Content DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS
|
|
- Neal Lawson
- 7 years ago
- Views:
Transcription
1 Content DESCRIPTIVE STATISTICS Dr Najib Majdi bin Yaacob MD, MPH, DrPH (Epidemiology) USM Unit of Biostatistics & Research Methodology School of Medical Sciences Universiti Sains Malaysia. Introduction to statistics Descriptive vs. inferential statistics Variables Types of variables Organizing and displaying data for categorical variables Organizing and displaying data for categorical variables Data & Statistic INTRODUCTION TO STATISTICS DATA VS. STATISTIC VS. STATISTICS Data: A collection of items of information. Statistic : A summary of value of some attribute of a sample, usually but not necessarily as an estimator of some population parameter. Is calculated by applying a function to the values of the items of the sample (Porta, M. (2014). A Dictionary of Epidemiology: Oxford University Press, USA) Statistics The science of collecting, summarizing, and analyzing data. Data may or may not subject to random variation. The data themselves and summarizations of the data. Porta, M. (2008). A Dictionary of Epidemiology: Oxford University Press, USA A Branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters. Example: Data; ID Gender Height (m) 1 Male Male Female Male Female Female Female
2 Example: Statistic; 4 (57.1%) Female, 3 (42.9%) Male Mean height = 1.62m Standard deviation for height = 0.06m Statistics The process of calculating the statistic. How to calculate the frequency and percentage for gender and how to calculate mean and standard deviation for height. Why use statistics? Modern society concern with reading & writing Statistics in used to make the strongest possible conclusions from limited amount of data. A more thorough understanding of research literature will lead to improves patient care. Descriptive statistics BRANCHES OF STATISTICS DESCRIPTIVE VS. INFERENTIAL Describe and summarize dataset Involves collection, organization, analysis, interpretation and presentation of sample data Can be presented in tables, graphs or narrative format Descriptive statistics How to describe this population? Purpose Describe the characteristics of study participants Understand the data Answer the research questions in descriptive study Detect outliers or extreme values 2
3 How to describe this population? samples Describe samples Descriptive statistics Frequency distribution Measures of central tendency Measures of dispersion Measures of position Exploratory data analysis Measures of shape of distribution: graphs, skewness, kurtosis Inferential statistics Estimation Hypothesis testing reach a decision Parametric statistics Non-parametric statistics (distribution free statistics) Modelling, predicting. How to make conclusion from this population? How to make conclusion from this population? samples Inferential statistics VARIABLE Infer findings to population 3
4 Y axis: Dependent variable Variables Any quantity that have different values across individuals or other study units. (Porta, M. (2014). A Dictionary of Epidemiology: Oxford University Press, USA) Variables Independent Dependent Variables Independent variable A variable that is hypothesized to influence an event or state (the dependent variable) The independent variable is not influenced by the event but may cause (or contribute to the occurrence of) the event, or contribute to change the (psychological, environmental, socioeconomic) status. Variables Dependent variable A variable the value of which is dependent on the effect of another variable(s) the independent variable(s) in the relationship under study. A manifestation or outcome whose variation we seek to explain or account for by the influence of independent variables. Variables Effect of sunlight to plant growth Variables Variables Effect of sunlight to plant growth Effect of sunlight to plant growth Independent variable Dependent variable X axis: Independent variable 4
5 Variables Controlled variable(s) Everything you want to remain constant and unchanged during the study period Example: Investigating effect of sunlight exposure duration (hours/day) to plant growth Independent variable: Duration of sunlight exposure Dependent variable: Plant height Controlled variable: type of plant, size of pot, amount of water, type of soil etc. TYPES OF VARIABLES MEASUREMENT SCALE Measurement scale Classification of data Different types of scale are measured differently Knowledge about the measurement scale/data helps in deciding how to organize, analyse and present the data. Four fundamental scale ; Nominal Ordinal Interval Ratio Nominal Categorical (qualitative) Ordinal Data Numerical (quantitative) Interval Ratio Less info More Info Categorical data: Nominal scales Names or categories, mutually exclusive Does not imply any ordering of responses Example; Sex: Male, Female Race: Malay, Chinese, Indian, Others Lowest and least informative level of measurement Categorical data: Ordinal scales Names or categorizes which are mutually exclusive and the order is meaningful Example; Severity: mild, moderate, severe Socioeconomic status: Low, Middle, High Limitation; Can t assume the differences between adjacent scale values are equal Can t make this assumption even if the labels are number 5
