stats help, I will need the pdf file of the results from SPSS and a results section written up where I will be able to edit it. Refer to the lecture for examples.
Post-hoc Tests and Two-way ANOVA Follow up Comparisons and Two-way ANOVA Plus SPSS Review One-way ANOVA Can use to examine the effect of an IV on a DV when there are 2+ independent groups for the IV Assumptions Homogeneity of variance DV is continuous and normally distributed IV is categorical Hypothesis Being Tested with a One-way ANOVA The null hypothesis is that there are no differences among groups Alternative hypothesis is that there are differences Hypotheses are set-up to be non-directional in F-test Example using 3 groups: Ho: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2 ≠ μ3 (or said differently - at least two of the means are not equal) PSYC A303 - CLASS 11 3 Determining Significance F-test p-value is conceptually similar to t-test test except always on right side Repeated Measures ANOVA The repeated measures ANOVA works like the regular ANOVA but we further partition SSw into SSs: variability that arises from individual differences between subjects SSE: variability that arises from other sources of error in our measurement We then subtract SSs from SSw to get SSE which will go into our F-ratio equation. SSw = SSs + SSE -> SSE = SSw – SSs dfE = (n-1)(k-1) We will not be calculating these by hand 5 Follow up Tests Limitations of F-test F-test only tells you that IV had a significant effect (i.e., at least one mean is different from another) It doesn’t tell you what means are different from each other In order to determine which differences between groups are significant, we need to now carry out a follow up test A test used to make direct comparisons between specific group means. It’s called post hoc because this happens after you run the ANOVA 7 Planned vs. Post Hoc Comparisons If we have specific predictions to how the means will turn out, we can conduct planned comparisons (or planned contrasts) In this case we just conduct independent samples t-tests No need to correct for multiple comparisons -> higher power Technically, the planned contrasts need to be orthogonal (linearly independent comparisons) We don’t need to correct for multiple comparisons here because we are clearly not just looking for significant effects after the fact. That’s a good way to find a false positive. 8 Post-Hoc Tests When comparisons are not planned (i.e., do not have good theoretical reasons to expect certain outcomes) need to correct for multiple comparisons (to avoid inflating Type I error) There are other ways to do this Bonferroni correction Tukey HSD to compare all pairwise comparisons 9 t-test with Bonferroni Correction Multiple comparisons will inflate the Type I error rate such that Type I error rate = 1- (1-alpha)c, where c is the number of comparisons Bonferroni correction divides alpha by number of comparison So p-value must meet a higher threshold to be significant Bonferroni Example Suppose you have want to test all pairwise comparisons between 3 groups. There are 3C2 = 3 comparisons. Bonferroni threshold is alpha/# comparisons If alpha is .05, then -> .05/3= .0167 11 Bonferroni Correction Characteristics The Bonferroni correction is considered very conservative Low power -> Higher level of Type II error Power OK when # of comparisons relatively low (i.e., <= 3)="" when="" #="" of="" comparisons="" high,="" too="" conservative="" example:="" if="" alpha="" is="" .05="" and="" there="" are="" 4="" groups,="" then="" 4c2="6" comparisons,="" then="" threshold="" is="" .05/6=".008" 12="" tukey="" honestly="" significant="" difference="" (hsd)="" tukey="" hsd="" corrects="" type="" i="" error="" for="" all="" possible="" pairwise="" comparisons="" works="" like="" a="" t-test,="" but="" with="" a="" different="" in="" how="" error="" is="" calculated="" to="" control="" for="" multiple="" comparisons="" then="" find="" qcrit="" in="" a="" look="" up="" table="" when="" sample="" sizes="" are="" equal="" with="" unequal="" sample="" sizes="" tukey="" hsd="" characteristics="" tukey="" hsd="" gives="" good="" results="" with="" moderately="" high="" power="" when="" sample="" sizes="" are="" equal="" when="" sample="" sizes="" are="" unequal,="" the="" test="" is="" conservative="" e.g.,="" the="" confidence="" intervals="" are="" go="" beyond="" 95%.