Gender and Drink Type Interactions in Advertising: An Analysis using SPSS, Lecture notes of Design

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DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     1   Chapter 15: Mixed design ANOVA Smart Alex’s Solutions Task 1 In  the  previous  chapter  we  looked  at  an  example  in  which  participants  viewed  a  total  of   nine  mock  adverts  over  three  sessions.  In  these  adverts  there  were  three  products  (a   brand  of  beer,  Brain  Death;  a  brand  of  wine,  Dangleberry;  and  a  brand  of  water,   Puritan).  These  could  be  presented  alongside  positive,  negative  or  neutral  imagery.  Over   the  three  sessions  and  nine  adverts,  each  type  of  product  was  paired  with  each  type  of   imagery  (read  the  previous  chapter  if  you  need  more  detail).  After  each  advert   participants  rated  the  drinks  on  a  scale  ranging  from  −100  (dislike  very  much)  through  0   (neutral)  to  100  (like  very  much).  The  design  had  two  repeated-­‐measures  independent   variables:  the  type  of  drink  (beer,  wine  or  water)  and  the  type  of  imagery  used  (positive,   negative  or  neutral).  Imagine  that  we  also  knew  each  participant’s  gender.  Men  and   women  might  respond  differently  to  the  products  (because,  in  keeping  with  stereotypes,   men  might  mostly  drink  lager  whereas  women  might  drink  wine).  Reanalyze  the  data,   taking  gender  (a  between-­‐group  variable)  into  account.  The  data  are  in  the  file   MixedAttitude.sav.  Run  a  three-­‐way  mixed  ANOVA  on  these  data.   Running the analysis To  carry  out  the  analysis  in  SPSS,  follow  the  same  instructions  that  we  did  before.  First  of  all,   access  the  define  factors  dialog  box  by  using  the  file  path   .  We  are  using  the  same  repeated-­‐measures  variables  as  in  Chapter  13  of  the   book,  so  complete  this  dialog  box  exactly  as  shown  there,  and  then  click  on    to  access  the   main  dialog  box.  This  box  should  be  completed  exactly  as  before,  except  that  we  must  specify   gender  as  a  between-­‐group  variable  by  selecting  it  in  the  variables  list  and  clicking    to   transfer  it  to  the  box  labelled  Between-­‐Subjects  Factors  (Figure  1).     DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     2     Figure  1   Gender  has  only  two  levels  (male  or  female),  so  there  is  no  need  to  specify  contrasts  for   this  variable;  however,  you  should  select  simple  contrasts  for  both  drink  and  imagery.  The   addition  of  a  between-­‐group  factor  means  that  we  can  select  post  hoc  tests  for  this  variable  by   clicking  on   .  This  action  brings  up  the  post  hoc  test  dialog  box,  which  can  be  used  as   previously  explained.  However,  we  need  not  specify  any  post  hoc  tests  here  because  the   between-­‐group  factor  has  only  two  levels.  The  addition  of  an  extra  variable  makes  it  necessary   to  choose  a  different  graph  than  the  one  in  the  previous  example.  Click  on      to  access   the  dialog  box  and  place  drink  and  imagery  in  the  same  slots  as  for  the  previous  example,  but   also  place  gender  in  the  slot  labelled  Separate  Plots.  When  all  three  variables  have  been   specified,  don’t  forget  to  click  on    to  add  this  combination  to  the  list  of  plots.  By  asking   SPSS  to  plot  the  drink  ×  imagery  ×  gender  interaction,  we  should  get  the  same  interaction   graph  as  before,  except  that  a  separate  version  of  this  graph  will  be  produced  for  male  and   female  subjects.   As  far  as  other  options  are  concerned,  you  should  select  the  same  ones  that  were  chosen  in   Chapter  13.  It  is  worth  selecting  estimated  marginal  means  for  all  effects  (because  these  values   will  help  you  to  understand  any  significant  effects),  but  to  save  space  I  did  not  ask  for   confidence  intervals  for  these  effects  because  we  have  considered  this  part  of  the  output  in   some  detail  already.  When  all  of  the  appropriate  options  have  been  selected,  run  the  analysis.     DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     5   were  previously  present  (in  a  balanced  design,  the  inclusion  of  an  extra  variable  should  not   affect  these  effects).  By  looking  at  the  significance  values  it  is  clear  that  this  prediction  is  true:   there  are  still  significant  effects  of  the  type  of  drink  used,  the  type  of  imagery  used,  and  the   interaction  of  these  two  variables.   In  addition  to  the  effects  already  described,  we  find  that  gender  interacts  significantly  with   the  type  of  drink  used  (so,  men  and  women  respond  differently  to  beer,  wine  and  water   regardless  of  the  context  of  the  advert).  There  is  also  a  significant  interaction  of  gender  and   imagery  (so,  men  and  women  respond  differently  to  positive,  negative  and  neutral  imagery   regardless  of  the  drink  being  advertised).  Finally,  the  three-­‐way  interaction  between  gender,   imagery  and  drink  is  significant,  indicating  that  the  way  in  which  imagery  affects  responses  to   different  types  of  drinks  depends  on  whether  the  subject  is  male  or  female.  