Lecture16-March+4th-Factorial+design

# Lecture16-March+4th-Factorial+design -  ...

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Unformatted text preview:   Exercise 5 due on Tuesday    Questions?    Extra credit will be available today after class,  for a week.    Once you start the assignment you will have 20  minutes to complete it.    Topics covered are the same as midterm 2.     Midterm 3 next Thursday.    Chapters 7, 8, 9, 10, 11    Lectures 12, 13, 14, 15, 16, 17    SKIP CHAPTER 12    Last minute Q&A session as usual Thursday 11.00  to 12.30  Multiple‐group Experiments     Eﬃciency    Reduce number of experiments & participants     Discovering relationship type    Improve validity    Control for confounding variables    Reduce participants guessing the hypothesis    Could we use t‐test?    Yes…but tedious, and increased chance of  Type I error…    We could use Bonferroni adjustment, but that  will increase chance of Type II error...    Better method is ANOVA    Between group variability: Random error  variability +treatment variability    Within group variability: due only to random  error within each group  Signal Noise = Variance between groups Variance within groups = F ratio   Between SS design    One‐Way Analysis of variance (ANOVA; F‐test)  ▪  Data are interval or ratio   ▪  The underlying distribution is normally distributed  ▪  The variances among the populations being compared  are similar   ▪  The observations are all independent of one another  (groups are independent)    One‐way = one factor, one IV    Within SS or matched design    One‐Way repeated measure ANOVA  ▪  One‐way = one factor, one IV    Diﬀerences?  MSB ▪  One‐way ANOVA =  F = MSW ▪  MSB= between treatment, not groups (there’s just one  group!)   € ▪  MSw= is MSE  No treatment Study B Group means 40 42 38 40 40 Meditation Exercise 60 60 58 62 60 78 82 80 80 80   One‐way RM ANOVA  Mean for each group  2.  Overall mean = 60  3.  Calculate “b/w treatment”  SS  1.  ( 2 )( 2 )( SSB = n M1 − M + n M 2 − M + n M 3 − M 2 SSB= 4(40‐60)2 + 4(60‐60)€ + 4(80‐60)2 = 3200  ) 2 No treatment Study B Group means 40 42 38 40 40 dfB= (k ‐ 1) = 2  Meditation Exercise 60 60 58 62 60 78 82 80 80 80 €   One‐way RM ANOVA  Mean for each group  2.  Overall mean = 60  3.  Calculate “b/w treat.” SS  4.  Calculate b/w treat. MS  1.  MSBETWEEN SSB = df B MSB= 3200/2= 1600  No treatment Study B Group means 40 42 38 40 40 0  2  ‐2  0  Meditation Exercise 60 60 58 62 60 0  0  ‐2  2  78 82 80 80 ‐2  2  0  0    One‐way RM ANOVA  5.  Calculate “w groups” SS  Split into 2 sources  80 PP variance  SSw= 0+4+4+0+0+0+4+4+4+4+0+0= 24  error variance  No treatment Study B Group means 59  61  59  61  Meditation Exercise   One‐way RM ANOVA  5.  Calculate “w groups” SS  40 42 38 40 60 60 58 62 78 82 80 80 6.  Calculate  participants SS  40 60 80€ SSerror= SSw – SSPP = 12  2 SSPARTICIPANT = ∑ ( M P − M ) K 7.  Calculate  error SS  SSPP= 3(59‐60)2+3(61‐60)2 + 3(59‐60)2 + 3(61‐60)2 = 12  No treatment Study B Group means 40 42 38 40 40 0  2  ‐2  0  Meditation Exercise 60 60 58 62 60 0  0  ‐2  2  78 82 80 80 ‐2  2  0  0  80   One‐way ANOVA  8.  Calculate error MS  € MSERROR SSE = df E dfE= (k ‐ 1) (n‐1) = 2 x 3 = 6  MSE= 12/6= 2  No treatment Study B Group means 40 42 38 40 40 0  2  ‐2  0  Meditation Exercise 60 60 58 62 60 0  0  ‐2  2  78 82 80 80 80 ‐2  2  0  0    One‐way ANOVA  9.  Calculate F ratio  MSB F= MSE F= 1600/2= 800  € Look at table for F value. Critical F is 4.26  F= 1600/2.6= 601.5  How do the groups diﬀer?    A signiﬁcant overall F requires follow‐up   (post hoc) analyses    Bonferroni: Planned comparisons    Tukey: Unplanned comparisons  What is the functional relationship?    Post hoc trend analyses  Multiple‐group Experiments     Basic terminology    2X2 factorial designs    Expanding on the 2X2 factorial    Factorial Study Example    Eﬀects of caﬀeine and alcohol on people’s  reaction time  Factor 1 No caffeine Level 1 Factor 2 200mg caffeine Level 2 400mg caffeine level3 No alcohol Level 1 Condition 1 Condition 2 Condition 3 Alcohol Level 2 Condition 4 Condition 5 Condition 6 Two-factor design 2X3 factorial design   Simple experiment    Multiple‐group experiment    2X3 Factorial design  No caffeine 200mg caffeine 400mg caffeine No alcohol Reaction Time Reaction Time Reaction Time Alcohol Reaction Time Reaction Time Reaction Time   Basic terminology    2X2 factorial designs    Expanding on the 2X2 factorial  2 levels of exercise 2 levels of caloric intake Experiment 1: 2 levels of exercise Experiment 2: 2 levels of caloric intake Advantages of factorial designs: –  more ‘realistic’ situation –  Combined effect of the factors on the dependant variable Exercise No Yes Not caloric reduced intake reduced •  Main effects: unique effect of each factor •  Interaction: combined effect of both factors •  Simple effects: effect of a factor in one level of the other factor Exercise No Not caloric reduced intake reduced 2 Yes 7 9 4 