6 Numerical data: Interval scales Interval scales Names or categorizes, the order is meaningful, the intervals are equal. Example; Fahrenheit temperature scale Celsius temperature scale Problem: No true zero point (Zero point is arbitrary) Zero does not mean complete absence of temperature Numerical data: Ratio scales Ratio scales Highest and most informative scale Contains the qualities of the nominal, ordinal and interval scale with the addition of an absolute zero point. Example: Amount of money Age Blood pressure The values were able to be multiple or divide Zero in Kelvin scale is absolute absence of thermal energy. Kelvin scale is therefore considered as ratio scale. Numerical data Interval and ratio variables are sometime indistinguishable, and handled the same way in data analysis. Both can be converted to categorical data Converting numerical to categorical data causes lost of information Summary of data types and scale measurement Provides Nominal Ordinal Interval Ratio Counts/frequency of distribution Mode, median The order of values is known Can quantify the difference between each value Can add or subtract values Can multiple and divide values Has true zero 6
7 ORGANIZING & DISPLAYING DATA FOR CATEGORICAL VARIABLE Organizing & displaying data for categorical variable Table: Frequency table Frequency Relative frequency (percentage) Cumulative frequency (cumulative percentage) Graphical: Bar chart Pie chart Output from SPSS Frequency table Bar chart Characteristics; 1. Y axis represent frequency 2. X axis represent categorical variables 3. Equal width of bars 4. Bars separated by equal gaps 5. Height represent frequency or percent Pie chart Characteristics; 1. Size of slice represent frequency or percent 2. Each piece of slice represent ach category 3. Combination of all slices must add up to 100% Excellent graphical presentation of data Accuracy: proper data entry, not misleading, distortion or susceptible to misinterpretation Clarity: The ideas and concept conveyed are clearly understood Simplicity: Straight forward, avoid gridlines or odd lettering Appearance: should be appealing Well-designed structure: pattern highlighted, letterings are horizontal 7
8 ORGANIZING & DISPLAYING DATA FOR NUMERICAL DATA Organizing & displaying data for numerical data Central tendency Dispersion Exploratory data analysis 1. Stem & leaf displays 2. Box and whisker plots Frequency 1. Histogram 2. Frequency polygon 3. Cumulative frequency Shape of distribution Measures of central tendency 1. Mean 2. Median 3. Mode Measures of central tendency 1. Mean Sample average Sum all values, divided by the number of values Sensitive to extreme values n X i i X 1 Example: n What is the mean height of these 9 students? id height (cm) Measures of central tendency 2. Median Middle value Not sensitive to extreme value Used to summarize a skewed data When n is odd, median=[(n+1)/2]th value When n is even, median=average of (n/2)th and [(n/2)+1]th value Measures of central tendency 2. Median Example: What is the median height of these 9 students? id height (cm)
9 Measures of central tendency 2. Median Example: What is the median height of these 9 students? Measures of central tendency 3. Mode Observation that occur most frequently Less useful in describing data N=9, median = (9+1)/2th value = 5 th value sort Measures of dispersion 1. Range 2. Variance 3. Standard deviation 4. Coefficient of variation 5. Inter quartile range Measures of dispersion 1. Range Largest value smallest value (max-min) Sensitive to extreme values Measures of dispersion 2. Variance Measures the amount of spread or variability of observation from mean The sample variance (s 2 )=the average of the square of the deviations about the sample mean (population variance= 2 ) Not used in descriptive statistics because difficulty in interpreting a square unit of data. s 2 n i1 ( X X ) 1 n 1 2 Measures of dispersion 3. Standard deviation Square root of variance Most widely used and better measure of variability The smaller the value, the closer to the mean Sensitive to extreme values s n i1 ( X X ) 1 n 1 2 9
10 Measures of dispersion 4. Coefficient of variation Ratio of the standard deviation to the mean Expressed as percentage Also known as relative standard deviation Shows the extent of variability in relation to the mean. s CoV X Hands-on Calculate/find the range, variance, standard deviation and coefficient of variation for numerical variables in the given data file. (5 minutes) id height (cm) Measures of dispersion 4. Inter quartile range: Data can be divided into quarter or four equal parts; Q1=25 th percentile Q2=50 th percentile Q3=75 th percentile IQR is the distance from Q1 to Q3 Measures of dispersion 4. Inter quartile range: The most common inter percentile measure Not sensitive to extreme values (outliers) Usually described together with median in skewed distribution observation Min Max In SPSS In SPSS 10
11 Exploratory data analysis 1. Stem & leaf displays 2. Box and whisker plots GRAPHICAL VISUALIZATION/ PRESENTATION FOR NUMERICAL DATA Exploratory data analysis Stem & leaf displays Allows easier identification of individual values in the sample id height (cm) height Stem-and-Leaf Plot Frequency Stem & Leaf 1.00 Extremes (=<162) Stem width: 10 Each leaf: 1 case(s) Exploratory data analysis Box and whisker plots Graphical display of percentile Also known as 5 number summary plot (min, Q1, Q2, Q3, max) Provide information on central tendency and variability of the middle 50% of the distribution Box represent 25 th to 75 th percentile Exploratory data analysis Box and whisker plots Observation >1.5 times IQR away from the edge of the box is/are the outlier(s) Observation >3 times IQR away is/are the extreme outlier(s) Whisker are made of smallest and largest value outside the outliers Continuous data in multiple groups can be displayed side by side Exploratory data analysis Box and whisker plots 11