The  effects  of  the   repeated-­‐measures  variables  have  been  outlined  in  Chapter  13  and  the  pattern  of  these   responses  will  not  have  changed,  so,  rather  than  repeat  myself,  I  will  concentrate  on  the  new   effects  and  the  forgetful  reader  should  look  back  at  Chapter  13!     Output  3   Tests of Within-Subjects Effects Measure: MEASURE_1 2092.344 2 1046.172 11.708 .000 2092.344 1.401 1493.568 11.708 .001 2092.344 1.567 1334.881 11.708 .000 2092.344 1.000 2092.344 11.708 .003 4569.011 2 2284.506 25.566 .000 4569.011 1.401 3261.475 25.566 .000 4569.011 1.567 2914.954 25.566 .000 4569.011 1.000 4569.011 25.566 .000 3216.867 36 89.357 3216.867 25.216 127.571 3216.867 28.214 114.017 3216.867 18.000 178.715 21628.678 2 10814.339 287.417 .000 21628.678 1.932 11196.937 287.417 .000 21628.678 2.000 10814.339 287.417 .000 21628.678 1.000 21628.678 287.417 .000 1998.344 2 999.172 26.555 .000 1998.344 1.932 1034.522 26.555 .000 1998.344 2.000 999.172 26.555 .000 1998.344 1.000 1998.344 26.555 .000 1354.533 36 37.626 1354.533 34.770 38.957 1354.533 36.000 37.626 1354.533 18.000 75.252 2624.422 4 656.106 19.593 .000 2624.422 3.251 807.186 19.593 .000 2624.422 4.000 656.106 19.593 .000 2624.422 1.000 2624.422 19.593 .000 495.689 4 123.922 3.701 .009 495.689 3.251 152.458 3.701 .014 495.689 4.000 123.922 3.701 .009 495.689 1.000 495.689 3.701 .070 2411.000 72 33.486 2411.000 58.524 41.197 2411.000 72.000 33.486 2411.000 18.000 133.944 Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Source DRINK DRINK * GENDER Error(DRINK) IMAGERY IMAGERY * GENDER Error(IMAGERY) DRINK * IMAGERY DRINK * IMAGERY * GENDER Error(DRINK*IMAGERY) Type III Sum of Squares df Mean Square F Sig. DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     6   The effect of gender The  main  effect  of  gender  is  listed  separately  from  the  repeated-­‐measures  effects  in  a  table   labelled  Tests  of  Between-­‐Subjects  Effects.  Before  looking  at  this  table  it  is  important  to  check   the  assumption  of  homogeneity  of  variance  using  Levene’s  test  (Output  4).  SPSS  produces  a   table  listing  Levene’s  test  for  each  of  the  repeated-­‐measures  variables  in  the  data  editor,  and   we  need  to  look  for  any  variable  that  has  a  significant  value.  The  table  showing  Levene’s  test   indicates  that  variances  are  homogeneous  for  all  levels  of  the  repeated-­‐measures  variables   (because  all  significance  values  are  greater  than  .05).  If  any  values  were  significant,  then  this   would  compromise  the  accuracy  of  the  F-­‐test  for  gender,  and  we  would  have  to  consider   transforming  all  of  our  data  to  stabilize  the  variances  between  groups  (one  popular   transformation  is  to  take  the  square  root  of  all  values).  Fortunately,  in  this  example  a   transformation  is  unnecessary.       Output  4     Output  5   Output  5  shows  the  ANOVA  summary  table  for  the  main  effect  of  gender,  and  (because  the   significance  of  .018  is  less  than  the  standard  cut-­‐off  point  of  .05)  we  can  report  that  there  was   a  significant  main  effect  of  gender,  F(1,  18)  =  6.75,  p  <  .05.  This  effect  tells  us  that  if  we  ignore   all  other  variables,  male  subjects’  ratings  were  significantly  different  than  females.  If  you   requested  that  SPSS  display  means  for  the  gender  effect  you  should  scan  through  your  output   and  find  the  table  in  a  section  headed  Estimated  Marginal  Means.  The  table  of  means  for  the   main  effect  of  gender  with  the  associated  standard  errors  is  plotted  alongside.  It  is  clear  from   this  graph  that  men’s  ratings  were  generally  significantly  more  positive  than  females.   Levene's Test of Equality of Error Variancesa 1.009 1 18 .328 1.305 1 18 .268 1.813 1 18 .195 2.017 1 18 .173 1.048 1 18 .320 .071 1 18 .793 .317 1 18 .580 .804 1 18 .382 1.813 1 18 .195 Beer + Sexy Beer + Corpse Beer + Person in Armchair Wine + Sexy Wine + Corpse Wine + Person in Armchair Water + Sexy Water + Corpse Water + Person in Armchair F df1 df2 Sig. Tests the null hypothesis that the error variance of the dependent variable is equal across groups. Design: Intercept+GENDER - Within Subjects Design: DRINK+IMAGERY+DRINK*IMAGERY a. Tests of Between-Subjects Effects Measure: MEASURE_1 Transformed Variable: Average 1246.445 1 1246.445 144.593 .000 58.178 1 58.178 6.749 .018 155.167 18 8.620 Source Intercept GENDER Error Type III Sum of Squares df Mean Square F Sig. DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     7   Therefore,  men  gave  more  positive  ratings  than  women  regardless  of  the  drink  being   advertised  and  the  type  of  imagery  used  in  the  advert.       Figure  3   The interaction between gender and drink Gender  interacted  in  some  way  with  the  type  of  drink  used  as  a  stimulus.  Remembering  that   the  effect  of  drink  violated  sphericity,  we  must  report  Greenhouse–Geisser-­‐corrected  values   for  this  interaction  with  the  between-­‐group  factor.  From  the  summary  table  (Output  3)  we   should  report  that  there  was  a  significant  interaction  between  the  type  of  drink  used  and  the   gender  of  the  subject,  F(1.40,  25.22)  =  25.57,  p  <  .001.  