Quantitative Data Analysis
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2. Graphing Distributions
2. Graphing Distributions A. Qualitative Variables B. Quantitative Variables 1. Stem and Leaf Displays 2. Histograms 3. Frequency Polygons 4. Box Plots 5. Bar Charts 6. Line Graphs 7. Dot Plots C. Exercises Graphing data is the first and often most important step in data analysis. In this day of computers, researchers all too often see only the results of complex computer analyses without ever taking a close look at the data themselves. This is all the more unfortunate because computers can create many types of graphs quickly and easily. This chapter covers some classic types of graphs such bar charts that were invented by William Playfair in the 18th century as well as graphs such as box plots invented by John Tukey in the 20th century. 65 by David M. Lane Prerequisites • Chapter 1: Variables Learning Objectives 1. Create a frequency table 2. Determine when pie charts are valuable and when they are not 3. Create and interpret bar charts 4. Identify common graphical mistakes When Apple Computer introduced the iMac computer in August 1998, the company wanted to learn whether the iMac was expanding Apple’s market share. Was the iMac just attracting previous Macintosh owners? Or was it purchased by newcomers to the computer market and by previous Windows users who were switching over? To find out, 500 iMac customers were interviewed. Each customer was categorized as a previous Macintosh owner, a previous Windows owner, or a new computer purchaser. This section examines graphical methods for displaying the results of the interviews. We’ll learn some general lessons about how to graph data that fall into a small number of categories. -
Chapter 16.Tst
Chapter 16 Statistical Quality Control- Prof. Dr. Samir Safi TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Statistical process control uses regression and other forecasting tools to help control processes. 1) 2) It is impossible to develop a process that has zero variability. 2) 3) If all of the control points on a control chart lie between the UCL and the LCL, the process is always 3) in control. 4) An x-bar chart would be appropriate to monitor the number of defects in a production lot. 4) 5) The central limit theorem provides the statistical foundation for control charts. 5) 6) If we are tracking quality of performance for a class of students, we should plot the individual 6) grades on an x-bar chart, and the pass/fail result on a p-chart. 7) A p-chart could be used to monitor the average weight of cereal boxes. 7) 8) If we are attempting to control the diameter of bowling bowls, we will find a p-chart to be quite 8) helpful. 9) A c-chart would be appropriate to monitor the number of weld defects on the steel plates of a 9) ship's hull. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following is not a popular definition of quality? 1) A) Quality is fitness for use. B) Quality is the totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs. -
Section 2.2: Bar Charts and Pie Charts
Section 2.2: Bar Charts and Pie Charts 1 Raw Data is Ugly Graphical representations of data always look pretty in newspapers, magazines and books. What you haven’tseen is the blood, sweat and tears that it some- times takes to get those results. http://seatgeek.com/blog/mlb/5-useful-charts-for-baseball-fans-mlb-ticket-prices- by-day-time 1 Google listing for Ru San’sKennesaw location 2 The previous examples are informative graphical displays of data. They all started life as bland data sets. 2 Bar Charts Bar charts are a visual way to organize data. The height or length of a bar rep- resents the number of points of data (frequency distribution) in a particular category. One can also let the bar represent the percentage of data (relative frequency distribution) in a category. Example 1 From (http://vgsales.wikia.com/wiki/Halo) consider the sales …g- ures for Microsoft’s videogame franchise, Halo. Here is the raw data. Year Game Units Sold (in millions) 2001 Halo: Combat Evolved 5.5 2004 Halo 2 8 2007 Halo 3 12.06 2009 Halo Wars 2.54 2009 Halo 3: ODST 6.32 2010 Halo: Reach 9.76 2011 Halo: Combat Evolved Anniversary 2.37 2012 Halo 4 9.52 2014 Halo: The Master Chief Collection 2.61 2015 Halo 5 5 Let’s construct a bar chart based on units sold. Translating frequencies into relative frequencies is an easy process. A rela- tive frequency is the frequency divided by total number of data points. Example 2 Create a relative frequency chart for Halo games. -
Bar Charts and Box Plots Normal Poisson Exponential Creating a Simple Yet Effective Plot Requires an 02468 C 1.0 Exponential Uniform Understanding of Data and Tasks
