# Experimental design and inferential statistics: An introduction. Dr. Alissa Melinger School of Psychology University of Dundee

Save this PDF as:

Size: px
Start display at page:

Download "Experimental design and inferential statistics: An introduction. Dr. Alissa Melinger School of Psychology University of Dundee"

## Transcription

1 Experimental design and inferential statistics: An introduction Dr. Alissa Melinger School of Psychology University of Dundee

2 Structure of Tutorial Block 1: Background and fundamental underpinnings to inferential statistics Block 2: Tests for evaluating differences Block 3: Tests for evaluating associations Block 4: New analyses that I m quite excited about Plus, your data and questions

3 Background and fundamental underpinnings to inferential statistics Block 1

4 The Goal We observe some behavior, of individuals, the economy, our computer models, etc. We want to say something about this behavior. We d like to say something that extends beyond just these observations, to future behaviors, past behaviors, unobserved behaviors.

5 Types of Analysis Descriptive statistics: summarizing and describing the important characteristics of the data. Inferential statistics: decide if a pattern, difference, or relation found with a sample is representative and true of the population.

6 Definitions Data Population: from a the population entire set of exhaustively entities that are collected classified data together from all relevant individuals No need for inferential statistics Population of native German speakers (large group) Population of native Lakhota speaker (medium sized group) Data from a sample collected data from a Population subset of 5 year of old your Lakhota population speakers (small group) Inferential Sample: is statistics subset of help entities determine that make if the up asample population reflects the population Random selection of 1000 native German speakers. Key point everyone is unique

7 Generalizing from a sample We want some measure of reassurance that our observations are representative of the population, and not just characteristic of the sample. Any DIFFERENCE we observe in descriptive statistics needs to be evaluated.

8 Is this difference REAL? Descriptive difference Milk costs.69 at Plus and.89 at Lidl Is this a real difference? Subjective difference Is the difference important enough to me? Is it worth my while to travel farther to pay less? Statistical difference Is Plus generally cheaper than Lidl? How representative of the prices is milk? Are all Plus stores cheaper than all Lidl? How representative of all Plus stores is my Plus?

9 Is a difference REAL? To answer this question we could go through the store and compare every item in each store and call every Plus and Lidl in the world If we can get information on a whole population, we don t need inferential statistics. OR We can look at a Sample of products and stores and then use statistics to determine whether our observation is true of other unobserved products and shops. Important to choose sample well (not only from the chocolate aisle) Statistics help us determine how well our Sample represents the Population.

10 A simple model of the data Different statistical methods attempt to build a model of the data using hypothesized factors to account for the characteristics of the observed pattern. One simple model of the data is the MEAN Mode, median are other simple models Distributions, counts, spreads, range, ect.

11 The mean Subjects A B C D E F # siblings How well does the mean model the data? ERROR Mean # siblings = 1.83

12 Error Variance is the average error between the mean and the observations. Sum of error is offset by positive and negative numbers Error is crucial to inferential statistics. Take the square of each error value #( x i " x) If you Sum don t of squared have Error errors in (SS) your will data increase (e.g., the if you are testing more data a model you collect. and 100 tests would give you the #( x i " x) 2 same Large result number because bad the estimate model of is # of deterministic) siblings you Divide do the not sum need of to squared do inferential errors by statistics. N-1 Variance (s 2 ) = SS/N-1

13 Variance Sum of error is offset by positive and negative numbers Take the square of each error value #( x i " x) Sum of squared errors (SS) #( x i " x) 2 Divide the sum of squared errors by N-1 Variance (s 2 ) = SS/N-1

14 Standard Deviation Variance gives us measure in units squared, so not comparable to directly to the units measured. Standard Deviation is measure of how well the mean represents the data. s = SS N "1

15 Sampling Sampling is a random selection of representative members of a population. If you had access to all members of a population then you would not need to conduct inferential statistics to see whether some observation generalizes to the whole population. Normally, we only have access to a (representative) subset. Most random samples tend to be fairly typical of the population, but there is always variation and the potential of selection bias.

