Experimental Research Methods (Subject) / L5 (Lesson)

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• Orthogonal contrasts • SSB represents the dispersion of means, and has dfB = K – 1 degrees of freedom• Contrast ‘explains’ part of the dispersion of the means (SScontrast), has dfcontrast = 1 degrees offreedom Orthogonal is difficult wording for saying that the contrasts are uncorrelated Æ each contrastuses unique information
• Helmert contrasts Helmert contrasts are created by comparing each group mean with the mean of thesubsequent groups The number of Helmert contrasts is always equal to K – 1 a priori
• Post-hoc contrasts • The idea is that you (1) can make as many contrasts as you want to detect which means differ• When setting up the contrasts you can (2) let the data guide you, i.e., the values of the means• Because (1) multiple post-hoc contrasts can be conducted and because you can (2) let the dataguide you, we need a method to control the probability of at least one Type-I error• How we control the probability of at least on Type-I error depends on the type of post-hoccontrasts: contrasts with 2 means (Tukey) or contrasts with t 2 means (Scheffé)
• Trend analysis • If the factor is measured on the interval or ratio level, the SSB is explained by K – 1 orthogonalcontrasts that each test a shape of the relation: linear, quadratic, cubic or higher… Trend analysis contrasts are only orthogonal when the group sizes are equal
• Positive linear effect predominantly rising trend• Negative linear effect Æ predominantly declining trend
• Negative linear effect Æ predominantly declining trend
• • Positive quadratic effect Æ effect increases
• Negative quadratic effect effect decreases
• “Multiple Comparisons” can only be used in case of equal sample sizes per group (��
• “Homogeneous Subsets” summarizes the “Multiple Comparisons” table and can be used with equal and unequalsample sizes per group
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• Planned contrasts A priori • Can be any contrast comparing 2 or moremeans• Syntax using “Special”• Bonferonni: Compare p-value to Dcontrast = D/C
• Trend analysis Testing shape of the relation when theindependent variable is interval or ratio• Syntax using “Polynomial”• Bonferonni: Compare p-value to Dcontrast = D/C
• Helmert contrasts • Comparing each group mean with the mean ofthe subsequent groups• Syntax using “Helmert”• Bonferonni: Compare p-value to Dcontrast = D/C
• Tukey • Simple contrast (2 groups)• Tests all possible pairs of means• Syntax using “TUKEY”• Interpret “Homogeneous subsets” output
• Scheffé • Complex contrast (≥2 groups)• Syntax using “Special”• Computing Fcontrast by hand and comparing itwith Fcv ANOVA

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