This  effect  tells  us  that  the  type  of  drink   being  advertised  had  a  different  effect  on  men  and  women.  We  can  use  the  estimated   marginal  means  to  determine  the  nature  of  this  interaction  (or  we  could  have  asked  SPSS  for  a   plot  of  gender  ×  drink).  The  means  and  interaction  graph  (Figure  4)  show  the  meaning  of  this   result.  The  graph  shows  the  average  male  ratings  of  each  drink  ignoring  the  type  of  imagery   with  which  it  was  presented  (circles).  The  women’s  scores  are  shown  as  squares.  The  graph   clearly  shows  that  male  and  female  ratings  are  very  similar  for  wine  and  water,  but  men  seem   to  rate  beer  more  highly  than  women  —  regardless  of  the  type  of  imagery  used.  We  could   interpret  this  interaction  as  meaning  that  the  type  of  drink  being  advertised  influenced  ratings   differently  in  men  and  women.  Specifically,  ratings  were  similar  for  wine  and  water  but  males   rated  beer  higher  than  women.  This  interaction  can  be  clarified  using  the  contrasts  specified   before  the  analysis.       Figure  4   The interaction between gender and imagery Gender  interacted  in  some  way  with  the  type  of  imagery  used  as  a  stimulus.  The  effect  of   imagery  did  not  violate  sphericity,  so  we  can  report  the  uncorrected  F-­‐value.  From  the   Estimates Measure: MEASURE_1 9.600 .928 7.649 11.551 6.189 .928 4.238 8.140 Gender Male Female Mean Std. Error Lower Bound Upper Bound 95% Confidence Interval 9.60 6.19 0.00 5.00 10.00 15.00 Male Female 2. Gender * DRINK Measure: MEASURE_1 20.600 2.441 15.471 25.729 7.333 .765 5.726 8.940 .867 1.414 -2.103 3.836 3.067 2.441 -2.062 8.196 9.333 .765 7.726 10.940 6.167 1.414 3.197 9.136 DRINK 1 2 3 1 2 3 Gender Male Female Mean Std. Error Lower Bound Upper Bound 95% Confidence Interval 0 5 10 15 20 25 Beer Wine Water DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     10   Contrasts for repeated-measures variables We  requested  simple  contrasts  for  the  drink  variable  (for  which  water  was  used  as  the  control   category)  and  for  the  imagery  category  (for  which  neutral  imagery  was  used  as  the  control   category).  The  table  (Output  5)  is  the  same  as  for  the  previous  example  except  that  the  added   effects  of  gender  and  its  interaction  with  other  variables  are  now  included.  So,  for  the  main   effect  of  drink,  the  first  contrast  compares  level  1  (beer)  against  the  base  category  (in  this   case,  the  last  category,  water);  this  result  is  significant,  F(1,  18)  =  15.37,  p  <  .01.  The  next   contrast  compares  level  2  (wine)  with  the  base  category  (water)  and  confirms  the  significant   difference  found  when  gender  was  not  included  as  a  variable  in  the  analysis,  F(1,  18)  =  19.92,  p   <  .001.  For  the  imagery  main  effect,  the  first  contrast  compares  level  1  (positive)  to  the  base   category  (neutral)  and  verifies  the  significant  effect  found  by  the  post  hoc  tests,  F(1,  18)  =   134.87,  p  <  .001.  The  second  contrast  confirms  the  significant  difference  found  for  the   negative  imagery  condition  compared  to  the  neutral,  F(1,  18)  =  129.18,  p  <  .001.  No  contrast   was  specified  for  gender.       Output  5   Drink × gender interaction 1: beer vs. water, male vs. female The  first  interaction  term  looks  at  level  1  of  drink  (beer)  compared  to  level  3  (water),   comparing  male  and  female  scores.  This  contrast  is  highly  significant,  F(1,  18)  =  28.97,  p  <  .001.   This  result  tells  us  that  the  increased  ratings  of  beer  compared  to  water  found  for  men  are  not   found  for  women.  So,  in  the  graph  the  squares  representing  female  ratings  of  beer  and  water   are  roughly  level;  however,  the  circle  representing  male  ratings  of  beer  is  much  higher  than   the  circle  representing  water.  The  positive  contrast  represents  this  difference,  and  so  we  can   conclude  that  male  ratings  of  beer  (compared  to  water)  were  significantly  greater  than   women’s  ratings  of  beer  (compared  to  water).     Tests of Within-Subjects Contrasts Measure: MEASURE_1 1383.339 1 1383.339 15.371 .001 464.006 1 464.006 19.923 .000 2606.806 1 2606.806 28.965 .000 54.450 1 54.450 2.338 .144 1619.967 18 89.998 419.211 18 23.290 3520.089 1 3520.089 134.869 .000 3690.139 1 3690.139 129.179 .000 .556 1 .556 .021 .886 975.339 1 975.339 34.143 .000 469.800 18 26.100 514.189 18 28.566 320.000 1 320.000 1.686 .211 720.000 1 720.000 8.384 .010 36.450 1 36.450 .223 .642 2928.200 1 2928.200 31.698 .000 441.800 1 441.800 2.328 .144 480.200 1 480.200 5.592 .029 4.050 1 4.050 .025 .877 405.000 1 405.000 4.384 .051 3416.200 18 189.789 3416.200 18 189.789 1545.800 18 85.878 1662.800 18 92.378 IMAGERY Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 DRINK Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Level 1 vs. Level 3 Level 2 vs. Level 3 Source DRINK DRINK * GENDER Error(DRINK) IMAGERY IMAGERY * GENDER Error(IMAGERY) DRINK * IMAGERY DRINK * IMAGERY * GENDER Error(DRINK*IMAGERY) Type III Sum of Squares df Mean Square F Sig. DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     11   Drink × gender interaction 2: wine vs. water, male vs. female The  second  interaction  term  compares  level  2  of  drink  (wine)  to  level  3  (water),  contrasting   male  and  female  scores.  