16 Standard Error Standard errors (SE) are similar to SD but they apply to sample means rather than individual means. Standard errors give you a measure of how representative your sample is of the population. A large standard error means your sample is not very representative of the population. Small SE means it is representative. MSE = S / N

17 types of tests / types of data Which test to choose depends on the type of data you have and the question you are asking. Parametric tests have certain assumptions about the data. Non-parametric tests are assumption free

18 Parametric Assumptions about your data Normally distributed Independent ** Homogeneity of variance At least interval scale **

19 Normality Your data should be from a normally distributed population. Normal distributions are symmetrical bellshaped distributions with the majority of scores around the center.

20 Normal Curves Normal curves can be defined by their mean and variance. Z-distribution has mean = 0 and variance = 1

21 Normal Curves 95% of the time, a sample population will fall in the white part of the distribution. Parametric tests assume your data conform to this pattern 95% of cases fall within 2 standard deviations of mean

22 Homogeneity of Variance The variance should not change systematically throughout the data. When you test different groups of subjects (monolinguals vs. bilinguals; test vs. control; trained vs. untrained), their variances should not differ. If you test two corpora, the variance should not differ.

23 Independence Data from different subjects (speakers, sentences) are independent. If trial n influences behavior on trial n+i, then trials are not independent. If two participants related (friends, partners), behavior might not be independent. Binary (either X or Y) classifications are nonindependent If you measure distance between anaphor and antecedent and you have more than one anaphor per antecedent, the individual distances will not be independent.

24 Types of Data Nominal scale (qualitative): Numbers represent qualitative features, not quantitative. 1 not bigger than 2, just different; 1=masculine, 2 = feminine Ordinal Scale (qualitative): Rankings, 1<2<3<4, but differences between values not important or constant; Likert scale data. Distance between 1&2 distance between 3&4 Interval Scale (quantitative): like ordinal, but distances are equal Differences make sense, but ratios don t (30-20 =20-10, but 20 /10 is not twice as hot) e.g., temperature, dates Ratio Scale (quantitative): interval, plus a meaningful 0 point. Weight, length, reaction times, age

25 Types of Measurement Scale Nominal Ordinal Interval Ratio Quantity Relative Quantity Quantity No No No Yes ID males vs. Females Judge who is 1st, 2nd, 3rd Convey over & under estimates Measure # of correct answers on test

26 Types of Measurement Scale Nominal Ordinal Interval Ratio Quantity / Categories No Relative No Quantity No Quantity Yes ID males vs. Females Judge who is 1st, 2nd, 3rd Convey over & under estimates What does the scale indicate? Measure # of correct answers on test

27 Types of Measurement Scale Nominal Ordinal Interval Ratio Quantity / Categories No Relative No Quantity No Quantity Yes ID males vs. Females Judge who is 1st, 2nd, 3rd Convey over & under estimates Is there a true Zero? Measure # of correct answers on test

28 Types of Measurement Scale Nominal Ordinal Interval Ratio Quantity / Relative Quantity Quantity Categories No No No Yes ID males vs. Females Judge who is 1st, 2nd, 3rd Convey over & under estimates Measure time to complete task How might the scale be used in research?

29 Experimental designs What I mean by experiment is likely quite different from what you mean, but hopefully the two terms will overlap sufficiently. An experiment should allow for a systematic observation of a particular behavior under controlled circumstances. Observed patterns in the data should be traceable to our manipulation.

30 Two types of experimental variables You manipulate the situations under which the behavior is observed and measured. The variables you manipulate are your independent variables. You observe and measure a particular behavior. This measurement is your dependent variable.

31 Hypotheses: what the IV should do to the DV The experimental hypothesis is what you are testing and what you are hoping to find. The NULL Hypothesis states manipulation will have not impact The goal of our statistical tests is not to prove our hypothesis but to reject the NULL Hypothesis.

