SEMINAR ON ONE WAY ANOVA

Slides:



Advertisements
Similar presentations
Chapter 10 Hypothesis Testing Using Analysis of Variance (ANOVA)
Advertisements

1 Analysis of Variance This technique is designed to test the null hypothesis that three or more group means are equal.
Independent Sample T-test Formula
Chapter 10 Hypothesis Testing III (ANOVA). Basic Logic  ANOVA can be used in situations where the researcher is interested in the differences in sample.
Lesson #23 Analysis of Variance. In Analysis of Variance (ANOVA), we have: H 0 :  1 =  2 =  3 = … =  k H 1 : at least one  i does not equal the others.
PSY 307 – Statistics for the Behavioral Sciences
Intro to Statistics for the Behavioral Sciences PSYC 1900
Lecture 9: One Way ANOVA Between Subjects
Statistics for the Social Sciences
Hypothesis Testing Using The One-Sample t-Test
Psy B07 Chapter 1Slide 1 ANALYSIS OF VARIANCE. Psy B07 Chapter 1Slide 2 t-test refresher  In chapter 7 we talked about analyses that could be conducted.
AM Recitation 2/10/11.
Calculations of Reliability We are interested in calculating the ICC –First step: Conduct a single-factor, within-subjects (repeated measures) ANOVA –This.
PSY 307 – Statistics for the Behavioral Sciences Chapter 16 – One-Factor Analysis of Variance (ANOVA)
Psychology 301 Chapters & Differences Between Two Means Introduction to Analysis of Variance Multiple Comparisons.
1 Chapter 13 Analysis of Variance. 2 Chapter Outline  An introduction to experimental design and analysis of variance  Analysis of Variance and the.
Copyright © 2004 Pearson Education, Inc.
Chapter 10: Analyzing Experimental Data Inferential statistics are used to determine whether the independent variable had an effect on the dependent variance.
One-Way Analysis of Variance
One-Way ANOVA ANOVA = Analysis of Variance This is a technique used to analyze the results of an experiment when you have more than two groups.
Chapter 17 Comparing Multiple Population Means: One-factor ANOVA.
Copyright © Cengage Learning. All rights reserved. 12 Analysis of Variance.
Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 1 Understandable Statistics S eventh Edition By Brase and Brase Prepared by: Lynn Smith.
Chapter 10 Hypothesis Testing III (ANOVA). Chapter Outline  Introduction  The Logic of the Analysis of Variance  The Computation of ANOVA  Computational.
Kin 304 Inferential Statistics Probability Level for Acceptance Type I and II Errors One and Two-Tailed tests Critical value of the test statistic “Statistics.
CHAPTER 10 ANOVA - One way ANOVa.
Significance Tests for Regression Analysis. A. Testing the Significance of Regression Models The first important significance test is for the regression.
Slide Slide 1 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Overview and One-Way ANOVA.
Chapter 13 Understanding research results: statistical inference.
 List the characteristics of the F distribution.  Conduct a test of hypothesis to determine whether the variances of two populations are equal.  Discuss.
The 2 nd to last topic this year!!.  ANOVA Testing is similar to a “two sample t- test except” that it compares more than two samples to one another.
Six Easy Steps for an ANOVA 1) State the hypothesis 2) Find the F-critical value 3) Calculate the F-value 4) Decision 5) Create the summary table 6) Put.
One-Way Between-Subjects Design and Analysis of Variance
Chapter 9 Hypothesis Testing.
Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc.
Chapter 10 Two-Sample Tests and One-Way ANOVA.
Hypothesis Testing: One Sample Cases
Statistics: A Tool For Social Research
An Introduction to Two-Way ANOVA
i) Two way ANOVA without replication
Applied Business Statistics, 7th ed. by Ken Black
10 Chapter Chi-Square Tests and the F-Distribution Chapter 10
Hypothesis Testing Review
Chapter 8 Hypothesis Testing with Two Samples.
CHAPTER 12 ANALYSIS OF VARIANCE
Comparing k Populations
Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays.
Kin 304 Inferential Statistics
What if. . . You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days a person.
Hypothesis Tests for a Population Mean in Practice
Levene's Test for Equality of Variances
Chapter 11 Analysis of Variance
Comparing k Populations
Analysis of Variance (ANOVA)
Introduction to ANOVA.
Lecture Slides Elementary Statistics Eleventh Edition
Comparing Three or More Means ANOVA (One-Way Analysis of Variance)
Hypothesis Testing.
What if. . . You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days.
One way ANALYSIS OF VARIANCE (ANOVA)
One-Way ANOVA ANOVA = Analysis of Variance
Statistics for the Social Sciences
Six Easy Steps for an ANOVA
Chapter 12: Introduction to Analysis of Variance
Psych 231: Research Methods in Psychology
Chapter 15 Analysis of Variance
Chapter 10 – Part II Analysis of Variance
Statistical Inference for the Mean: t-test
ANalysis Of VAriance Lecture 1 Sections: 12.1 – 12.2
Quantitative Methods ANOVA.
Presentation transcript:

SEMINAR ON ONE WAY ANOVA PRESENTED BY: AMISH GANDHI ROLL NO: 2 M.PHARM-II GUIDED BY: DR. M. C. GOHEL ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

CONTENTS DEFINITION TYPES OF ANOVA WHY DO AN ANOVA, NOT MULTIPLE T-TESTS? ASSUMPTIONS OF ONE WAY ANOVA COMPUTING A ONE WAY ANOVA ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

One-Way ANOVA The one-way analysis of variance is used to test the claim that three or more population means are equal. This is an extension of the two independent samples t-test. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

TYPES OF ANOVA ONE WAY ANOVA TWO WAY ANOVA ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

HOW THEY DIFFER? ANOVA One-Way ANOVA Two way ANOVA One independent variable Only one ‘p’ value is obtained. Two independent Variables. Three different ‘p’ values are obtained. Outcome of factorial Design. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Why do an ANOVA? when there are 3 or more means being compared, statistical significance can be ascertained by conducting one statistical test, ANOVA, or by repeated t-tests. Why not conduct repeated t-tests? Each statistical test is conducted with a specified chance of making a type I–error—the alpha level. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Why do an ANOVA? Why not several t-tests? Imagine we have a design with three groups that have to be compared: G1, G2, G3 We will have to run several separate t-tests (one to compare G1 with G2, one to compare G1 with G3, and one to compare G2 with G3) For every test we use a general α-level of 0.05 ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Our scope is too reduce the possibilities to have Type I error α -level=0.05 5% possibility to make Type I error, i.e. rejecting H0, when H0 is actually true. Our scope is too reduce the possibilities to have Type I error If we were to run 3 separate t-tests to compare G1, G2 and G3, each with a α-level of 0.05, the overall possibility not to make Type I error would be 0.857 [i.e. (0.95)3] Therefore subtracting that from the overall possibility not to make Type 1 error (1=100%) 1-0.857=0.14 We have 14% of possibilities to make Type 1 error. 14% >> than the usual 5% We can’t be happy with that! ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

27% of possibilities to make type I error!! FER: The familiwise errorrate FER: 1 – (0.95)n Where n is the number of tests that have to be carried out The larger the number of tests that have to be carried out the larger the possibility to have Type I error. Example with 4 groups 1 – (0.95)6=0.27 27% of possibilities to make type I error!! ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Assumptions of one way ANOVA The data are randomly sampled and independently chosen from the populations The variances of each sample are assumed equal. The residuals are normally distributed. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

State the null hypothesis and alpha level The null hypothesis is that all the groups have equal means. H0: μ1 = μ 2 = μ 3 The alternative hypothesis is that there is at least one significant difference between the means Level of significance α is selected as 0.05 ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Computing a one-way ANOVA Here is the basic one-way ANOVA table Source SS df MS F p F crit Between Within Total ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Sum of squares (SS) • Sum of squares are nothing but sum of squared deviations around the mean i.e. ( X- )2 To calculate the various sums of squares, we need: i) the ΣX2 (sum of each score squared) in the whole sample ii) the ΣX (sum of all scores) for the whole sample iii) and the Group ΣX (sum of scores separately for each group): represented as ΣXg in as follows