There  is  no  significant  difference  for  this  contrast,  F(1,  18)  =  2.34,  p  =   0.14,  which  tells  us  that  the  difference  between  ratings  of  wine  compared  to  water  in  males  is   roughly  the  same  as  in  females.     Therefore,  overall,  the  drink  ×  gender  interaction  has  shown  up  a  difference  between  males   and  females  in  how  they  rate  beer  (regardless  of  the  type  of  imagery  used).     Imagery × gender interaction 1: positive vs. neutral, male vs. female The  first  interaction  term  looks  at  level  1  of  imagery  (positive)  compared  to  level  3  (neutral),   comparing  male  and  female  scores.  This  contrast  is  not  significant  (F  <  1).  This  result  tells  us   that  ratings  of  drinks  presented  with  positive  imagery  (relative  to  those  presented  with  neutral   imagery)  were  equivalent  for  males  and  females.  This  finding  represents  the  fact  that  in  the   earlier  graph  of  this  interaction  the  squares  and  circles  for  both  the  positive  and  neutral   conditions  overlap  (therefore  male  and  female  responses  were  the  same).   Imagery × gender interaction 2: negative vs. neutral, male vs. female The  second  interaction  term  looks  at  level  2  of  imagery  (negative)  compared  to  level  3   (neutral),  comparing  male  and  female  scores.  This  contrast  is  highly  significant,  F(1,  18)  =   34.13,  p  <  .001.  This  result  tells  us  that  the  difference  between  ratings  of  drinks  paired  with   negative  imagery  compared  to  neutral  was  different  for  men  and  women.  Looking  at  the   earlier  graph  of  this  interaction,  this  finding  represents  the  fact  that  for  men,  ratings  of  drinks   paired  with  negative  imagery  were  relatively  similar  to  ratings  of  drinks  paired  with  neutral   imagery  (the  circles  have  a  fairly  similar  vertical  position).  However,  if  you  look  at  the  female   ratings,  then  drinks  were  rated  much  less  favourably  when  presented  with  negative  imagery   than  when  presented  with  neutral  imagery  (the  square  in  the  negative  condition  is  much  lower   than  the  neutral  condition).     Therefore,  overall,  the  imagery  ×  gender  interaction  has  shown  up  a  difference  between   males  and  females  in  terms  of  their  ratings  of  drinks  presented  with  negative  imagery   compared  to  neutral;  specifically,  men  seem  less  affected  by  negative  imagery.   Drink × imagery × gender interaction 1: beer vs. water, positive vs. neutral imagery, male vs. female The  first  interaction  term  compares  level  1  of  drink  (beer)  to  level  3  (water),  when  positive   imagery  (level  1)  is  used  compared  to  neutral  (level  3)  in  males  compared  to  females,  F(1,  18)  =   2.33,  p  =  .144.  The  non-­‐significance  of  this  contrast  tells  us  that  the  difference  in  ratings  when   positive  imagery  is  used  compared  to  neutral  imagery  is  roughly  equal  when  beer  is  used  as  a   stimulus  and  when  water  is  used,  and  these  differences  are  equivalent  in  male  and  female   subjects.  In  terms  of  the  interaction  graph  it  means  that  the  distance  between  the  circle  and   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     12   the  triangle  in  the  beer  condition  is  the  same  as  the  distance  between  the  circle  and  the   triangle  in  the  water  condition  and  that  these  distances  are  equivalent  in  men  and  women.   Drink × imagery × gender interaction 2: beer vs. water, negative vs. neutral imagery, male vs. female The  second  interaction  term  looks  at  level  1  of  drink  (beer)  compared  to  level  3  (water),  when   negative  imagery  (level  2)  is  used  compared  to  neutral  (level  3).  This  contrast  is  significant,  F(1,   18)  =  5.59,  p  <  .05.  This  result  tells  us  that  the  difference  in  ratings  between  beer  and  water   when  negative  imagery  is  used  (compared  to  neutral  imagery)  is  different  between  men  and   women.  If  we  plot  ratings  of  beer  and  water  across  the  negative  and  neutral  conditions,  for   males  (circles)  and  females  (squares)  separately,  we  see  that  ratings  after  negative  imagery  are   always  lower  than  ratings  for  neutral  imagery  except  for  men’s  ratings  of  beer,  which  are   actually  higher  after  negative  imagery.  As  such,  this  contrast  tells  us  that  the  interaction  effect   reflects  a  difference  in  the  way  in  which  males  rate  beer  compared  to  females  when  negative   imagery  is  used  compared  to  neutral.  Males  and  females  are  similar  in  their  pattern  of  ratings   for  water  but  different  in  the  way  in  which  they  rate  beer.     Figure  7   Drink × imagery × gender interaction 3: wine vs. water, positive vs. neutral imagery, male vs. female. The  third  interaction  term  looks  at  level  2  of  drink  (wine)  compared  to  level  3  (water),  when   positive  imagery  (level  1)  is  used  compared  to  neutral  (level  3)  in  males  compared  to  females.   