Statistical Analysis

Code:

CN32003

Acronym:

ANEST

Keywords
Classification	Keyword
OFICIAL	Physical Sciences

Instance: 2020/2021 - 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	102	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	0,00
Trabalho prático ou de projeto	30,00
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

To pass at this chair, he/she must obtain at least 8.0 points (out of 20) in the group work and in the written evaluation and a final grade of at least 9.5 (out ot 20).

In case of repetition of this chair, the final grade will be computed having in consideration their best grade, among this academic year and the two previous ones, regarding the group grade and regarding the participation grade.

Calculation formula of final grade

The evaluation of the participation, synchronous or assynchronous, of each student P, between -2 and 2, is computed in the following way:

P = sum(ai) / ns , where ns is the number of teaching weeks of the semester and ai is the evaluation of the participation between -2 and 2.

 

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Students will do, along the semester, a group work that will be evaluated by an oral presentation in the end of the semester. 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 this classification it will be added an ammount, positive or negative, regarding the individual performance.
To be approved, the individual classification of the group work G will have to be greater than or equal to 8.0 out of 20.
This component will not be assessed in the Recourse Period.

 

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Students that have obtained at least 8.0 (out of 20) in the individual classification of the group work may do the written evaluation E. This evaluation 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.

 

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The quantity X, between 0 and 20, computed without the participation, is obtained by considering the written classification with weight 70% and the individual classification of the group work with weight 30%:
X = 0.7 * E + 0.3 * G.

 

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In order to compute the bonus due to the participation, it is necessary to compute the proportion of the difference D betwen the quantity X and 20, a value between 0 and 1.

	{ (20 - X) / 10	if P>0  and  X>10
D =	{
	{ 1	if P≤0  or  X≤10

 

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

	{ X + P * D	if E≥8.0 and  G≥8.0
F =	{
	{ min(E; G)	if Eor  G<8.0

Therefore, in case the participation has the maximum value of 2 points, the bonus shall correspond to a quantity between 0 and 2 (out of 20), proportional to D. In the event of a negative value of the participation, the final grade shall be less than the quantity X.

Special assessment (TE, DA, ...)

Students that are not enrolled in Public Health Nutrition will have access to a database in order to do their group work.

Classification improvement

The improvement of classification will only focus on the classification of the final exam E, with 70% weight.

Observations

The support schedule will be defined and disclosed as soon as possible. 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.

In the presential 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.

It will not be registered the absence to theoretical, theoretical-practical nor laboratorial practice classes.

According to the Rector Order GR.06 / 12/2017, Article 12, point e), students are not allowed to capture images or sound of the school activities.