THIS MONTH a Uniform POINTS OF VIEW Normal Poisson Exponential 02468 b Uniform Bar charts and box plots Normal Poisson Exponential Creating a simple yet effective plot requires an 02468 c 1.0 Exponential Uniform understanding of data and tasks. λ = 1 Min = 5.5 Normal Max = 6.5 0.5 Poisson σμ= 1, = 5 μ = 2 Bar charts and box plots are omnipresent in the scientific literature. 0 02468 They are typically used to visualize quantities associated with a set of Figure 2 | Representation of four distributions with bar charts and box plots. items. Representing the data accurately, however, requires choosing (a) Bar chart showing sample means (n = 1,000) with standard-deviation the appropriate plot according to the nature of the data and the task at error bars. (b) Box plot (n = 1,000) with whiskers extending to ±1.5 × IQR. hand. Bar charts are appropriate for counts, whereas box plots should (c) Probability density functions of the distributions in a and b. λ, rate; be used to represent the characteristics of a distribution. µ, mean; σ, standard deviation. Bar charts encode quantities by length, which is a highly accurate visual encoding and preferred over the angle-based strategy used in to represent such uncertainty. However, because the bars always start pie charts (Fig. 1a). Often the counts that we want to represent are at zero, they can be misleading: for example, part of the range covered sums over multiple categories. There are several options to visualize by the bar might have never been observed in the sample. -
UNIT 1 INTRODUCTION to STATISTICS Introduction to Statistics
UNIT 1 INTRODUCTION TO STATISTICS Introduction to Statistics Structure 1.0 Introduction 1.1 Objectives 1.2 Meaning of Statistics 1.2.1 Statistics in Singular Sense 1.2.2 Statistics in Plural Sense 1.2.3 Definition of Statistics 1.3 Types of Statistics 1.3.1 On the Basis of Function 1.3.2 On the Basis of Distribution of Data 1.4 Scope and Use of Statistics 1.5 Limitations of Statistics 1.6 Distrust and Misuse of Statistics 1.7 Let Us Sum Up 1.8 Unit End Questions 1.9 Glossary 1.10 Suggested Readings 1.0 INTRODUCTION The word statistics has different meaning to different persons. Knowledge of statistics is applicable in day to day life in different ways. In daily life it means general calculation of items, in railway statistics means the number of trains operating, number of passenger’s freight etc. and so on. Thus statistics is used by people to take decision about the problems on the basis of different type of quantitative and qualitative information available to them. However, in behavioural sciences, the word ‘statistics’ means something different from the common concern of it. Prime function of statistic is to draw statistical inference about population on the basis of available quantitative information. Overall, statistical methods deal with reduction of data to convenient descriptive terms and drawing some inferences from them. This unit focuses on the above aspects of statistics. 1.1 OBJECTIVES After going through this unit, you will be able to: Define the term statistics; Explain the status of statistics; Describe the nature of statistics; State basic concepts used in statistics; and Analyse the uses and misuses of statistics. -
Measurement & Transformations
Chapter 3 Measurement & Transformations 3.1 Measurement Scales: Traditional Classifica- tion Statisticians call an attribute on which observations differ a variable. The type of unit on which a variable is measured is called a scale.Traditionally,statisticians talk of four types of measurement scales: (1) nominal,(2)ordinal,(3)interval, and (4) ratio. 3.1.1 Nominal Scales The word nominal is derived from nomen,theLatinwordforname.Nominal scales merely name differences and are used most often for qualitative variables in which observations are classified into discrete groups. The key attribute for anominalscaleisthatthereisnoinherentquantitativedifferenceamongthe categories. Sex, religion, and race are three classic nominal scales used in the behavioral sciences. Taxonomic categories (rodent, primate, canine) are nomi- nal scales in biology. Variables on a nominal scale are often called categorical variables. For the neuroscientist, the best criterion for determining whether a variable is on a nominal scale is the “plotting” criteria. If you plot a bar chart of, say, means for the groups and order the groups in any way possible without making the graph “stupid,” then the variable is nominal or categorical. For example, were the variable strains of mice, then the order of the means is not material. Hence, “strain” is nominal or categorical. On the other hand, if the groups were 0 mgs, 10mgs, and 15 mgs of active drug, then having a bar chart with 15 mgs first, then 0 mgs, and finally 10 mgs is stupid. Here “milligrams of drug” is not anominalorcategoricalvariable. 1 CHAPTER 3. MEASUREMENT & TRANSFORMATIONS 2 3.1.2 Ordinal Scales Ordinal scales rank-order observations. -
Chapter 6 Presenting Your Data in Graphic Form Political Orientations
