Simple ANOVA Example - Experimental Research Methods - Lecture Slides, Slides of Research Methodology

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Multifactor Experiments-FirstDesigning and Analyzing

a SIMPLE Example docsity.com

The Observations and Theory

• I would like to know if the temperatureof a room has an influence on

aggression.

The Design

• I will bring children into myexperiment and randomly assign

them to be in either a 60 100 o room. o, 80o^ or

• The IV will be temperature ofroom and it has 3 levels.
• This is a between-subjectsfactor.

The Design

• After being in the room for an hour, I will frustratethem by taking away the toys which they are playing with (they’re for some other kid), but I’ll

leave a Bobo doll. – I’ll measure the number of times the kids hit the

• Bobo doll in a ten min period.The DV, which as a hypothetical construct is

aggression, will be operationally defined as thenumber of hits.

The Data

Person 1 601 o^802 o^10012 o Person 2 Total 34 46 1426 36 Mean 2 3 13 6

Sum of Squares

• SS = Sum of the squareddeviations from the mean
• If you recall from stats class (andour earlier discussions) SS/n =

variance

SS   ^ X  X ^2

SSTotal

• Scores 1 Mean 6 -5 - 32 66 -3-4 - 124 66 -2
  • Total^14 6 80 SSTotal^64 = -  X  X   X  X 

Partitioning the SS

• Of this SSsome is bad.Total, some is good and
  • If I put two people intodifferent treatment groups,

they should act differently(SSBetween).

SSWithin

Score Mean^ •^ In the 80o^ group

Total 2

 X  X ^2 Score 2 Mean 3 1 Total^4 3 Score 12 Mean 13 1 Total^14 13

 X  X ^2

 In the 60o^ group  X  X  2

 In the 100o^ group 2  2  2  6   SSWithin SS in  each group

SSBetween

9 ^3  2680 ^218 ^9

For^ o  4913 26  9849

(^1002)   

For^ o 16 ^2  2660  ^232 ^16

For^ o

32  18  98  148  SSBetween

SSBetween  (^)  ( GroupMeans  Grand Mean )^2  n

Summary Table

Source SS df MS F Obt F Crit Between (^148) 3-1=2 k -1= Within (^6) 6-3=3 N - k = Total (^154) 6-1=5 N -1=

Summary Table

Source SS df MS F Obt F Crit Between 148 2 148/2= 74 Within 6 3 6/3= Total 154 5

Summary Table

Betwee^ Source^ SS^ df^ MS^ F Obt^ F Crit Within^ n^1486 23 742 37 9. Total 154 5

Conclusion for the Omnibus F

• Since F Obt > F Crit, we reject H 0
• • If we reject HBut which outcome is true? 0 , we’re left with Ha
• We do NOT know yet!!!

HH a^0 ::^  Not^60  all ^80 ' s are ^100 equal

6060 8080 100100

60 80 100   

    

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