This  contrast  is  non-­‐significant,  F(1,  18)  <  1.  This  result  tells  us  that  the  difference  in  ratings   when  positive  imagery  is  used  compared  to  neutral  imagery  is  roughly  equal  when  wine  is   used  as  a  stimulus  and  when  water  is  used,  and  these  differences  are  equivalent  in  male  and   female  subjects.  In  terms  of  the  interaction  graph  it  means  that  the  distance  between  the   -20 -10 0 10 20 30 Negative Neutral Negative Neutral DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     15     Output  6   Output  6  shows  the  table  of  descriptive  statistics  from  the  two-­‐way  mixed  ANOVA;  the   table  has  means  at  time  1  split  according  to  whether  the  people  were  in  the  text  messaging   group  or  the  control  group,  and  then  the  means  for  the  two  groups  at  time  2.  These  means   correspond  to  those  plotted  in  Figure  9.     Output  7     Output  8   We  know  that  when  we  use  repeated-­‐measures  we  have  to  check  the  assumption  of   sphericity  (Output  7).  We  also  know  that  for  independent  designs  we  need  to  check  the   homogeneity  of  variance  assumption.  If  the  design  is  a  mixed  design  then  we  have  both   repeated  and  independent  measures,  so  we  have  to  check  both  assumptions.  In  this  case,  we   have  only  two  levels  of  the  repeated  measure  so  the  assumption  of  sphericity  does  not  apply.   Levene’s  test  produces  a  different  test  for  each  level  of  the  repeated-­‐measures  variable   (Output  8).  In  mixed  designs,  the  homogeneity  assumption  has  to  hold  for  every  level  of  the   repeated-­‐measures  variable.  At  both  levels  of  time,  Levene’s  test  is  non-­‐significant  (p  =  0.77   before  the  experiment  and  p  =  .069  after  the  experiment).  This  means  the  assumption  has  not   been  broken  at  all  (but  it  was  quite  close  to  being  a  problem  after  the  experiment).     Descriptive Statistics 64.8400 10.67973 25 65.6000 10.83590 25 65.2200 10.65467 50 52.9600 16.33116 25 61.8400 9.41046 25 57.4000 13.93278 50 Group Text Messagers Controls Total Text Messagers Controls Total Grammer at Time 1 Grammar at Time 2 Mean Std. Deviation N Mauchly's Test of Sphericityb Measure: MEASURE_1 1.000 .000 0 . 1.000 1.000 1.000 Within Subjects Effect TIME Mauchly's W Approx. Chi-Square df Sig. Greenhouse- Geisser Huynh-Feldt Lower-bound Epsilona Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table. a. Design: Intercept+GROUP Within Subjects Design: TIME b. Levene's Test of Equality of Error Variancesa .089 1 48 .767 3.458 1 48 .069 Grammer at Time 1 Grammar at Time 2 F df1 df2 Sig. Tests the null hypothesis that the error variance of the dependent variable is equal across groups. Design: Intercept+GROUP Within Subjects Design: TIME a. DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     16     Output  9     Output  10   Outputs  9  and  10  shows  the  main  ANOVA  summary  tables.  Like  any  two-­‐way  ANOVA,  we   still  have  three  effects  to  find:  two  main  effects  (one  for  each  independent  variable)  and  one   interaction  term.  The  main  effect  of  time  is  significant,  so  we  can  conclude  that  grammar   scores  were  significantly  affected  by  the  time  at  which  they  were  measured.  The  exact  nature   of  this  effect  is  easily  determined  because  there  were  only  two  points  in  time  (and  so  this  main   effect  is  comparing  only  two  means).  Figure  10  shows  that  grammar  scores  were  higher  before   the  experiment  than  after.  So,  before  the  experimental  manipulation  scores  were  higher  than   after,  meaning  that  the  manipulation  had  the  net  effect  of  significantly  reducing  grammar   scores.  This  main  effect  seems  rather  interesting  until  you  consider  that  these  means  include   both  text  messagers  and  controls.  There  are  three  possible  reasons  for  the  drop  in  grammar   scores:  (1)  the  text  messagers  got  worse  and  are  dragging  down  the  mean  after  the   experiment;  (2)  the  controls  somehow  got  worse;  or  (3)  the  whole  group  just  got  worse  and  it   had  nothing  to  do  with  whether  the  children  text-­‐messaged  or  not.  Until  we  examine  the   interaction,  we  won’t  see  which  of  these  is  true.   Tests of Within-Subjects Effects Measure: MEASURE_1 1528.810 1 1528.810 15.457 .000 1528.810 1.000 1528.810 15.457 .000 1528.810 1.000 1528.810 15.457 .000 1528.810 1.000 1528.810 15.457 .000 412.090 1 412.090 4.166 .047 412.090 1.000 412.090 4.166 .047 412.090 1.000 412.090 4.166 .047 412.090 1.000 412.090 4.166 .047 4747.600 48 98.908 4747.600 48.000 98.908 4747.600 48.000 98.908 4747.600 48.000 98.908 Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound Source TIME TIME * GROUP Error(TIME) Type III Sum of Squares df Mean Square F Sig. Tests of Between-Subjects Effects Measure: MEASURE_1 Transformed Variable: Average 375891.610 1 375891.610 1933.002 .000 580.810 1 580.810 2.987 .090 9334.080 48 194.460 Source Intercept GROUP Error Type III Sum of Squares df Mean Square F Sig. DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     17     Figure  10   The  main  effect  of  group  is  shown  by  the  F-­‐ratio  in  Output  10.  