Student Factorial ANOVA JASP

Factorial ANOVA: Between-Subjects Design  We have done: one-way between and one-way within designs - One-way: One independent variable, one dependent variable. __________________________________________________________  Factorial designs involve more than one IV, at least two, could be more.  Sometimes they are referred to as two-way, three-way, four-way, etc.  This tells you the number of IV involved. Always only one DV.  Sometimes they are referred to by the number of levels of the IVs and at the same time telling you the number of IVs themselves. o For example: a 2 x 3 x 2 design or a 4 x 3 x 3 x 2 design.  With factorial designs, you have more than one effect. If only two IVs, you have three effects: two main effects and one interaction effect.  The main effects are informative, but, if you find and interaction effect, the focus of your meaningful interpretation is on the interaction as it tells you more.  Factorial Between Subjects ANOVA – different subjects in all conditions  Factorial Within Subjects ANOVA – the same subject in all conditions

Example: Factorial Between Subjects ANOVA A B C IV2 Y Mean DV Mean DV Mean DV Marginal Mean Y Main Effect of IV 2 Z Mean DV Mean DV Mean DV Marginal Mean X Marginal mean A Marginal Mean B Marginal Mean C Main Effect of IV 1 IV1 A B C Mean DV Mean DV Mean DV Mean DV Mean DV Mean DV Marginal mean A Marginal Mean B Marginal Mean C Main Effect of IV 1 Main Effect of IV 1 IV2 Y Mean DV Mean DV Mean DV Marginal Mean Y Main Effect of IV 2 Z Mean DV Mean DV Mean DV Marginal Mean X Main effects of IV2

Factorial ANOVA: Between-Subjects Design Data Set – goggles (Field, Miles & Field, 2012) Question An anthropologist was interested in the effects of alcohol on mate selection at nightclubs. Her rationale was that after alcohol had been consumed; subjective perceptions of physical attractiveness would become inaccurate (called beer- goggles effect). She was also interested in whether this effect was different for men and women. She picked 48 students: 24 males and 24 females. She took groups of eight participants to a nightclub and gave them no alcohol (given non-alcoholic drinks), 2 pints of strong lager, or 4 pints of strong lager. At the end of the evening, she took a photograph of the person that the participant was chatting up. She then got a pool of independent judges to assess the attractiveness of the person in each photograph (1 to 100) (Field et al. 2012). What is the DV? _______________________________ What is the IV? IV1 = IV2 =

Questions: 1. Determine if men and women differ in their rating of attractiveness? 2. Determine if alcohol level affected the rating of attractiveness? 3. Determine if the attractiveness rating depends on both one sex and how much alcohol one consumed? - this is what we are interested in

Frequency Tables Frequencies for gender gender Frequenc y Percent Valid PercentCumulative Percent Female 24 50.000 50.000 50.000 Male 24 50.000 50.000 100.000 Missin g 0 0.000     Total 48 100.000       Frequencies for alcohol alcohol Frequenc y Percent Valid PercentCumulative Percent 2 Pints 16 33.333 33.333 33.333 4 Pints 16 33.333 33.333 66.667 None 16 33.333 33.333 100.000 Missin g 0 0.000     Total 48 100.000     What does this tell you? ______________________________________________________________________________ _____________________________________________________________________________ Top Tool Bar Select ANOVA Select ANOVA Move attractiveness into the Dependent Variable Box Move gender and alcohol into the Fixed Factors Box Display Check Descriptive Statistics Check Estimates of effect size eta square Model Check Type 111 Assumption Checks Homogeneity test We are not going to check for the assumption of normality – it is not violated Post Hoc Select- gender, alcohol and gender*alcohol Type : Standard Correction: Tukey

Plots Put gender in the Separate line box Put alcohol in the horizontal axis The order of the variable alcohol was changed “alcohol ordered” – graph display None, 2 Pints, 4 Pints Top Tool Bar Select Descriptives Move attractives into the variable box Move Alcohol order into the split box – copy table Move Alcohol back and place gender into the split box – copy table Check the assumptions for the interaction – that is our primary focus – if we use the main effects we must check the assumption for these as well. Assumption of Homogeneity- Assumption Checks Test for Equality of Variances (Levene's) F df1 df2 p 1.527 5.000 42.000 0.202   What does this tell you? ______________________________________________________________________________ ______________________________________________________________________________ ___________________________________________________________________________ Assumption of Normality- Shapiro Wilk –You do not have to test the assumption of normality for an assignment. Shapiro-Wilk normality test data: dd[x, ] W = 0.89896, p-value = 0.2828 ---------------------------------------------------------------------- interaction(goggles$gender, goggles$alcohol): Male.2 Pints Shapiro-Wilk normality test data: dd[x, ] W = 0.96664, p-value = 0.8704

