34 Lecture 8 - Single-Factor ANOVA (updated Nov 10)

# 34 Lecture 8 - Single-Factor ANOVA (updated Nov 10) -...

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Lecture 8: Single-Factor ANOVA Section 11-1

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2 ANOVA ANOVA stands for  AN alysis  O VA riance ANOVA allows us to: Do multiple tests of means at one time more than two groups Test for multiple effects simultaneously more than one variable
3 ANOVA Tests The types of ANOVA we will look at are: Single-Factor (One Way) ANOVA Today Randomized block design ANOVA Two-Factor ANOVA Both next class We will also see ANOVA in regression  analysis

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4 ANOVA Assumptions 1. All populations are normally distributed 2. The population variances are equal ANOVA tests assume that variances can be  pooled 3. The observations are independent These are important in order to  understand ANOVA See page 410 in textbook
5 One-Way ANOVA One-way ANOVA allows us to  simultaneously test to determine if two  or more population means are equal H 0 : μ 1  =  μ 2  =  μ 3 H A : At least two means differ

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6 Example We are interested in seeing if the  advertising strategies employed in  different cities made a difference We assume that these cities have been  shown to be similar in the past The sales results for 10 weeks in each  of the these cities is displayed on the  next slide
7 Example Data 529 498 804 492 672 691 658 663 630 719 531 733 793 604 774 787 443 698 514 495 717 699 596 776 663 485 679 572 602 561 719 557 604 523 502 572 711 353 620 584 659 469 606 557 697 634 689 581 461 542 706 580 675 679 529 614 615 624 512 532 City 1 City 2 City 3 Convenience Quality Price

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8 Terminology We have a  response variable , the level  of weekly sales There is one  factor  (i.e. variable): type  of advertising strategy  There are three  treatments or levels  (i.e. variable values): the different  strategies used in these cities
529 498 804 492 672 691 658 663 630 719 531 733 793 604 774 787 443 698 514 495 717 699 596 776 663 485 679 572 602 561 719 557 604 523 502 572 711 353 620 584 659 469 606 557 697 634 689 581 461 542 706 580 675 679 529 614 615 624 512 532 Mean 577.55 Mean 653.00 Mean 608.65 613.0667 Grand Mean City 1 City 2 City 3 Convenience Quality Price Means and Grand Mean X ij  values of  response variable     i  values X X

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10 The Logic of ANOVA Let’s learn to think in terms of  variation: Variation of X values around Variation of    values around   Variation in some set of values means
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## This note was uploaded on 09/25/2010 for the course OMIS OMIS 1000 taught by Professor Alexandershoumarov during the Fall '09 term at York University.

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34 Lecture 8 - Single-Factor ANOVA (updated Nov 10) -...

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