12 Exploratory data analysis Box and whisker plots Measures of frequency of distribution: Graphs 1. Histogram 2. Frequency polygon 3. Cumulative frequency Measures of frequency of distribution: Graphs Histogram Graphical representation of the frequency distribution of a variable. Bar height represent frequency or percent Bar width represent the interval class No gap between the interval class Gives us idea of the distribution: normal distribution or skewed Measures of frequency of distribution: Graphs Histogram Measures of frequency of distribution: Graphs Frequency polygon A graph that displays the data using lines to connect points plotted for the frequency The frequency represent the heights of the vertical bars in the histogram Measures of frequency of distribution: Graphs Frequency polygon 12
13 Measures of frequency of distribution: Graphs Cumulative frequency Used to determine the number of observation that lie below or above a particular value Calculated using a frequency distribution table Can be constructed from stem and leaf plots or directly from data Measures of frequency of distribution: Graphs Cumulative frequency Measures of shape of distribution Skewness Kurtosis Measures of shape of distribution Skewness: measure of asymmetry of a distribution around its mean. Graphically examined by plotting normal curve on histogram Negative skewness: left tail is more pronounced than the right tail Positive skewness: right tail is more prominent than the left tail. Measures of shape of distribution Skewness: Measures of shape of distribution Kurtosis; Relative peakness or flatness of a distribution compared with the normal distribution. Visualised by plotting a normal curve on histogram Types; Distribution with a high peak: leptokurtic Distribution with a flat-topped curve: platykurtic Normal distribution: mesokurtic 13
14 Measures of shape of distribution Kurtosis; HOW TO PRESENT General rule Can be presented in either graphical, table or text format Categorical variable: n (%) Numerical variable: Symmetric data: mean (standard deviation) Skewed data: median (IQR) How to decide symmetric or skewed? Statistical Mean = median = mode Skewness Kurtosis Kolmogorov-Smirnov test (p>0.05) Shapiro Wilk test (P>0.05) How to decide symmetric or skewed? Graphical Histogram Stem and Leaf plot Box and whisker plot Table presentation Table 1: Characteristic of study participants (n=30) Variable Mean (SD) n (%) Age (yrs) Sex Female Male Race Malay Chinese Indian Education Primary Secondary Tertiary BMI (kg/m 2 ) DBP (mmhg) SBP (mmhg) *median (IQR) 14
15 THANK YOU. 15
STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI
STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationExploratory data analysis (Chapter 2) Fall 2011
Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,
More informationDescriptive Statistics
Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web
More informationDESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS
DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi - 110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics
More informationDescriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),
More informationDescriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion
Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research
More informationLecture 1: Review and Exploratory Data Analysis (EDA)
Lecture 1: Review and Exploratory Data Analysis (EDA) Sandy Eckel seckel@jhsph.edu Department of Biostatistics, The Johns Hopkins University, Baltimore USA 21 April 2008 1 / 40 Course Information I Course
More informationDescriptive Statistics and Measurement Scales
Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample
More informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More informationExploratory Data Analysis. Psychology 3256
Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find
More informationVariables. Exploratory Data Analysis
Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is
More informationLecture 2: Descriptive Statistics and Exploratory Data Analysis
Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals
More informationWeek 1. Exploratory Data Analysis
Week 1 Exploratory Data Analysis Practicalities This course ST903 has students from both the MSc in Financial Mathematics and the MSc in Statistics. Two lectures and one seminar/tutorial per week. Exam
More informationStatistics. Measurement. Scales of Measurement 7/18/2012
Statistics Measurement Measurement is defined as a set of rules for assigning numbers to represent objects, traits, attributes, or behaviors A variableis something that varies (eye color), a constant does
More informationThe right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median
CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box
More informationData Exploration Data Visualization
Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select
More informationExercise 1.12 (Pg. 22-23)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationMBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
