Extracting Seasonality and Trend from Data: Decomposition Using R

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Uma excelente descrição da decomposição clássica com Python e R.

Time series decomposition works by splitting a time series into three components: seasonality, trends and random fluctiation. To show how this works, we will study the decompose( ) and STL( ) functions in the R language.

Understanding Decomposition

Decompose One Time Series into Multiple Series

Time series decomposition is a mathematical procedure which transforms a time series into multiple different time series. The original time series is often split into 3 component series:

  • Seasonal: Patterns that repeat with a fixed period of time. For example, a website might receive more visits during weekends; this would produce data with a seasonality of 7 days.
  • Trend: The underlying trend of the metrics. A website increasing in popularity should show a general trend that goes up.
  • Random: Also call “noise”, “irregular” or “remainder,” this is the residuals of the original time series after the seasonal and trend series are removed.

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Controlling for test variables

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alguns apontamentos sobre testes com vars de controlo

3.2  Three (or more) variables

[Page last updated 3 August 2016]

Introducing a third variable. Controlling for test variables. Elaboration.

Logical model is X Y . T (the effect of X on Y controlling for T) where:

Y = Dependent variable
X = Independent variable
T = Test variable(s)

3.2.1 Elaboration

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INTRODUCTORY STATISTICS book

http://www.psychstat.missouristate.edu/IntroBook3/sbk.htm

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Um webBook sobre estatística com exercícios e exemplos em SPSS

INTRODUCTORY STATISTICS:
CONCEPTS, MODELS, AND APPLICATIONS

3rd Web Edition

David W. Stockburger

Missouri State University

@Copyright 2013 by David W. Stockburger

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Research Methods Knowledge Base

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Um webBook pensado para investigadores sobre temas de estatística

What is the Research Methods Knowledge Base?

The Research Methods Knowledge Base is a comprehensive web-based textbook that addresses all of the topics in a typical introductory undergraduate or graduate course in social research methods.  It covers the entire research process including: formulating research questions; sampling (probability and nonprobability); measurement (surveys, scaling, qualitative, unobtrusive); research design (experimental and quasi-experimental); data analysis; and, writing the research paper.  It also addresses the major theoretical and philosophical underpinnings of research including: the idea of validity in research; reliability of measures; and ethics.  The Knowledge Base was designed to be different from the many typical commercially-available research methods texts.  It uses an informal, conversational style to engage both the newcomer and the more experienced student of research.  It is a fully hyperlinked text that can be integrated easily into an existing course structure or used as a sourcebook for the experienced researcher who simply wants to browse.

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A New View of Statistics

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Um webBook com montes de temas bem explicados

Mar 2013. Coming very soon: a slideshow and Excel workbook for an introductory course of 10 lectures on statistics. Aug 2011. Check out the following 2010 articles at Sportscience: assigning subjects to treatments in a controlled trial; regression vs limits of agreement in measure-comparison studies; magnitudes of effects derived from linear models. See the frame at right for links to much more, including the progressive statistics and research design articles. Previous updates…
New original approaches to statistics for researchers: the examples are taken from exercise and sport science, but the principles apply to all empirical sciences. Read more in the preface.
Feedback wanted: if you can’t understand something here, it’s my fault. Email me.
Become a license holder…eventually! Not yet. More…
Full Contents
Short Contents:
Preface: About These Pages
Summarizing Data
Simple Statistics & Effect Statistics
Dimension Reduction
Precision of Measurement
Generalizing to a Population
Confidence Limits & Statistical Significance
Statistical Models
Estimating Sample Size
Summary: The Most Important Points
Quiz
Reference: Hopkins, W. G. (2000). A new view of statistics. Internet Society for Sport Science: http://www.sportsci.org/resource/stats/.

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Probability and statistics EBook

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Um bom ebook com boas animações

SOCR Books: This is a General Statistics Curriculum E-Book, which includes Advanced-Placement (AP) materials.

Contents

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Seeing Statistics

clique na imagem para seguir o linkUma excelente maneira de aprender estatística com um webBook dinâmico e muito visual

Seeing Statistics ® is a new approach to teaching statistics using the World Wide Web. This webbook is based on three premises:

  • The important principles of statistics are remarkably easy if they can be seen.
  • Active involvement of the student facilitates learning.
  • Statistics can be fun!

Most of the graphs and figures in this textbook are dynamic and under the  control of the reader. Interacting with the graphs allows you to see the important statistical principles in action.

Rather than talk about it, it is best to view Seeing Statistics in action. To access Seeing Statistics, click on the “Enter Seeing Statistics” button to begin your exploration of Seeing Statistics!

Table of Contents
0. Introduction

1. Data & Comparisons

2. Seeing Data

3. Describing the Center

4. Describing the Spread

5. Seeing Data, Again

6. Probability

7. Normal Distribution
7. Outline

7.0 Introduction

7.1 Origins of Normal

7.2 Size and Shape

7.3 Working with the Normal

7.4 Means have Normal Distributions

7.5 Evaluating Normality (optional)

7.6 Review

7.7 Exercises


8. Inference & Confidence

9. One-Sample Comparisons

10. Two-Sample Comparisons

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Chance Lecture Video Series

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Bons vídeos ainda q antigos de alguns temas em probabilidade e estatística

This page has links to:

  • 2000 Chance Lecture Video Series
  • 1998 Chance Lecture Video Series
  • 1997 Chance Lecture Video Series
  • Chance Workshop Video Lectures
  • Other Videos
  • Audios
  • The talks featured below require the latest version of the Realplayer software. More particularly, they require that the “Realplayer plug-in” be installed in the plug-ins folder of your browser. If you do not have the “Realplayer plug-in,” a free version of Realplayer (which includes the plug-in) is available here

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    Science Isn’t Broken

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    Um bom blog com discussões interessantes e ilustrações muito boas

    The Scientific Method 7:00 AM Aug 19, 2015

    Science Isn’t Broken

    It’s just a hell of a lot harder than we give it credit for.

    By

    Graphics by Ritchie King

    If you follow the headlines, your confidence in science may have taken a hit lately.

    Peer review? More like self-review. An investigation in November uncovered a scam in which researchers were rubber-stamping their own work, circumventing peer review at five high-profile publishers.

    Hack Your Way To Scientific Glory

    You’re a social scientist with a hunch: The U.S. economy is affected by whether Republicans or Democrats are in office. Try to show that a connection exists, using real data going back to 1948. For your results to be publishable in an academic journal, you’ll need to prove that they are “statistically significant” by achieving a low enough p-value.
    “Science is great, but it’s low-yield. Most experiments fail. That doesn’t mean the challenge isn’t worth it, but we can’t expect every dollar to turn a positive result. Most of the things you try don’t work out — that’s just the nature of the process.”

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    visualização do intervalo de confiança

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    Boa forma de visualizar o conceito de Intervalo de Confiança Aleatório.

    About the visualization

    Some say that a shift from hypothesis testing to confidence intervals and estimation will lead to fewer statistical misinterpretations. Personally, I am not sure about that. But I agree with the sentiment that we should stop reducing statistical analysis to binary decision-making. The problem with CIs is that they are as unintuitive and as misunderstood p-values and null hypothesis significance testing. Moreover, CIs are often used to perform hypothesis tests and are therefore prone to the same misuses as p-values.

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