11 6 14 20 Two simple effects for ‘caloric intake’ Two simple effects for ‘exercise’ •  Simple effects: effect of a factor in one level of the other factor Exercise No Not caloric reduced intake Yes 2 9 5.5 7.5 6 20 4 reduced 14.5 Not caloric reduced intake reduced 13 5.5 13 Main Effect of ‘caloric intake’ on weight loss Exercise No Not caloric reduced intake reduced Yes 2 9 5.5 6 20 13 4 10.5 14.5 Exercise No Yes 4 14.5 Main Effect of ‘exercise’ on weight loss   Interaction: combined eﬀect of both factors  on the dependent variable  –  One shot of alcohol => ‘2’  –  One painkiller pill     => ‘2’  –  One shot of alcohol+ one pill => ‘7’    Interaction: combined eﬀect of both factors  Exercise No Not caloric reduced intake reduced 2 Yes 7 9 4 11 6 14 20   Possible outcomes:    The 2 factors combined have an intensiﬁed eﬀect  on the dependent variable    The 2 factors combined have a weakening eﬀect  on the dependent variable    The 2 factors combined have a reversed eﬀect on  the dependent variable    One main eﬀect, no interaction    Two main eﬀects, no interaction    No main eﬀects, no interaction    One main eﬀect, interaction    Two main eﬀects, interaction    No main eﬀects, interaction    Are there gender diﬀerences in diet eﬃcacy?  Gender Males Diet No diet diet 1 Females 0 1 9 1 9 10 0 10 5.5 0 5.5 9 10 Amount of weight loss diet no diet 12 10 8 6 4 2 0 males females Gender   Eﬀects of alcohol and caﬀeine on reaction time?  Caffeine 0mg No alcohol Alcohol 2 shots of alcohol 225 400mg -50 175 50 200 50 275 -50 225 250 -50 200 50 250 Reaction Time (in Msec) no alcohol 300 275 250 225 200 175 150 0mg 400mg Level of Caffeine 2 shots   Eﬀect of ﬂowers & dating status on happiness?  Receiving Flowers no flowers Single Dating Status 1 flowers 8 9 4 Dating 5 -4 5 0 5 3 4 7 0 5   Eﬀects of team allegiance and game result on happiness?  Game Outcome Kings win Kings fans Team Allegiance Lakers fans 9 Lakers win -8 1 -8 5 8 1 8 9 5 0 5 0 5   Analyses of Variance    For single factor: one‐way ANOVA  ▪  Multiple group study (1 IV, more than 2 groups of scores)    For two factors design: two‐way ANOVA  ▪  We get F‐ratio for each of the components:  ▪  For main eﬀect of factor 1  ▪  For main eﬀect of factor 2  ▪  For the interaction    For three factors: three‐way ANOVA etc…    Main eﬀect    On average the factor has an eﬀect    Interaction    Eﬀect of one factor moderated by the other  Receiving Flowers no flowers Single Dating Status Dating flowers 1 9 5 5 3 5 7 5   Is there an interaction between the 2 factors?    If the diﬀerence in groups’ means changes within   each pair of simple eﬀects     Or when graphing – lines are NOT parallel  There is an interaction  * Assuming all diﬀerences are statistically signiﬁcant    If there is an interaction, what kind?    Ordinal  ▪  lines in graphs have same direction of slope  ▪  Or one line is horizontal (the other is slanted)     Disordinal  ▪  lines in graph have diﬀerent direction of slopes    Ordinal Interaction: same direction of slope  level 2 level 1 80 Dependent variable Dependent variable level 1 70 60 50 40 level 2 80 70 60 50 40 30 30 20 20 10 10 0 0 level 1 level 2 Factor 1 level 1 level 2 Factor 1   Disordinal Interaction: diﬀerent direction of  slopes  Kings fans Lakers fans 10 Happiness 8 6 4 2 0 Kings win Lakers win Game Outcome   Basic terminology    2X2 factorial designs    Expanding on the 2X2 factorial  No caffeine   Experimental    Factors are manipulated  caffeine R.T. R.T. R.T. R.T. Male Female Single Hap Hap Dating Hap Hap Male Female No alcohol R.T. R.T. alcohol R.T. R.T. No alcohol alcohol   Quasi‐experimental    Factors are not manipulated  ▪  Participant variable    Combined strategies    Some factors are manipulated    Some factors are not manipulated    All examples were of between‐participants  factorials designs    We can also do factorial designs within  participants    Every participant goes through the diﬀerent  conditions    Or – we can do a mixed factorial  Imaginar   One between one within  3-yearolds 5-yearolds Real y How afraid How afraid How afraid How afraid   More than two factors    The complexity of the experimental design  increases    More main eﬀects    More interactions    Example ‐ With 3 factors we have    3 main eﬀects (A; B; C)    3 two‐way interactions (A x B; B x C; A x C)    1 three‐way interaction (A x B x C)  YES NO ONE GROUP? YES Z test t test Population parameters known? NO YES TWO GROUPS YES Independent groups t-test Are scores independent? NO Correlated groups t-test YES NO 3 or more GROUPS? YES ONE-WAY ANOVA ONE-WAY RM ANOVA Are scores independent? YES More than 1 factor? TWO-WAY (3-way..) ANOVA NO RM ANOVA Are scores independent? ...
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## This note was uploaded on 06/21/2011 for the course PSYCHOLOGY Psych 41 taught by Professor Castelli during the Winter '10 term at UC Davis.

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