More informationIntroduction to Statistics for Psychology. Quantitative Methods for Human Sciences
Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html
More informationSummarizing and Displaying Categorical Data
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
More informationDiagrams and Graphs of Statistical Data
Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in
More informationChapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs
Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)
More informationBNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I
BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential
More informationNorthumberland Knowledge
Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about
More informationMEASURES OF VARIATION
NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are
More informationCA200 Quantitative Analysis for Business Decisions. File name: CA200_Section_04A_StatisticsIntroduction
CA200 Quantitative Analysis for Business Decisions File name: CA200_Section_04A_StatisticsIntroduction Table of Contents 4. Introduction to Statistics... 1 4.1 Overview... 3 4.2 Discrete or continuous
More informationWhy Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012
Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization GENOME 560, Spring 2012 Data are interesting because they help us understand the world Genomics: Massive Amounts
More informationPie Charts. proportion of ice-cream flavors sold annually by a given brand. AMS-5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.
Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of
More informationHow To Write A Data Analysis
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
More informationUsing SPSS, Chapter 2: Descriptive Statistics
1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,
More informationFoundation of Quantitative Data Analysis
Foundation of Quantitative Data Analysis Part 1: Data manipulation and descriptive statistics with SPSS/Excel HSRS #10 - October 17, 2013 Reference : A. Aczel, Complete Business Statistics. Chapters 1
More informationStatistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013
Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
More informationThe Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)
Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,
More informationModule 2: Introduction to Quantitative Data Analysis
Module 2: Introduction to Quantitative Data Analysis Contents Antony Fielding 1 University of Birmingham & Centre for Multilevel Modelling Rebecca Pillinger Centre for Multilevel Modelling Introduction...
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
More informationChapter 2: Frequency Distributions and Graphs
Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct
More informationMeans, standard deviations and. and standard errors
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
More informationExploratory Data Analysis
Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction
More informationIntroduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data
A Few Sources for Data Examples Used Introduction to Environmental Statistics Professor Jessica Utts University of California, Irvine jutts@uci.edu 1. Statistical Methods in Water Resources by D.R. Helsel
More informationHow To: Analyse & Present Data
INTRODUCTION The aim of this How To guide is to provide advice on how to analyse your data and how to present it. If you require any help with your data analysis please discuss with your divisional Clinical
More informationSta 309 (Statistics And Probability for Engineers)
Instructor: Prof. Mike Nasab Sta 309 (Statistics And Probability for Engineers) Chapter 2 Organizing and Summarizing Data Raw Data: When data are collected in original form, they are called raw data. The
More informationAP * Statistics Review. Descriptive Statistics
AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production
More informationDescribing, Exploring, and Comparing Data
24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter
More informationBiostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY
Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More informationDescribing and presenting data
Describing and presenting data All epidemiological studies involve the collection of data on the exposures and outcomes of interest. In a well planned study, the raw observations that constitute the data
More informationBASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS
BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi-110 012 seema@iasri.res.in Genomics A genome is an organism s
More informationVisualizing Data. Contents. 1 Visualizing Data. Anthony Tanbakuchi Department of Mathematics Pima Community College. Introductory Statistics Lectures
Introductory Statistics Lectures Visualizing Data Descriptive Statistics I Department of Mathematics Pima Community College Redistribution of this material is prohibited without written permission of the
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More informationStatistics Chapter 2
Statistics Chapter 2 Frequency Tables A frequency table organizes quantitative data. partitions data into classes (intervals). shows how many data values are in each class. Test Score Number of Students
More informationIntroduction to Statistics and Quantitative Research Methods
Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.
