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Topic 12 - Topic 12 Further Topics in ANOVA Unequal Cell...

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1 Topic 12 – Further Topics in ANOVA Unequal Cell Sizes (Chapter 20)
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2 Overview We’ll start with the Learning Activity. More practice in interpreting ANOVA results; and a baby-step into 3-way ANOVA. An illustration of the problems that an unbalanced design will cause. We’ll then continue with a discussion of unbalanced designs (Chapter 20)
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3 Collaborative Learning Activity Take your time going through this. Ask questions as needed!
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4 Question 1 Analyze the design elements.
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5 Design Chart Unequal Cell Sizes – but there is SOME balance achieved Single Factor Analyses will be balanced. Gender*Age = 6 observations per cell Time*Age = 6 observations per cell Gender*Time = Unbalanced Age Young Middle Elderly Young Middle Elderly Weekday xxxx xxx xxxxx xx xxx x Weekend xx xxx x xxxx xxx xxxxx Gender Male Female Time
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6 Question 2 Analyze Age*Time
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7 Interaction Plot (ignoring gender)
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8 Interpretations No interaction is evident between age and time Seems middle age group gets generally higher offers. Seems offers during the week are generally higher than on the weekend (this effect is not as big as the age effect)
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9 Main Effects Plots
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10 ANOVA Sum of Source DF Squares Mean Square F Value Pr > F age 2 316.7222222 158.3611111 169.67 <.0001 time 1 53.7777778 53.7777778 57.62 <.0001 age*time 2 0.3888889 0.1944444 0.21 0.8131 Error 30 28.0000000 0.9333333 Total 35 398.8888889 Type I vs Type III?
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11 LSMeans #3 (middle aged, weekday) is the highest Using Tukey comparisons it is significantly higher than all others. “Slicing” will show the same things that we guessed from the plots.
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12 LSMeans (sliced) Least Squares Means age*time Effect Sliced by time for offer Sum of time DF Squares Mean Square F Value Pr > F wkday 2 148.111111 74.055556 79.35 <.0001 wkend 2 169.000000 84.500000 90.54 <.0001 age*time Effect Sliced by age for offer Sum of age DF Squares Mean Square F Value Pr > F Elderly 1 18.750000 18.750000 20.09 0.0001 Middle 1 14.083333 14.083333 15.09 0.0005 Young 1 21.333333 21.333333 22.86 <.0001
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13 Slicing of LSMeans Sums of Squares add to??? DF add to??? Effect of slicing is to look at differences for one of the two factors at a specific level of the other factor . Interpretations???
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14 Question 3 Analyze Age*Gender
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15 Interaction Plot (ignoring Time)
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16 Interpretations Small interaction is seen; might be described as follows: There is still a clear main effect: Middle aged get higher offers in general There seem to be no gender differences for middle aged or young. For elderly, women may be getting lower offers than men.
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17 LSMeans (sliced comparisons) Least Squares Means age*gender Effect Sliced by gender for offer Sum of gender DF Squares Mean Square F Value Pr > F Female 2 184.333333 92.166667 38.58 <.0001 Male 2 137.444444 68.722222 28.77 <.0001 age*gender Effect Sliced by age for offer Sum of age DF Squares Mean Square F Value Pr > F Elderly 1 10.083333 10.083333 4.22 0.0487 Middle 1 0.083333 0.083333 0.03 0.8531 Young 1 0.333333 0.333333 0.14 0.7114
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18 ANOVA / LSMeans Only age differences show up in the ANOVA.
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