The  probability  associated   with  this  F-­‐ratio  is  .09,  which  is  just  above  the  critical  value  of  .05.  Therefore,  we  must   conclude  that  there  was  no  significant  main  effect  on  grammar  scores  of  whether  children   text-­‐messaged  or  not.  Again,  this  effect  seems  interesting  enough,  and  mobile  phone   companies  might  certainly  choose  to  cite  it  as  evidence  that  text  messaging  does  not  affect   your  grammatical  ability.  However,  remember  that  this  main  effect  ignores  the  time  at  which   grammatical  ability  is  measured.  It  just  means  that  if  we  took  the  average  grammar  score  for   text  messagers  (that’s  including  their  score  both  before  and  after  they  started  using  their   phone),  and  compared  this  to  the  mean  of  the  controls  (again  including  scores  before  and   after)  then  these  means  would  not  be  significantly  different.  The  graph  shows  that  when  you   ignore  the  time  at  which  grammar  was  measured,  the  controls  have  slightly  better  grammar   than  the  text  messagers,  but  not  significantly  so.     Main  effects  are  not  always  that  interesting  and  should  certainly  be  viewed  in  the  context   of  any  interaction  effects.  The  interaction  effect  in  this  example  is  shown  by  the  F-­‐ratio  in  the   row  labelled  Time*Group,  and  because  the  probability  of  obtaining  a  value  this  big  by  chance   is  .047,  which  is  just  less  than  the  criterion  of  .05,  we  can  say  that  there  is  a  significant   interaction  between  the  time  at  which  grammar  was  measured  and  whether  or  not  children   were  allowed  to  text-­‐message  within  that  time.  The  mean  ratings  in  all  conditions  help  us  to   interpret  this  effect.  The  significant  interaction  tells  us  that  the  change  in  grammar  scores  was   significantly  different  in  text  messagers  compared  to  controls.  Looking  at  the  interaction   graph,  we  can  see  that  although  grammar  scores  fell  in  controls,  the  drop  was  much  more   marked  in  the  text  messagers;  so,  text  messaging  does  seem  to  ruin  your  ability  at  grammar   compared  to  controls.1                                                                                                                               1  It’s  interesting  that  the  control  group  means  dropped  too.  This  could  be  because  the  control  group  were   undisciplined  and  still  used  their  mobile  phones,  or  it  could  just  be  that  the  education  system  in  this  country  is   so  underfunded  that  there  is  no  one  to  teach  English  anymore!   Group Before After M ea n G ra m m ar S co re (% ) 0 10 40 50 60 70 DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     20     Figure  13:  Error  bar  chart  of  mean  personality  disorder  score  before  entering  and  after  leaving  the  Big  Brother   house     Output  11   Output  11  shows  the  table  of  descriptive  statistics  from  the  two-­‐way  mixed  ANOVA;  the   table  has  mean  borderline  personality  disorder  (BPD)  scores  before  entering  the  Big  Brother   house  split  according  to  whether  the  people  were  a  contestant  or  not,  and  then  the  means  for   the  two  groups  after  leaving  the  house.  These  means  correspond  to  those  plotted  in  Figure  13.     Output  12   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     21     Output  13   We  know  that  when  we  use  repeated-­‐measures  we  have  to  check  the  assumption  of   sphericity  (Output  12).  However,  we  also  know  that  for  sphericity  to  be  an  issue  we  need  at   least  three  conditions.  We  have  only  two  conditions  here  so  sphericity  does  not  need  to  be   tested  (and,  therefore,  SPSS  produces  a  blank  in  the  column  labeled  Sig.).  We  also  need  to   check  the  homogeneity  of  variance  assumption  (Output  13).  Levene’s  test  produces  a  different   test  for  each  level  of  the  repeated-­‐measures  variable.  In  mixed  designs,  the  homogeneity   assumption  has  to  hold  for  every  level  of  the  repeated-­‐measures  variable.  At  both  levels  of   time,  Levene’s  test  is  non-­‐significant  (p  =  0.061  before  entering  the  Big  Brother  house  and  p  =   .088  after  leaving).  This  means  the  assumption  has  not  been  significantly  broken  (but  it  was   quite  close  to  being  a  problem).       Output  14     Output  15   Output  14  and  15  show  the  main  ANOVA  summary  tables.  Like  any  two-­‐way  ANOVA,  we   still  have  three  effects  to  find:  two  main  effects  (one  for  each  independent  variable)  and  one   interaction  term.  The  main  effect  of  time  is  not  significant,  so  we  can  conclude  that  BPD  scores   were  significantly  affected  by  the  time  at  which  they  were  measured.  The  exact  nature  of  this   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     22   effect  is  easily  determined  because  there  were  only  two  points  in  time  (and  so  this  main  effect   is  comparing  only  two  means).  Figure  14  shows  that  BPD  scores  were  not  significantly  different   after  leaving  the  Big  Brother  house  compared  to  before  entering  it.     