="" summary="" of="" follow-up="" comparisons="" when="" possible,="" have="" a="" priori="" planned="" comparisons="" higher="" power="" when="" comparisons="" are="" post-hoc,="" choosing="" the="" appropriate="" post-hoc="" test="" depends="" upon="" a="" number="" of="" factors="" in="" general="" best="" to="" use="" tukey="" hsd="" as="" it="" give="" relatively="" high="" power="" two-way="" anova="" two-way="" anova="" with="" a="" one-way="" anova,="" you="" calculated="" an="" f-ratio="" to="" determine="" if="" group="" means="" differ="" with="" a="" two="" way="" anova,="" you="" will="" be="" doing="" the="" f-test="" three="" times="" once="" for="" each="" main="" effect="" using="" columns="" means="" (1="" “way”)="" and="" row="" means="" (the="" other="" “way”)="" once="" for="" the="" interaction="" effect="" between="" your="" factors="" using="" cell="" means="" example:="" bandura’s="" bo-bo="" doll="" experiment="" do="" you="" think="" we="" humans="" need="" to="" be="" rewarded="" or="" punished="" to="" learn="" effectively="" or="" can="" just="" watching="" what="" happens="" to="" other="" people="" teach="" us="" how="" to="" behave?="" albert="" bandura,="" along="" with="" two="" colleagues,="" set="" up="" a="" now="" famous="" experiment="" to="" see="" just="" that="" (bandura,="" ross,="" &="" ross,="" 1963).="" they="" asked="" 40="" boys="" and="" 40="" girls,="" selected="" at="" random,="" to="" watch="" one="" of="" two="" movies.="" both="" movies="" showed="" adults="" hitting,="" pounding="" on,="" pushing,="" and="" assaulting="" a="" balloon="" doll="" called="" a="" bobo="" doll.="" bobo="" has="" a="" weighted="" bottom="" so="" he="" always="" bounces="" back="" for="" more="" punishment.="" in="" half="" of="" the="" movies,="" the="" adult="" assaulting="" the="" doll="" was="" the="" same="" sex="" as="" the="" observer="" child,="" and="" in="" the="" other="" half="" the="" adult="" beating="" up="" the="" doll="" was="" the="" opposite="" sex="" of="" the="" observer="" child.="" in="" the="" end,="" bandura="" et="" al.="" had="" four="" groups:="" (1)="" male="" children="" who="" saw="" the="" male="" adult="" model="" (2)="" male="" children="" who="" saw="" the="" female="" adult="" model="" (3)="" female="" children="" who="" saw="" the="" male="" model="" and="" (4)="" female="" children="" who="" saw="" the="" female="" model.="" 18="" the="" results="" of="" the="" study="" ="" male="" female="" row="" totals="" male="" 106="" 41="" ="" 117="" 40="" σx="724" 108="" 34="" n="10" 101="" 38="72.4" 97="" 42="" ="" σx="529" σx="195" ="" n="5" n="5" ="105.8" =="" 39.0="" ="" female="" 51="" 58="" ="" 50="" 51="" σx="531" 49="" 60="" n="10" 49="" 56="53.1" 45="" 62="" ="" σx="244" σx="287" ="" n="5" n="5" ="48.8" =="" 57.4="" ="" ="" ="" ="" overall="" column="" totals="" σx="773" σx="482" σx="1,255" n="10" n="10" n="20" =="" 77.3="48.2" =="" 62.75="" sex="" of="" the="" child="" observer="" sex="" of="" the="" adult="" model="" main="" effect="" of="" sex="" of="" the="" adult="" model="" main="" effect="" of="" sex="" of="" the="" child="" observer="" we="" will="" not="" be="" doing="" two-way="" anovas="" by="" hand="" instead="" i="" will="" focus="" the="" rest="" of="" the="" lecture="" on="" reading="" spss="" output="" spss="" anova="" example="" create="" variables="" for="" your="" between-subjects="" ivs="" need="" to="" create="" a="" grouping="" variable="" even="" though="" groups="" are="" categorical,="" it’s="" best="" to="" label="" them="" with="" a="" number="" and="" then="" specify="" the="" category="" level="" that="" each="" number="" corresponds="" to="" (e.g.,="" 1="" for="" male="" and="" 2="" for="" female).