UNIVARIATE ANALYSIS Chapter 6 Presenting Your Data in Graphic Form Political Orientations Now let’s turn our attention from religion to politics. Some people feel so strongly about politics that they joke about it being a religion. The General Social Survey distribute(GSS) data set has several items that reflect political issues. Two are key political items: POLVIEWS and PARTYID. These items will be the primary focus in this chapter. In the process of examining these variables, we are going to learn not only more about the politicalor orientations of respon- dents to the 2012 GSS but also how to use SPSS Statistics to produce and interpret data in graphic form. You will recall that in the previous chapter, we focused on a variety of ways of displaying univariate distributions (frequency tables) and summarizing them (measures of central ten- dency and dispersion). In this chapter, we are going to build on that discussion by focusing on several ways of presenting your data graphically. We will begin by focusing on two charts thatpost, are useful for variables at the nominal and ordinal levels: bar charts and pie charts. We will then consider two graphs appropriate for interval/ratio variables: histograms and line charts. Graphing Data With Direct “Legacy” Dialogs SPSS Statistics gives us acopy, variety of ways to present data graphically. Clicking the Graphs option on the menu bar will give you three options for building charts: Chart Builder, Interactive, and Legacy Dialogs. These take you to two chart-building methods developed by SPSS over the past 20 years. Chart Builder is the most recent. -
Standardized Regression Coefficients and Newly Proposed Estimators for R2 in Multiply Imputed Data
psychometrika—vol. 85, no. 1, 185–205 March 2020 https://doi.org/10.1007/s11336-020-09696-4 STANDARDIZED REGRESSION COEFFICIENTS AND NEWLY PROPOSED ESTIMATORS FOR R2 IN MULTIPLY IMPUTED DATA Joost R. van Ginkel LEIDEN UNIVERSITY Whenever statistical analyses are applied to multiply imputed datasets, specific formulas are needed to combine the results into one overall analysis, also called combination rules. In the context of regression analysis, combination rules for the unstandardized regression coefficients, the t-tests of the regression coefficients, and the F-tests for testing R2 for significance have long been established. However, there is still no general agreement on how to combine the point estimators of R2 in multiple regression applied to multiply imputed datasets. Additionally, no combination rules for standardized regression coefficients and their confidence intervals seem to have been developed at all. In the current article, two sets of combination rules for the standardized regression coefficients and their confidence intervals are proposed, and their statistical properties are discussed. Additionally, two improved point estimators of R2 in multiply imputed data are proposed, which in their computation use the pooled standardized regression coefficients. Simulations show that the proposed pooled standardized coefficients produce only small bias and that their 95% confidence intervals produce coverage close to the theoretical 95%. Furthermore, the simulations show that the newly proposed pooled estimates for R2 are less biased than two earlier proposed pooled estimates. Key words: missing data, multiple imputation, coefficient of determination, standardized coefficient, regression analysis. 1. Introduction Multiple imputation (Rubin 1987) is a widely recommended procedure to deal with missing data. -
Stacked Bar Charts……………………………………………12
Effective Use of Bar Charts Purpose This tool provides guidelines and tips on how to effectively use bar charts to communicate research findings. Format This tool provides guidance on bar charts and their purposes, shows examples of preferred practices and practical tips for bar charts, and provides cautions and examples of misuse and poor use of bar charts and how to make corrections. Audience This tool is designed primarily for researchers from the Model Systems that are funded by the National Institute on Disability, Independent Living, and Rehabilitation Research (NIDILRR). The tool can be adapted by other NIDILRR-funded grantees and the general public. The contents of this tool were developed under a grant from the National Institute on Disability, Independent Living, and Rehabilitation Research (NIDILRR grant number 90DP0012-01-00). The contents of this fact sheet do not necessarily represent the policy of Department of Health and Human Services, and you should not assume endorsement by the Federal Government. 1 Overview and Organization Simple Bar Charts……………………………………..……....3 Clustered Bar Charts…………………………………………10 Stacked Bar Charts……………………………………………12 Paired Bar Charts…………………………………………..…14 Simple Bar Chart – Categorical Comparisons A bar chart is basically a vertical column chart oriented horizontally instead. Data values are displayed as horizontal bars. The magnitude of each data element is represented by the length of the bar. Can be used to display values for categorical items (diabetes prevalence by state, hospital performance rankings on a preferred clinical practice measure etc). Shows comparisons among the categorical groups on the measure. Categories displayed on the vertical axis. Simple Bar Chart – Categorical Comparisons Bar charts are preferred over column charts: When the categorical axis labels are lengthy; When you have 12 or more categories; When the metric to be displayed is duration (such as clinic lobby wait time per health center). -
The Landscape of R Packages for Automated Exploratory Data Analysis by Mateusz Staniak and Przemysław Biecek