32 P-value Each test provides a test statistic and a p-value. In parametric tests, the test statistic is a ratio of the variance within the data not attributable to your IV to the variance that is attributable to the IV. Signal to noise ratio The p-value is a probability that the observed difference is real. probability that difference occurred by chance. probability that it would not replicate.

33 Variance between conditions attributable to experimental manipulation The ratio Variance within conditions reflects random variance from multiple sources. A significant effect requires more between variance than within variance

34 Some common designs 1 IV, 2 levels (state or value of IV) Reading times Main clause 1 Subordinate clause 2 2 IVs, 2 Levels each Reading times Main clause Subordinate clause Transitive 1 2 Intransitive 3 4

35 Repeated Measures Designs (Within Sample) Repeated measures = more than one observation from each subject. To reduce subject variance, use same subjects in all conditions; within subjects take multiple measures from same individual. Observe a single sentence in multiple contexts. but be sure to control for order effects and sequence effects.

36 Between sample design If each subject only experiences one condition (1 level of the IV), then you make comparisons between individuals. No way to factor out the inherent differences between the individuals Necessary when comparing monolinguals to bilinguals, boys to girls, dyslexics to nondyslexics, etc.

37 Type of Research Design One- Sample Two-Sample K sample Correlation Type of Data Parametric Onesample Z One sample t Related Related t Indepen dent Independe nt Z- Independe nt t- Variance Ratio (F) Related Variance Ratio (F) Independe nt Variance Ratio (F) Productmoment correlation coefficient (Pearson s r) Linear regression Non-parametric Onesample proportion Wilcoxon Sign Mann- Whitney χ 2 Page s L trend Jonckheere trend Spearman s rank correlation coefficient

38 Between analyses # of conditions Parametric scores Nonparame tric - ordinal Nonparame tric - nominal two Independen t samples t Mann- Whitney χ 2 Three or more Betweensubjects ANOVA Kruskal- Wallis χ 2

39 Within analyses # of conditions Parametric scores Nonparame tric - ordinal Nonparame tric - nominal two Dependent samples t Wilcoxon Linear mixed effects Three or more Withinsubjects ANOVA Friedman Linear mixed effects

### DESCRIPTIVE 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,

### Statistics 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

### Analysis of Data. Organizing Data Files in SPSS. Descriptive Statistics

Analysis of Data Claudia J. Stanny PSY 67 Research Design Organizing Data Files in SPSS All data for one subject entered on the same line Identification data Between-subjects manipulations: variable to

There 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

### DATA ANALYSIS. QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University

DATA ANALYSIS QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University Quantitative Research What is Statistics? Statistics (as a subject) is the science

### Introduction 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.

### Measurement & 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.

### COMPARING DATA ANALYSIS TECHNIQUES FOR EVALUATION DESIGNS WITH NON -NORMAL POFULP_TIOKS Elaine S. Jeffers, University of Maryland, Eastern Shore*

COMPARING DATA ANALYSIS TECHNIQUES FOR EVALUATION DESIGNS WITH NON -NORMAL POFULP_TIOKS Elaine S. Jeffers, University of Maryland, Eastern Shore* The data collection phases for evaluation designs may involve

### Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:

### Statistics in Medicine Research Lecture Series CSMC Fall 2014

Catherine Bresee, MS Senior Biostatistician Biostatistics & Bioinformatics Research Institute Statistics in Medicine Research Lecture Series CSMC Fall 2014 Overview Review concept of statistical power

### DATA 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

### Basic Concepts in Research and Data Analysis

Basic Concepts in Research and Data Analysis Introduction: A Common Language for Researchers...2 Steps to Follow When Conducting Research...3 The Research Question... 3 The Hypothesis... 4 Defining the