ΣXg= ΣX2 = FRONT ROW MIDDLE ROW BACK ROW 8 13 9 11 6 15 14 12 10 17 112 153 129 1082 1993 1413 9.33 12.75 10.75 ΣXg= = 394 ΣX2 = = 4488 Mean = ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

SStotal = ΣX2 - (ΣX)2 N = 4488 - 3942 / 36 = 4488 - 4312.11 = 175.88 FRONT ROW MIDDLE ROW BACK ROW TOTAL ΣXg 112 153 129 394 ΣX2 1082 1993 1413 4488 SStotal = ΣX2 - (ΣX)2 N = 4488 - 3942 / 36 = 4488 - 4312.11 = 175.88 ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

SSbetween = (ΣXg)2 - (ΣX)2 FRONT ROW MIDDLE ROW BACK ROW TOTAL ΣXg 112 153 129 394 ΣX2 1082 1993 1413 4488 SSbetween = (ΣXg)2 - (ΣX)2 = 1122 + 1532 + 1292 - (3942 / 36) 12 = 4382.83 - 4312.11 = 70.72 n N

SStotal = 175.88 SSbetween = 70.72 SSwithin = SStotal – SSbetween = 175.88 - 70.72 = 105.16

After filling in the sum of squares, we have … Source SS df MS F p F crit Between 70.72 Within 105.16 Total 175.88

Degrees of Freedom The degrees of freedom, noted in are calculated as Ni -1 for the total(Ni is the total number of observations); number of groups minus one for the between groups; And for the within error, subtract d.f. for groups from the total degrees of freedom.

Total degrees of freedom = total number of observations - 1 = 36-1 = 35 Degrees of freedom between groups = Total number of groups – 1 = 3-1 = 2 Degrees freedom within groups = Total d.f – Between group d.f = 35-2 = 33 ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Filling in the degrees of freedom gives this … Source SS df MS F p F crit Between 70.72 2 Within 105.16 33 Total 175.88 35 ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

Mean Squares-MS (Variance) Why variance estimates are called Mean Squares? A population variance is equal to the sum of the squared deviations about the mean divided by N. So the population variance is really the mean of the squared deviations about the mean, or the mean square(d) deviation about the mean. This is why the term mean square is used in place of variance. It is obtained by dividing each sum of squares with corresponding degrees of freedom. Σ( X - )2 N ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

So, Ms between MS within = 70.7222 / 2 = 105.1667 / 33 = 35.36 = 3.18 Source SS df MS F p F crit Between 70.72 2 35.36 Within 105.16 33 3.18 Total 175.88 35

Fcalculated value It is the ratio of MSbetween and MSwithin F = MS(B) / MS(W) So, F = 35.3611 = 11.10 3.1869 Source SS df MS F p F crit Between 70.72 2 35.36 11.10 Within 105.16 33 3.18 Total 175.88 35

Source SS df MS F p F crit Between Within Total Putting value of F crit to ANOVA table Source SS df MS F p F crit Between 70.72 2 35.36 11.10 3.32 Within 105.16 33 3.18 Total 175.88 35 ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

P- value It is the area under the F distribution curve that is to the right of your observed F-statistic. This area may be obtained by integral calculus P-value F-distribution: If the P-value is less than or equal to a, reject H0. It the P-value is greater than a, fail to reject H0. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

One-Way ANOVA: Interpretation Our obtained F of 11.10 is greater than the critical F of 3.32 i.e. Fcalculated > Fcritical and p- value is less than 0.05 We reject the null hypothesis and accept the alternative hypothesis that there is at least a difference between two of the group means. If Fcal < Fcrit,We fail to reject the null hypothesis and conclude that there are no significant differences between the group means. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

HOW TO CALCULATE P- VALUE IN EXCEL? ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI

QUITERS NEVER WIN AND WINNERS NEVER QUIT. THANK YOU…. ROLL NO. 2 M.PHARM II (2008-09) AMISH GANDHI