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# example_twoway - Stat 2225 Handout Two-Way ANOVA Example...

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Stat 2225 Handout Two-Way ANOVA Example Q15.49 on p. 510. Want to see if the “whiteness” scores depend on the brand of detergent (reduced to three brands from five brands originally) and the temperature in which the detergent is used (cold, warm and hot). Considering only Temperature as the single factor, i.e. doing one-way ANOVA ANOVA Table for Score by Temperature Analysis of Variance ----------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value ----------------------------------------------------------------------------- Between groups 1644.2 2 822.1 5.91 0.0039 Within groups 12105.4 87 139.143 ----------------------------------------------------------------------------- Total (Corr.) 13749.6 89 Considering both Temperature and Brand, without interaction term Analysis of Variance for Score - Type III Sums of Squares -------------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value -------------------------------------------------------------------------------- MAIN EFFECTS A:Temperature 1644.2 2 822.1 6.21 0.0030 B:Detegent 858.2 2 429.1 3.24 0.0439 RESIDUAL 11247.2 85 132.32 -------------------------------------------------------------------------------- TOTAL (CORRECTED) 13749.6 89 -------------------------------------------------------------------------------- All F-ratios are based on the residual mean square error. Note: the SSE (12105.4) from one-way ANOVA is again broken down into SS(B) (now it’s the SS for factor B, not SS for blocking) and SSE (585.2 + 11247.2 = 12105.4). Considering both Temperature and Brand, with interaction term Analysis of Variance for Score - Type III Sums of Squares -------------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value -------------------------------------------------------------------------------- MAIN EFFECTS A:Temperature 1644.2 2 822.1 6.51 0.0024 B:Detegent 858.2 2 429.1 3.40 0.0382 INTERACTIONS AB 1023.4 4 255.85 2.03 0.0983 RESIDUAL 10223.8 81 126.22 -------------------------------------------------------------------------------- TOTAL (CORRECTED) 13749.6 89 -------------------------------------------------------------------------------- All F-ratios are based on the residual mean square error.

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example_twoway - Stat 2225 Handout Two-Way ANOVA Example...

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