Part IV Significantly Different: Using Inferential Statistics

Slides:



Advertisements
Similar presentations
What is Chi-Square? Used to examine differences in the distributions of nominal data A mathematical comparison between expected frequencies and observed.
Advertisements

Kruskal Wallis and the Friedman Test.
Lecture (11,12) Parameter Estimation of PDF and Fitting a Distribution Function.
Hypothesis Testing IV Chi Square.
Smith/Davis (c) 2005 Prentice Hall Chapter Thirteen Inferential Tests of Significance II: Analyzing and Interpreting Experiments with More than Two Groups.
 What is chi-square  CHIDIST  Non-parameteric statistics 2.
S519: Evaluation of Information Systems
1 1 Slide © 2009, Econ-2030 Applied Statistics-Dr Tadesse Chapter 10: Comparisons Involving Means n Introduction to Analysis of Variance n Analysis of.
Chapter Seventeen HYPOTHESIS TESTING
PSY 307 – Statistics for the Behavioral Sciences
Chapter 14 Conducting & Reading Research Baumgartner et al Chapter 14 Inferential Data Analysis.
Analysis of Variance: Inferences about 2 or More Means
Inferential Stats for Two-Group Designs. Inferential Statistics Used to infer conclusions about the population based on data collected from sample Do.
CJ 526 Statistical Analysis in Criminal Justice
S519: Evaluation of Information Systems
Statistics for the Social Sciences
PSY 307 – Statistics for the Behavioral Sciences Chapter 19 – Chi-Square Test for Qualitative Data Chapter 21 – Deciding Which Test to Use.
Chapter 14 Inferential Data Analysis
Chapter 12 Inferential Statistics Gay, Mills, and Airasian
Nonparametric or Distribution-free Tests
Inferential Statistics
Choosing Statistical Procedures
Statistics for the Social Sciences Psychology 340 Fall 2013 Thursday, November 21 Review for Exam #4.
AM Recitation 2/10/11.
Research Methods for Counselors COUN 597 University of Saint Joseph Class # 9 Copyright © 2014 by R. Halstead. All rights reserved.
1 1 Slide © 2006 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University.
1 1 Slide © 2005 Thomson/South-Western Chapter 13, Part A Analysis of Variance and Experimental Design n Introduction to Analysis of Variance n Analysis.
Education 793 Class Notes T-tests 29 October 2003.
CJ 526 Statistical Analysis in Criminal Justice
Week 10 Chapter 10 - Hypothesis Testing III : The Analysis of Variance
Chapter 11 HYPOTHESIS TESTING USING THE ONE-WAY ANALYSIS OF VARIANCE.
Chapter 9: Non-parametric Tests n Parametric vs Non-parametric n Chi-Square –1 way –2 way.
Educational Research: Competencies for Analysis and Application, 9 th edition. Gay, Mills, & Airasian © 2009 Pearson Education, Inc. All rights reserved.
Experimental Design: One-Way Correlated Samples Design
FOUNDATIONS OF NURSING RESEARCH Sixth Edition CHAPTER Copyright ©2012 by Pearson Education, Inc. All rights reserved. Foundations of Nursing Research,
Chapter 10: Analyzing Experimental Data Inferential statistics are used to determine whether the independent variable had an effect on the dependent variance.
Inference and Inferential Statistics Methods of Educational Research EDU 660.
Statistics for the Social Sciences Psychology 340 Fall 2013 Tuesday, October 15, 2013 Analysis of Variance (ANOVA)
Education 793 Class Notes Presentation 10 Chi-Square Tests and One-Way ANOVA.
1 Introduction to Policy Processes Dan Laitsch. 2 Overview (Class meeting 5) Sign in Agenda –PBL break out, final project polishing –Centre Jobs –Review.
Educational Research Chapter 13 Inferential Statistics Gay, Mills, and Airasian 10 th Edition.
ANOVA: Analysis of Variance.
Chapter 13 CHI-SQUARE AND NONPARAMETRIC PROCEDURES.
Section 10.2 Independence. Section 10.2 Objectives Use a chi-square distribution to test whether two variables are independent Use a contingency table.
1 Analysis of Variance (ANOVA) Educational Technology 690.
Inferential Statistics. The Logic of Inferential Statistics Makes inferences about a population from a sample Makes inferences about a population from.
Chapter Outline Goodness of Fit test Test of Independence.
Non-parametric Tests e.g., Chi-Square. When to use various statistics n Parametric n Interval or ratio data n Name parametric tests we covered Tuesday.
Econ 3790: Business and Economic Statistics Instructor: Yogesh Uppal
Statistics for the Social Sciences Psychology 340 Spring 2009 Analysis of Variance (ANOVA)
Copyright c 2001 The McGraw-Hill Companies, Inc.1 Chapter 11 Testing for Differences Differences betweens groups or categories of the independent variable.
Research Methods and Data Analysis in Psychology Spring 2015 Kyle Stephenson.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 12 Tests of Goodness of Fit and Independence n Goodness of Fit Test: A Multinomial.
© 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Chapter 11 Testing for Differences Differences betweens groups or categories of the independent.
Chapter 13 Understanding research results: statistical inference.
S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 15: Chi-square.
Aron, Aron, & Coups, Statistics for the Behavioral and Social Sciences: A Brief Course (3e), © 2005 Prentice Hall Chapter 10 Introduction to the Analysis.
Educational Research Inferential Statistics Chapter th Chapter 12- 8th Gay and Airasian.
Oneway ANOVA comparing 3 or more means. Overall Purpose A Oneway ANOVA is used to compare three or more average scores. A Oneway ANOVA is used to compare.
McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc.,All Rights Reserved. Part Four ANALYSIS AND PRESENTATION OF DATA.
CHAPTER 15: THE NUTS AND BOLTS OF USING STATISTICS.
I. ANOVA revisited & reviewed
Part Four ANALYSIS AND PRESENTATION OF DATA
Part Three. Data Analysis
Econ 3790: Business and Economic Statistics
Last class Tutorial 1 Census Overview
Part IV Significantly Different Using Inferential Statistics
UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE
Parametric versus Nonparametric (Chi-square)
CLASS 6 CLASS 7 Tutorial 2 (EXCEL version)
Presentation transcript:

Part IV Significantly Different: Using Inferential Statistics Chapter 13  Two Groups Too Many? Try Analysis of Variance (ANOVA)

What you will learn in Chapter 13 What Analysis of Variance (ANOVA) is and when it is appropriate to use How to compute the F statistic How to interpret the F statistic How to use SPSS to conduct an ANOVA single factor design

Analysis of Variance (ANOVA) Used when more than two group means are being tested simultaneously Group means differ from one another on a particular score / variable Example: DV = GRE Scores & IV = Ethnicity Test statistic = F test R.A. Fisher, creator

Path to Wisdom & Knowledge How do I know if ANOVA is the right test?

Different Flavors of ANOVA ANOVA examines the variance between groups and the variances within groups These variances are then compared against each other Similar to the t Test…only in this case you have more than two groups One-way ANOVA Simple ANOVA Single factor (grouping variable)

More Complicated ANOVA Factorial Design More than one treatment/factor examined Multiple Independent Variables One Dependent Variable Example – 3x2 factorial design Number of Hours in Preschool G e n d r Male 5 hours per week 10 hours 20 hours Female

Computing the F Statistic Rationale…want the within group variance to be small and the between group variance to be large in order to find significance.

Hypotheses Null hypothesis Research hypothesis

Source Table Source SS df MS F Between 1,133.07 27 566.54 8.799 Within 1,738.40 29 64.39 Note: F value for two group is the same as t2

Degrees of Freedom (df) Numerator Number of groups minus one k-1 3 groups --- 3 – 1 = 2 Denominator Total number of observations minus the number of groups N-1 100 participants --- 30 – 3 = 97 Represented: F (2, 27)

How to Interpret F (2,27) = 8.80, p < .05 F = test statistic 2,27 = df between groups & df within groups {Ah ha…3 groups and 30 total scores examined} 8.80 = obtained value Which we compared to the critical value p < .05 = probability less than 5% that the null hypothesis is true Meaning the obtained value is GREATER than the critical value

Omnibus Test The F test is an “omnibus test” and only tells you that a difference exists Must conduct follow-up t tests to find out where the difference is… BUT…Type I error increases with every follow-up test / possible comparison made 1 – (1 – alpha)k Where k = number of possible comparisons

Using the Computer SPSS and the One-Way ANOVA

SPSS Output What does it all mean?

Post Hoc Comparison

Glossary Terms to Know Analysis of variance Omnibus test Simple ANOVA One-way ANOVA Factorial design Omnibus test Post Hoc comparisons Source table

Part IV Significantly Different: Using Inferential Statistics Chapter 17     What to Do When You’re Not Normal: Chi-Square and Some Other Nonparametric Tests

What you will learn in Chapter 17 A brief survey of nonparametric statistics When they should be used How they should be used

Introduction Parametric statistics have certain assumptions Variances of each group are similar Sample is large enough to represent the population Nonparametric statistics don’t require the same assumptions Allow data that comes in frequencies to be analyzed…they are “distribution free”

One-Sample Chi-Square Chi-square allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance. One-sample chi-square (goodness of fit test) only has one dimension Two-sample chi-square has two dimensions

Computing Chi-Square What do those symbols mean?

More Hypotheses H0: P1 = P2 = P3 H1: P1 P2 P3 Null hypothesis Research hypothesis H1: P1 P2 P3

Computing Chi Square C2 = 20.6 For 23 30 7 49 1.63 Maybe 17 13 169 Category O E D (O-E)2 (O-E)2/2 For 23 30 7 49 1.63 Maybe 17 13 169 5.63 Against 50 20 400 13.33 Total 90 C2 = 20.6

So How Do I Interpret… x2(2) = 20.6, p < .05 x2 represents the test statistic 2 is the number of degrees of freedom 20.6 is the obtained value p < .05 is the probability

Using the Computer One-Sample Chi Square using SPSS

SPSS Output What does it all mean?

Other Nonparametric Tests

Glossary Terms to Know Parametric Nonparametric One-sample Chi Square