More informationProbability and Statistics Vocabulary List (Definitions for Middle School Teachers)
Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence
More informationModule 4: Data Exploration
Module 4: Data Exploration Now that you have your data downloaded from the Streams Project database, the detective work can begin! Before computing any advanced statistics, we will first use descriptive
More informationDESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 1
DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 1 OVERVIEW STATISTICS PANIK...THE THEORY AND METHODS OF COLLECTING, ORGANIZING, PRESENTING, ANALYZING, AND INTERPRETING DATA SETS SO AS TO DETERMINE THEIR ESSENTIAL
More information3: Summary Statistics
3: Summary Statistics Notation Let s start by introducing some notation. Consider the following small data set: 4 5 30 50 8 7 4 5 The symbol n represents the sample size (n = 0). The capital letter X denotes
More informationDescriptive statistics parameters: Measures of centrality
Descriptive statistics parameters: Measures of centrality Contents Definitions... 3 Classification of descriptive statistics parameters... 4 More about central tendency estimators... 5 Relationship between
More informationCenter: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.)
Center: Finding the Median When we think of a typical value, we usually look for the center of the distribution. For a unimodal, symmetric distribution, it s easy to find the center it s just the center
More informationbusiness statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
More informationHISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS
Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS
More informationDescribing Data: Measures of Central Tendency and Dispersion
100 Part 2 / Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics Chapter 8 Describing Data: Measures of Central Tendency and Dispersion In the previous chapter we
More information4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"
Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses
More informationMeasurement & Data Analysis. On the importance of math & measurement. Steps Involved in Doing Scientific Research. Measurement
Measurement & Data Analysis Overview of Measurement. Variability & Measurement Error.. Descriptive vs. Inferential Statistics. Descriptive Statistics. Distributions. Standardized Scores. Graphing Data.
More informationDescriptive Statistics
Descriptive Statistics Suppose following data have been collected (heights of 99 five-year-old boys) 117.9 11.2 112.9 115.9 18. 14.6 17.1 117.9 111.8 16.3 111. 1.4 112.1 19.2 11. 15.4 99.4 11.1 13.3 16.9
More informationSummary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)
Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume
More informationIntroduction; Descriptive & Univariate Statistics
Introduction; Descriptive & Univariate Statistics I. KEY COCEPTS A. Population. Definitions:. The entire set of members in a group. EXAMPLES: All U.S. citizens; all otre Dame Students. 2. All values of
More informationData Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining
Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar What is data exploration? A preliminary exploration of the data to better understand its characteristics.