_____________________________________________________________________ Run Factorial Between Subjects ANOVA ANOVA - attractiveness Cases Sum of Squares df Mean Square F p gender 168.750 1 168.750 2.032 0.161 alcohol 3332.292 2 1666.146 20.065 7.649×10 -7 gender ✻ alcohol 1978.125 2 989.063 11.911 7.987×10 -5 Residuals 3487.500 42 83.036 Note.  Type III Sum of Squares What does this tell you? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ __________________________________________________________________________ Tukey Post Hoc What is this? ______________________________________________________________________________ ______________________________________________________________________________ ____________________________________________________________________________ We are only interested in the interaction, but we will look at the main effect of gender and alcohol and how to interpret these. Post Hoc Test Main Effect of Gender Post Hoc Comparisons - gender Mean Difference SE t p tukey Female Male 3.750 2.63 1.426 0.161

Post Hoc Comparisons - gender Mean Difference SE t p tukey 1 Note.  Results are averaged over the levels of: alcohol Descriptive Statistics attractiveness   Female Male Valid 24 24 Missing 0 0 Mean 60.208 56.458 Std. Deviation 6.338 18.503 Minimum 50.000 20.000 Maximum 70.000 85.000 What is this telling you? ______________________________________________________________________________ ______________________________________________________________________________ _________________________________________________________________________ Main Effect of Alcohol ordered

Post Hoc Comparisons - gender ✻ alcohol Mean Difference SE t p tukey Female 2 Pints Male 2 Pints -4.375 4.556 -0.960 0.928   Female 4 Pints 5.000 4.556 1.097 0.880   Male 4 Pints 26.875 4.556 5.899 7.959×10 -6   Female None 1.875 4.556 0.412 0.998   Male None -4.375 4.556 -0.960 0.928 Male 2 Pints Female 4 Pints 9.375 4.556 2.058 0.329   Male 4 Pints 31.250 4.556 6.859 3.374×10 -7   Female None 6.250 4.556 1.372 0.743   Male None -3.553×10 -15 4.556 -7.798×10 -16 1.000 Female 4 Pints Male 4 Pints 21.875 4.556 4.801 2.776×10 -4   Female None -3.125 4.556 -0.686 0.983   Male None -9.375 4.556 -2.058 0.329 Male 4 Pints Female None -25.000 4.556 -5.487 3.061×10 -5   Male None -31.250 4.556 -6.859 3.374×10 -7 Female None Male None -6.250 4.556 -1.372 0.743 Note.  P-value adjusted for comparing a family of 6 What is this? ______________________________________________________________ Descriptives Descriptives - attractiveness gender alcohol N Mean SD SE Coefficient of variation Female 2 Pints 8 62.500 6.547 2.315 0.105   4 Pints 8 57.500 7.071 2.500 0.123   None 8 60.625 4.955 1.752 0.082 Male 2 Pints 8 66.875 12.518 4.426 0.187   4 Pints 8 35.625 10.836 3.831 0.304   None 8 66.875 10.329 3.652 0.154   What are these? _________________________________________________________

Graph Write your means beside your Tukey post hoc output Cell 1 Cell2 Mean Cell1 Mean Cell2 p value 2 Pints:Female None:Female 62.50 60.63 .998 Not sign- 4 Pints: Female None:Female 57.50 60.63 .983 Not sign None: Male None:Female 66.88 60.63 .743 Not sign 2 Pints: Male None:Female 66.88 60.63 .743 Not sign 4 Pints: Male None:Female 35.63 60.63 .0000306 Significant- 4pints: males – lower than none:female 4 Pints: Female 2 Pints:Female 57.50 62.50 .880 Not sign None: Male 2 Pints:Female 66.88 62.50 .928 Not sign 2 Pints: Male 2 Pints:Female 66.88 62.50 .928 Not sign 4 Pints: Male 2 Pints:Female 35.63 62.50 .0000080 Significant- 4 pints:male lower than 2 pints:Female None: Male 4 Pints: Female 66.88 57.50 .329 Not sign 2 Pints Male 4 Pints: Female 66.88 57.50 .329 Not sign 4 Pints:Male 4 Pints: Female 35.63 57.50 .0002776 Significant-4 pints: Male lower than 4 pints: female 2 Pints: Male None: Male 66.88 66.88 1.0000 Not sign 4 Pints: Male None: Male 35.63 66.88 .0000003 Significant-4 pints:male lower than none:male 4 Pints: Male 2 Pints: Male 35.63 66.88 .0000003 Significant- 4 pints:male lower than 2 pints: male What does this tell you: ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

1. Graph Interaction Write UP