).

Students eligible for the Statistical Analysis exams in one of the two previous academic years can be dispensed from classes. Their final grade will be computed having in consideration their best practical classes grade in this academic year and the two previous ones.

Calculation formula of final grade

The presencial grade of the practical classes of each student depends on two parameters: his/her participation, and his/her assiduity.

The evaluation of the classes in which the student was present A, between 0 and 20, is computed in the following way:

A = 10 + np/Na + (nap + 2 * sum(ai) / am) * 2 / Na , where np is the number of classes in which the student was present, Na is the number of classes in the semester, nap is the number of classes with positive participation, ai is the evaluation of the participation in each class, and am is the maximum grade of the class evaluation.


The presencial grade AP, between 0 and 20, results from the application of the penalization for each unjustified missed class. It is computed by the expression:

AP = 0.5 * (2 - pf - pf^2) * A , where  pf is the proportion, between 0 and 1, of unjustified missed classes in the semester.
To obtain frequency, the presencial grade AP must be greater than or equal to 9.5.

Students will do a group work that will be evaluated by an oral presentation. The classifications G, betwen 0 and 20, have in consideration the following items:
- Dificulty of the statistical techniques (25%);
- Scientific correction (25%);
- Deepness and critical analysis in the Nutrition Sciences (25%);
- Presentation quality (25%).
To be approved, the classification of the group work G will have to be greater than or equal to 8.0 out of 20.

The final practical grade P will be computed in the following way:

	{ (AP + 2 * G) / 3	if AP≥9.5 and G≥8.0
P =	{
	{ min(AP,G)	if APor G<8.0

To be approved, it is necessary that the students have a practical classes grade P≥9.5 (except if they are dispensed from the practical classes).



The written evaluation E has to be above 8.0 out of 20 and may be obtained from the exam in the Normal Period or in the Recourse Period. There may still exist the possibility of the written evaluation being done through two tests. For that to happen, it is necessary that at least 20 students register. On this assumption, the students that wish it, may take two tests (each with a minimum grade of 8.0 out of 20), instead of taking the exam in the Normal Period. In case they take the first test, they will not be allowed to take the exam in the Normal Period.

The students that take the tests will have a written grade E in the Normal Period, between 0 and 20, computed in the following way:

	{ 0.5 * T1 + 0.5 * T2	if T1≥8.0 and T2≥8.0
E =	{
	{ min(T1,T2)	if T1or T2<8.0

where T₁ and T₂ represent the grade obtained in each test.

For the students that take the exam, the written grade E will be the exam grade.

The final grade F, between 0 and 20, is computed in the following way:

	{ 0.7 * E + 0.3 * P	if P>E  and  E≥8.0
F =	{
	{ E	if P≤E  or  E<8.0

Therefore, if the practical grade is greater than or equal to the written grade, the final grade will be the weighted average of the written grade E, with a weight of 70%, the presencial grade AP, with a weight of 10% and the group work grade G, with a weight of 20%.

In the written evaluation, the answers must be written in blue or black ink in the given sheets. It will not be allowed the use of corrective (white) ink. Scientific calculators will be allowed, provided they have not the ability of plotting graphs and are not programmable. Furthermore, it will not be allowed the use of equipment with the ability of remote communication.

Special assessment (TE, DA, ...)

Students may request, until the end of March, excuse from attending the classes (TP and PL). For the students that were excused, the final grade will be the written exam grade.

Observations

The support schedule agreed with the students is the following:
- Wednesday, from 17h00 to 20h00, Bruno Oliveira, room B339;
- Friday, 45min from 09h00 to 09h30 or from 11h00 to 11h30, Rui Poínhos, room B340.

To avoid periods of large affluence of students, we ask to schedule personally or by email up to the beginning of the afternoon of the previous weekday.

The support schedule during the examination period will be 5h15 before the exam of the Normal period and 4h30 before the exam of the Recouse period. The support schedule will be arranged after the publication of the exam calendar and will be available inside the Documents of Statistical Analysis.

According to the Rector's Order GR.06/12/2017, Article 12, letter e), we inform that students are not allowed to capture images or sound during classes.