More informationIBM SPSS Statistics for Beginners for Windows
ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationDescriptive Statistics and Exploratory Data Analysis
Descriptive Statistics and Exploratory Data Analysis Dean s s Faculty and Resident Development Series UT College of Medicine Chattanooga Probasco Auditorium at Erlanger January 14, 2008 Marc Loizeaux,
More informationA Picture Really Is Worth a Thousand Words
4 A Picture Really Is Worth a Thousand Words Difficulty Scale (pretty easy, but not a cinch) What you ll learn about in this chapter Why a picture is really worth a thousand words How to create a histogram
More informationAnalyzing Research Data Using Excel
Analyzing Research Data Using Excel Fraser Health Authority, 2012 The Fraser Health Authority ( FH ) authorizes the use, reproduction and/or modification of this publication for purposes other than commercial
More informationData exploration with Microsoft Excel: univariate analysis
Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating
More informationDongfeng Li. Autumn 2010
Autumn 2010 Chapter Contents Some statistics background; ; Comparing means and proportions; variance. Students should master the basic concepts, descriptive statistics measures and graphs, basic hypothesis
More informationMeasures of Central Tendency and Variability: Summarizing your Data for Others
Measures of Central Tendency and Variability: Summarizing your Data for Others 1 I. Measures of Central Tendency: -Allow us to summarize an entire data set with a single value (the midpoint). 1. Mode :
More informationQuantitative Methods for Finance
Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain
More informationModule 3: Correlation and Covariance
Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis
More informationIris Sample Data Set. Basic Visualization Techniques: Charts, Graphs and Maps. Summary Statistics. Frequency and Mode
Iris Sample Data Set Basic Visualization Techniques: Charts, Graphs and Maps CS598 Information Visualization Spring 2010 Many of the exploratory data techniques are illustrated with the Iris Plant data
More information2. Filling Data Gaps, Data validation & Descriptive Statistics
2. Filling Data Gaps, Data validation & Descriptive Statistics Dr. Prasad Modak Background Data collected from field may suffer from these problems Data may contain gaps ( = no readings during this period)
More informationMind on Statistics. Chapter 2
Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table
More informationMeasurement with Ratios
Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical
More informationEXPLORING SPATIAL PATTERNS IN YOUR DATA
EXPLORING SPATIAL PATTERNS IN YOUR DATA OBJECTIVES Learn how to examine your data using the Geostatistical Analysis tools in ArcMap. Learn how to use descriptive statistics in ArcMap and Geoda to analyze
More informationCHAPTER THREE. Key Concepts
CHAPTER THREE Key Concepts interval, ordinal, and nominal scale quantitative, qualitative continuous data, categorical or discrete data table, frequency distribution histogram, bar graph, frequency polygon,
More informationBasics of Statistics
Basics of Statistics Jarkko Isotalo 30 20 10 Std. Dev = 486.32 Mean = 3553.8 0 N = 120.00 2400.0 2800.0 3200.0 3600.0 4000.0 4400.0 4800.0 2600.0 3000.0 3400.0 3800.0 4200.0 4600.0 5000.0 Birthweights
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationChapter 2 Data Exploration
Chapter 2 Data Exploration 2.1 Data Visualization and Summary Statistics After clearly defining the scientific question we try to answer, selecting a set of representative members from the population of
More informationCHAPTER THREE COMMON DESCRIPTIVE STATISTICS COMMON DESCRIPTIVE STATISTICS / 13
COMMON DESCRIPTIVE STATISTICS / 13 CHAPTER THREE COMMON DESCRIPTIVE STATISTICS The analysis of data begins with descriptive statistics such as the mean, median, mode, range, standard deviation, variance,
More informationInterpreting Data in Normal Distributions
Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,
More informationSCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
More informationThere are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month
More informationGeostatistics Exploratory Analysis
Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt
More informationThe correlation coefficient
The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative
More informationValor Christian High School Mrs. Bogar Biology Graphing Fun with a Paper Towel Lab
1 Valor Christian High School Mrs. Bogar Biology Graphing Fun with a Paper Towel Lab I m sure you ve wondered about the absorbency of paper towel brands as you ve quickly tried to mop up spilled soda from
More informationDemographics of Atlanta, Georgia:
Demographics of Atlanta, Georgia: A Visual Analysis of the 2000 and 2010 Census Data 36-315 Final Project Rachel Cohen, Kathryn McKeough, Minnar Xie & David Zimmerman Ethnicities of Atlanta Figure 1: From
More informationA Correlation of. to the. South Carolina Data Analysis and Probability Standards
A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards
More informationNonparametric Two-Sample Tests. Nonparametric Tests. Sign Test
Nonparametric Two-Sample Tests Sign test Mann-Whitney U-test (a.k.a. Wilcoxon two-sample test) Kolmogorov-Smirnov Test Wilcoxon Signed-Rank Test Tukey-Duckworth Test 1 Nonparametric Tests Recall, nonparametric
More informationMEASURES OF LOCATION AND SPREAD
Paper TU04 An Overview of Non-parametric Tests in SAS : When, Why, and How Paul A. Pappas and Venita DePuy Durham, North Carolina, USA ABSTRACT Most commonly used statistical procedures are based on the
More informationProjects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
More information