Figure  14   The  main  effect  of  group  (bb)  is  shown  by  the  F-­‐ratio  in  Output  15.  The  probability   associated  with  this  F-­‐ratio  is  .43,  which  is  above  the  critical  value  of  .05.  Therefore,  we  must   conclude  that  there  was  no  significant  main  effect  on  BPD  scores  of  whether  the  person  was  a   Big  Brother  contestant  or  not.  The  graph  shows  that  when  you  ignore  the  time  at  which  BPD   was  measured,  the  contestants  and  controls  are  not  significantly  different.     DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     25     Figure  17   SPSS output Figure    is  a  line  graph  of  the  angry  pigs  data.  We  can  see  that  when  participants  played  Tetris   (blue  line)  in  general  their  aggressive  behaviour  towards  pigs  decreased  over  time  (except  for   between  6  months  and  12  months  when  it  actually  increased  slightly).  However,  when   participants  played  Angry  Birds,  their  aggressive  behaviour  towards  pigs  increased  over  time.       Figure  18   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     26     Output  16     Output    shows  the  estimated  marginal  means  for  the  interaction  between  Tetris  and  time.   These  values  correspond  with  those  plotted  in  Figure  .       Output  17     Output    shows  the  table  of  descriptive  statistics  from  the  two-­‐way  mixed  ANOVA.     Output  18   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     27     Output  19   We  know  that  when  we  use  repeated-­‐measures  we  have  to  check  the  assumption  of   sphericity.  We  also  know  that  for  independent  designs  we  need  to  check  the  homogeneity  of   variance  assumption.  If  the  design  is  a  mixed  design  then  we  have  both  repeated  and   independent  measures,  so  we  have  to  check  both  assumptions.  Output    shows  the  results  of   Mauchly’s  test  for  our  repeated-­‐measures  variable  Time.  The  value  in  the  column  labelled  Sig   is  .170,  which  is  larger  than  the  cut  off  of  .05,  therefore  it  is  non-­‐significant  and  the  assumption   of  sphericity  has  been  met.  Levene’s  test  produces  a  different  test  for  each  level  of  the   repeated-­‐measures  variable.  In  mixed  designs,  the  homogeneity  assumption  has  to  hold  for   every  level  of  the  repeated-­‐measures  variable.  Output    reveals  that  at  each  level  of  the   variable  Time,  Levene’s  test  is  significant  (p  <  0.05  in  every  case).  This  means  the  assumption   has  been  broken.       Output  20   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     30     Figure  19   Looking  at  Figure    in  comparison  to  Figure  ,  we  can  see  that  aggressive  behaviour  in  the  real   world  was  more  erratic  for  the  two  video  games  than  aggressive  behaviour  towards  pigs.   Figure    shows  that  for  Tetris,  aggressive  behaviour  in  the  real  world  increased  from  time  1   (baseline)  to  time  3  (6  months)  and  then  decreased  from  time  3  (6  months)  to  time  4  (12   months).  For  Angry  Birds,  on  the  other  hand,  aggressive  behaviour  in  the  real  world  initially   increased  from  baseline  to  1  month,  it  then  decreased  from  1  month  to  6  months  and  then   dramatically  increased  from  6  months  to  12  months.  The  graph  also  shows  that  more   aggressive  behaviour  was  displayed  when  participants  played  Tetris  compared  to  when  they   played  Angry  Birds  at  baseline,  1  month  and  6  months;  however,  at  12  months  participants   engaged  in  more  aggressive  behaviour  when  playing  Angry  Birds  compared  to  Tetris.     Output  23   Output    shows  the  results  of  Mauchly’s  test  for  our  repeated  measures  variable  Time.  The   value  in  the  column  labelled  Sig  is  .808  which  is  larger  than  the  cut  off  of  .05,  therefore  it  is   non-­‐significant  and  the  assumption  of  sphericity  has  been  met.     DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     31       Output  24       Output  25   Output    and  Output    show  the  main  ANOVA  summary  tables.  The  main  effect  of  Game  was   non-­‐significant,  indicating  that  (ignoring  the  time  at  which  the  aggression  scores  were   measured),  the  type  of  game  being  played  did  not  significantly  affect  participants’  aggression   in  the  real  world.  The  main  effect  of  Time  was  also  non-­‐significant,  so  we  can  conclude  that   (ignoring  the  type  of  game  being  played),  aggression  was  not  significantly  different  at  different   points  in  time.  The  effect  that  we  are  most  interested  in  is  the  Time  ×  Game  interaction,  which   was  again  non-­‐significant.  This  effect  tells  us  that  change  in  aggression  scores  over  time  were   not  significantly  different  when  participants  played  Tetris  compared  to  when  they  played   Angry  Birds.  Because  none  of  the  effects  were  significant  it  doesn’t  make  sense  to  conduct  any   contrasts.  Therefore,  we  can  conclude  that  playing  Angry  Birds  does  not  make  people  more   violent  in  general,  just  towards  pigs.     Task 6 My  wife  believes  that  she  has  received  less  friend  requests  from  random  men  on   Facebook  since  she  changed  her  profile  picture  to  a  photo  of  us  both.  