CONTRIBUTED RESEARCH ARTICLE 1 The Landscape of R Packages for Automated Exploratory Data Analysis by Mateusz Staniak and Przemysław Biecek Abstract The increasing availability of large but noisy data sets with a large number of heterogeneous variables leads to the increasing interest in the automation of common tasks for data analysis. The most time-consuming part of this process is the Exploratory Data Analysis, crucial for better domain understanding, data cleaning, data validation, and feature engineering. There is a growing number of libraries that attempt to automate some of the typical Exploratory Data Analysis tasks to make the search for new insights easier and faster. In this paper, we present a systematic review of existing tools for Automated Exploratory Data Analysis (autoEDA). We explore the features of fifteen popular R packages to identify the parts of the analysis that can be effectively automated with the current tools and to point out new directions for further autoEDA development. Introduction With the advent of tools for automated model training (autoML), building predictive models is becoming easier, more accessible and faster than ever. Tools for R such as mlrMBO (Bischl et al., 2017), parsnip (Kuhn and Vaughan, 2019); tools for python such as TPOT (Olson et al., 2016), auto-sklearn (Feurer et al., 2015), autoKeras (Jin et al., 2018) or tools for other languages such as H2O Driverless AI (H2O.ai, 2019; Cook, 2016) and autoWeka (Kotthoff et al., 2017) supports fully- or semi-automated feature engineering and selection, model tuning and training of predictive models. Yet, model building is always preceded by a phase of understanding the problem, understanding of a domain and exploration of a data set. -
Prediction of Exercise Behavior Using the Exercise and Self-Esteem Model" (1995)
University of Rhode Island DigitalCommons@URI Open Access Master's Theses 1995 Prediction of Exercise Behavior Using the Exercise and Self- Esteem Model Gerard Moreau University of Rhode Island Follow this and additional works at: https://digitalcommons.uri.edu/theses Recommended Citation Moreau, Gerard, "Prediction of Exercise Behavior Using the Exercise and Self-Esteem Model" (1995). Open Access Master's Theses. Paper 1584. https://digitalcommons.uri.edu/theses/1584 This Thesis is brought to you for free and open access by DigitalCommons@URI. It has been accepted for inclusion in Open Access Master's Theses by an authorized administrator of DigitalCommons@URI. For more information, please contact [email protected]. PREDICTION OF EXERCISE BEHAVIOR USING THE EXERCISE AND SELF-ESTEEM MODEL BY GERARD MOREAU A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN PHYSICAL EDUCATION UNIVERSITY OF RHODE ISLAND 1995 Abstract The intent of this study was to compare the capability of self-efficacies and self-concept of physical ability to predict weight training and jogging behavior. The study consisted of 295 college students ( 123 males and 172 females), from the University of Rhode Island. The subjects received a battery of psychological tests consisting of the Physical Self-Perception Profile (PSPP), the Perceived Importance Profile (PIP), the General Self-Worth Scale (GSW), three self-efficacy scales, assessing jogging , weight training, and hard intensive studying, and a survey of recreational activities that recorded the number of sessions per week and number of minutes per session of each recreational activity the subject participated in. -
Download the Answers
ANSWERS TO EXERCISES AND REVIEW QUESTIONS PART FOUR: STATISTICAL TECHNIQUES TO EXPLORE RELATIONSHIPS AMONG VARIABLES You should review the material in the introduction to Part Four and in Chapters 11, 12, 13, 14 and 15 of the SPSS Survival Manual before attempting these exercises. Correlation 4.1 Using the data file survey.sav follow the instructions in Chapter 11 to explore the relationship between the total mastery scale (measuring control) and life satisfaction (tlifesat). Present the results in a brief report. Correlations tlifesat total tmast total life satisfaction mastery tlifesat total life satisfaction Pearson Correlation 1 .444** Sig. (2-tailed) .000 N 436 436 tmast total mastery Pearson Correlation .444** 1 Sig. (2-tailed) .000 N 436 436 **. Correlation is significant at the 0.01 level (2-tailed). The relationship between mastery and life satisfaction was explored using Pearson’s product moment correlation. There was a moderate positive correlation (r=.44, p<.0001) suggesting that people who felt they had control over their lives had higher levels of life satisfaction. 4.2 Use the instructions in Chapter 11 to generate a full correlation matrix to check the intercorrelations among the following variables. (a) age (b) perceived stress (tpstress) (c) positive affect (tposaff) (d) negative affect (tnegaff) (e) life satisfaction (tlifesat) 1 Correlations tpstress total tposaff total tnegaff total tlifesat total age perceived stress positive affect negative affect life satisfaction age Pearson Correlation 1 -.127** .069 -.171** .059 Sig. (2-tailed) .008 .150 .000 .222 N 439 433 436 435 436 tpstress total Pearson Correlation -.127** 1 -.442** .674** -.494** perceived stress Sig.