### Reporting Statistics in Psychology

This document contains general guidelines for the reporting of statistics in psychology research. The details of statistical reporting vary slightly among different areas of science and also among different

### Levels of measurement in psychological research:

Research Skills: Levels of Measurement. Graham Hole, February 2011 Page 1 Levels of measurement in psychological research: Psychology is a science. As such it generally involves objective measurement of

### Introduction to Regression and Data Analysis

Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

### COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.

277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies

### NORTHERN VIRGINIA COMMUNITY COLLEGE PSYCHOLOGY 211 - RESEARCH METHODOLOGY FOR THE BEHAVIORAL SCIENCES Dr. Rosalyn M.

NORTHERN VIRGINIA COMMUNITY COLLEGE PSYCHOLOGY 211 - RESEARCH METHODOLOGY FOR THE BEHAVIORAL SCIENCES Dr. Rosalyn M. King, Professor DETAILED TOPICAL OVERVIEW AND WORKING SYLLABUS CLASS 1: INTRODUCTIONS

### ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall

### Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

### Foundation 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

### Analyzing 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

### Lecture 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

### Assumptions. Assumptions of linear models. Boxplot. Data exploration. Apply to response variable. Apply to error terms from linear model

Assumptions Assumptions of linear models Apply to response variable within each group if predictor categorical Apply to error terms from linear model check by analysing residuals Normality Homogeneity

### Chapter 4 and 5 solutions

Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,

### Simple Predictive Analytics Curtis Seare

Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

### Chapter 7. One-way ANOVA

Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

### ANOVA ANOVA. Two-Way ANOVA. One-Way ANOVA. When to use ANOVA ANOVA. Analysis of Variance. Chapter 16. A procedure for comparing more than two groups

ANOVA ANOVA Analysis of Variance Chapter 6 A procedure for comparing more than two groups independent variable: smoking status non-smoking one pack a day > two packs a day dependent variable: number of

### Likert Scales. are the meaning of life: Dane Bertram

are the meaning of life: Note: A glossary is included near the end of this handout defining many of the terms used throughout this report. Likert Scale \lick urt\, n. Definition: Variations: A psychometric

### Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

### List of Examples. Examples 319

Examples 319 List of Examples DiMaggio and Mantle. 6 Weed seeds. 6, 23, 37, 38 Vole reproduction. 7, 24, 37 Wooly bear caterpillar cocoons. 7 Homophone confusion and Alzheimer s disease. 8 Gear tooth strength.

### Mathematics within the Psychology Curriculum

Mathematics within the Psychology Curriculum Statistical Theory and Data Handling Statistical theory and data handling as studied on the GCSE Mathematics syllabus You may have learnt about statistics and

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Ch. 1 Introduction to Statistics 1.1 An Overview of Statistics 1 Distinguish Between a Population and a Sample Identify the population and the sample. survey of 1353 American households found that 18%

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### Northumberland 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

### Tutorial 5: Hypothesis Testing

Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrc-lmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................

### Descriptive Inferential. The First Measured Century. Statistics. Statistics. We will focus on two types of statistical applications

Introduction: Statistics, Data and Statistical Thinking The First Measured Century FREC 408 Dr. Tom Ilvento 213 Townsend Hall ilvento@udel.edu http://www.udel.edu/frec/ilvento http://www.pbs.org/fmc/index.htm

### THE UNIVERSITY OF TEXAS AT TYLER COLLEGE OF NURSING COURSE SYLLABUS NURS 5317 STATISTICS FOR HEALTH PROVIDERS. Fall 2013

THE UNIVERSITY OF TEXAS AT TYLER COLLEGE OF NURSING 1 COURSE SYLLABUS NURS 5317 STATISTICS FOR HEALTH PROVIDERS Fall 2013 & Danice B. Greer, Ph.D., RN, BC dgreer@uttyler.edu Office BRB 1115 (903) 565-5766

### Parametric and Nonparametric: Demystifying the Terms

Parametric and Nonparametric: Demystifying the Terms By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD

### Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

### 4.1 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

### One-Way Analysis of Variance (ANOVA) Example Problem

One-Way Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two or more population (or treatment) means

### MASTER COURSE SYLLABUS-PROTOTYPE PSYCHOLOGY 2317 STATISTICAL METHODS FOR THE BEHAVIORAL SCIENCES

MASTER COURSE SYLLABUS-PROTOTYPE THE PSYCHOLOGY DEPARTMENT VALUES ACADEMIC FREEDOM AND THUS OFFERS THIS MASTER SYLLABUS-PROTOTYPE ONLY AS A GUIDE. THE INSTRUCTORS ARE FREE TO ADAPT THEIR COURSE SYLLABI

### Why 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

### DESCRIPTIVE 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

### STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### M.A. PSYCHOLOGY FIRST YEAR COURSES (MAPC) Assignments For July 2015 and January 2016 Sessions

MPC M.A. PSYCHOLOGY FIRST YEAR COURSES (MAPC) Assignments For July 2015 and January 2016 Sessions Discipline of Psychology School of Social Sciences Indira Gandhi National Open University Maidan Garhi,

### OUTLIER ANALYSIS. Data Mining 1

OUTLIER ANALYSIS Data Mining 1 What Are Outliers? Outlier: A data object that deviates significantly from the normal objects as if it were generated by a different mechanism Ex.: Unusual credit card purchase,

### Two-sample hypothesis testing, II 9.07 3/16/2004

Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,

### Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to

### STAT 350 Practice Final Exam Solution (Spring 2015)

PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

### Validation and Calibration. Definitions and Terminology

Validation and Calibration Definitions and Terminology ACCEPTANCE CRITERIA: The specifications and acceptance/rejection criteria, such as acceptable quality level and unacceptable quality level, with an

### Mathematics. Probability and Statistics Curriculum Guide. Revised 2010

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

### Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

### Introduction to Statistics with GraphPad Prism (5.01) Version 1.1

Babraham Bioinformatics Introduction to Statistics with GraphPad Prism (5.01) Version 1.1 Introduction to Statistics with GraphPad Prism 2 Licence This manual is 2010-11, Anne Segonds-Pichon. This manual

### www.rmsolutions.net R&M Solutons

Ahmed Hassouna, MD Professor of cardiovascular surgery, Ain-Shams University, EGYPT. Diploma of medical statistics and clinical trial, Paris 6 university, Paris. 1A- Choose the best answer The duration

### Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

### c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

### DESCRIPTIVE STATISTICS & DATA PRESENTATION*

Level 1 Level 2 Level 3 Level 4 0 0 0 0 evel 1 evel 2 evel 3 Level 4 DESCRIPTIVE STATISTICS & DATA PRESENTATION* Created for Psychology 41, Research Methods by Barbara Sommer, PhD Psychology Department

### January 26, 2009 The Faculty Center for Teaching and Learning

THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i

### One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups

One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups In analysis of variance, the main research question is whether the sample means are from different populations. The

### Data analysis process

Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis

### Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.

Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative

### Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools

Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................

### Calculating, Interpreting, and Reporting Estimates of Effect Size (Magnitude of an Effect or the Strength of a Relationship)

1 Calculating, Interpreting, and Reporting Estimates of Effect Size (Magnitude of an Effect or the Strength of a Relationship) I. Authors should report effect sizes in the manuscript and tables when reporting

### 12: Analysis of Variance. Introduction

1: Analysis of Variance Introduction EDA Hypothesis Test Introduction In Chapter 8 and again in Chapter 11 we compared means from two independent groups. In this chapter we extend the procedure to consider

### Analysis of Questionnaires and Qualitative Data Non-parametric Tests

Analysis of Questionnaires and Qualitative Data Non-parametric Tests JERZY STEFANOWSKI Instytut Informatyki Politechnika Poznańska Lecture SE 2013, Poznań Recalling Basics Measurment Scales Four scales

### Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

### Normality Testing in Excel

Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com

### Experimental Designs (revisited)

Introduction to ANOVA Copyright 2000, 2011, J. Toby Mordkoff Probably, the best way to start thinking about ANOVA is in terms of factors with levels. (I say this because this is how they are described

### " Y. Notation and Equations for Regression Lecture 11/4. Notation:

Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

### Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

### CHAPTER 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,

### The Statistics Tutor s Quick Guide to

statstutor community project encouraging academics to share statistics support resources All stcp resources are released under a Creative Commons licence The Statistics Tutor s Quick Guide to Stcp-marshallowen-7

### How To Run Statistical Tests in Excel

How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting

### STATISTICS FOR PSYCHOLOGISTS

STATISTICS FOR PSYCHOLOGISTS SECTION: STATISTICAL METHODS CHAPTER: REPORTING STATISTICS Abstract: This chapter describes basic rules for presenting statistical results in APA style. All rules come from

### Regression Analysis: A Complete Example

Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

### Published entries to the three competitions on Tricky Stats in The Psychologist

Published entries to the three competitions on Tricky Stats in The Psychologist Author s manuscript Published entry (within announced maximum of 250 words) to competition on Tricky Stats (no. 1) on confounds,

### Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data. Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York

Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York . NONPARAMETRIC STATISTICS I. DEFINITIONS A. Parametric

### Prospects, Problems of Marketing Research and Data Mining in Turkey

Prospects, Problems of Marketing Research and Data Mining in Turkey Sema Kurtulu, and Kemal Kurtulu Abstract The objective of this paper is to review and assess the methodological issues and problems in

### E10: Controlled Experiments

E10: Controlled Experiments Quantitative, empirical method Used to identify the cause of a situation or set of events X is responsible for Y Directly manipulate and control variables Correlation does not

### business 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

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### 11. Analysis of Case-control Studies Logistic Regression

Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

### Intro to GIS Winter 2011. Data Visualization Part I

Intro to GIS Winter 2011 Data Visualization Part I Cartographer Code of Ethics Always have a straightforward agenda and have a defining purpose or goal for each map Always strive to know your audience

### Exploratory 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,

### Descriptive 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),

### TABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2

About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (One-way χ 2 )... 1 Test of Independence (Two-way χ 2 )... 2 Hypothesis Testing

### SAS Software to Fit the Generalized Linear Model

SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling

### An Empirical Study on the Influence of Perceived Credibility of Online Consumer Reviews

An Empirical Study on the Influence of Perceived Credibility of Online Consumer Reviews GUO Guoqing 1, CHEN Kai 2, HE Fei 3 1. School of Business, Renmin University of China, 100872 2. School of Economics

### Applying Statistics Recommended by Regulatory Documents

Applying Statistics Recommended by Regulatory Documents Steven Walfish President, Statistical Outsourcing Services steven@statisticaloutsourcingservices.com 301-325 325-31293129 About the Speaker Mr. Steven

### LIST OF SUBJECTS MBA (EXECUTIVE) SEM.I 2015 1. Fundamental of Management 2. Organizational Behaviour 3. Accounting for Managers 4.

LIST OF SUBJECTS MBA (EXECUTIVE) SEM.I 2015 1. Fundamental of Management 2. Organizational Behaviour 3. Accounting for Managers 4. Statistics for Management 5. Business Communication 6. Managerial Economics

### Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish

Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish Statistics Statistics are quantitative methods of describing, analysing, and drawing inferences (conclusions)

### Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study)

Cairo University Faculty of Economics and Political Science Statistics Department English Section Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study) Prepared

### An analysis method for a quantitative outcome and two categorical explanatory variables.

Chapter 11 Two-Way ANOVA An analysis method for a quantitative outcome and two categorical explanatory variables. If an experiment has a quantitative outcome and two categorical explanatory variables that