Imagine  we  took  40   women  who  had  profiles  on  a  social  networking  website;  17  of  them  had  a  relationship   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     32   status  of  ‘single’  and  the  remaining  23  had  their  status  as  ‘in  a  relationship’   (relationship_status).  We  asked  these  women  to  set  their  profile  picture  to  a  photo  of   them  on  their  own  (alone)  and  to  count  how  many  friend  request  they  got  from  men   over  3  weeks,  then  to  switch  it  to  a  photo  of  them  with  a  man  (couple)  and  record  their   friend  requests  from  random  men  over  3  weeks.  The  data  are  in  the  file   ProfilePicture.sav.  Run  a  mixed  ANOVA  to  see  if  friend  requests  are  affected  by   relationship  status  and  type  of  profile  picture.     We  need  to  run  a  2  (relationship_status:  single  vs.  in  a  relationship)   ×  2(photo:  couple  vs.   alone)  mixed  ANOVA  with  repeated  measures  on  the  second  variable.  Your  completed  dialog   box  should  look  like  Figure  .       Figure  20       Figure  21   DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     35     Output  28   Output    and  Output    show  the  main  ANOVA  summary  tables.  Like  any  two-­‐way  ANOVA,  we   still  have  three  effects  to  find:  two  main  effects  (one  for  each  independent  variable)  and  one   interaction  term.  The  main  effect  of  relationship_status  is  significant,  so  we  can  conclude  that,   ignoring  the  type  of  profile  picture,  the  number  of  friend  requests  was  significantly  affected  by   the  relationship  status  of  the  woman.  The  exact  nature  of  this  effect  is  easily  determined   because  there  were  only  two  levels  of  relationship  status  (and  so  this  main  effect  is  comparing   only  two  means).     Output  29    If  we  look  at  the  estimated  marginal  means  for  relationship  status  in  Output  ,  we  can  see   that  the  number  of  friend  requests  was  significantly  higher  for  single  women  (M  =  5.94)   compared  to  women  who  were  in  a  relationship  (M  =  4.47).     The  main  effect  of  Profile_Picture  is  shown  by  the  F-­‐ratio  in  Output  .  The  probability   associated  with  this  F-­‐ratio  is  shown  as  .000,  which  is  smaller  than  the  critical  value  of  .05.   Therefore,  we  can  conclude  that  when  ignoring  relationship  status,  there  was  a  significant   main  effect  of  whether  the  person  was  alone  in  their  profile  picture  or  with  a  partner  on  the   number  of  friend  requests.     DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     36     Output  30   Looking  at  the  estimated  marginal  means  for  the  profile  picture  variable  (Output  ),  we  can   see  that  the  number  of  friend  requests  was  significantly  higher  when  women  were  alone  in   their  profile  picture  (M  =  6.78)  than  when  they  were  with  a  partner  (M  =  3.63).  Note:  we  know   that  1  =  ‘in  a  couple’  and  2  =  ‘alone’  in  Output    because  this  is  how  we  coded  the  levels  of  the   profile  picture  variable  in  the  define  dialog  box  in  Figure  .   The  interaction  effect  is  the  effect  that  we  are  most  interested  in  and  it  is  shown  by  the   significance  of  the  F-­‐ratio  in  Output  .  We  can  see  that  the  significance  of  the  F-­‐ratio  is  .010,   which  is  less  than  the  criterion  of  .05;  therefore,  we  can  say  that  there  is  a  significant   interaction  between  the  relationship  status  of  women  and  whether  they  had  a  photo  of   themselves  alone  or  with  a  partner.  The  estimated  marginal  means  in  Output    and  the   interaction  graph  (Figure  )  help  us  to  interpret  this  effect.  The  significant  interaction  seems  to   indicate  that  when  displaying  a  photo  of  themselves  alone  rather  than  with  a  partner,  the   number  of  friend  requests  increases  in  both  women  in  a  relationship  and  single  women.   However,  for  single  women  this  increase  is  greater  than  for  women  who  are  in  a  relationship.         Output  31   Writing the results We  can  report  the  three  effects  from  this  analysis  as  follows:   ! The  main  effect  of  relationship  status  was  significant,  F(1,  38)  =  16.29,  p  <  .001,   indicating  that  single  women  received  more  friend  requests  than  women  who  were  in   a  relationship,  regardless  of  their  type  of  profile  picture.   ! The  main  effect  of  profile  picture  was  significant,  F(1,  38)  =  114.77,  p  <  .001,  indicating   that  across  all  women,  the  number  of  friend  requests  was  greater  when  displaying  a   photo  alone  rather  than  with  a  partner.     DISCOVERING  STATISTICS  USING  SPSS   PROFESSOR  ANDY  P  FIELD     37   ! The  relationship  status  ×  profile  picture  interaction  was  significant,  F(1,  38)  =  7.41,  p  =   .010,  indicating  that  although  number  of  friend  requests  increased  in  all  women  when   they  displayed  a  photo  of  themselves  alone  compared  to  when  they  displayed  a  photo   of  themselves  with  a  partner,  this  increase  was  significantly  greater  for  single  women   than  for  women  who  were  in  a  relationship.