="" create="" a="" variable="" for="" your="" dv="" if="" you="" have="" a="" within-subjects="" iv,="" then="" you="" will="" need="" to="" create="" multiple="" variables="" for="" you="" dv,="" one="" for="" each="" level="" of="" your="" within-subject="" variable="" create="" variables="" for="" your="" between-subjects="" ivs="" need="" to="" create="" a="" grouping="" variable="" even="" though="" groups="" are="" categorical,="" it’s="" best="" to="" label="" them="" with="" a="" number="" and="" then="" specify="" the="" category="" level="" that="" each="" number="" corresponds="" to="" (e.g.,="" 1="" for="" male="" and="" 2="" for="" female).="" insert="" values="" to="" represent="" groups="" 6="" infants="" in="" each="" group="" note,="" there="" are="" 6="" infants="" in="" group="" 1.="" if="" there="" are="" 6="" infants="" in="" each="" group="" and="" 4="" groups,="" n="24" input="" your="" data="" spss="" anova="" analyze="" -=""> General Linear Model -> Univariate... You can also use Compare Means -> One-Way ANOVA If you have a Repeated Measures Design, need to go to Repeated Measures Univariate DV goes into Dependent Variable IVs go into your Fixed Factor(s) Random factors and Covariates are more advanced features you don’t need to worry about yet Post Hoc Click Post Hoc... Post Hoc Here you can decide which post hoc tests you want to run We will mostly be using Tukey Under Options and/or EM Means In Display, pick Descriptive statistics, Estimates of effect size, and Homogeneity tests Under EM Means or Options depending upon your version of SPSS Move your OVERALL and IV over to get mean estimates Can also Compare main effects (means), if you have planned comparisons Double check your n and N Means and SDs of all groups Again, you do not want this to be significant. .807>.05, not significant df: 3 and 20 Examine data for IV. F = 7.43, p = .002. Is p< .05,="" yes.="" statistically="" significant.="" partial="" eta="" squared="" of="" .53="" is="" your="" effect="" size.="" note:="" 95%="" ci="" appears="" in="" next="" box.="" 31="" these="" are="" your="" post="" hoc="" results="" to="" determine="" where="" significant="" differences="" between="" means="" lie.="" an="" asterix="" indicates="" the="" difference="" is="" significant="" at="" the="" .05="" level.="" less="" than="" .05?="" statistically="" significant="" difference!="" so,="" for="" example,="" the="" difference="" between="" non="" and="" mod="" smokers="" is="" 1.45,="" which="" is="" significant="" at="" p=".015" (and=""><.05). notice, no difference between non and light. p=.993 which is greater than .05 practice time f = msb msw = ssb / dfb ssw / dfw f= ms b ms w = ss b /df b ss w /df w qobt = x 1 − x 2 msw / n q obt = x 1 -x 2 ms w /n qobt = x 1 − x 2 msw 2 1 n1 + 1 n2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ q obt = x 1 -x 2 ms w 2 1 n 1 + 1 n 2 æ è ç ö ø ÷ microsoft word - spss_lab4_instructions.docx lab assignment #4 to test whether memory changes with age, a researcher conducts an experiment in which there are four groups of 6 subjects each. the groups differ according to age. in group 1, the subjects are 30 years old; group 2, 40 years old; group 3, 50 years old; and group 4, 60 years old. each subject is shown a series of nonsense words at a rate of one word every 4 seconds. the series is shown twice, after which the subjects are asked to write down as many of the words as they can remember. the number of words remembered by each subject is shown below. 30 years 40 years 50 years 60 years 15 12 17 12 18 15 14 9 16 16 14 7 18 11 9 8 13 12 13 6 11 18 15 9 a. conduct the anova (include descriptive statistics and effect size). use a tukey test for your post-hoc test. remember to test for homogeneity of variance. b. notice,="" no="" difference="" between="" non="" and="" light.="" p=".993" which="" is="" greater="" than="" .05="" practice="" time="" f="MSb" msw="SSb" dfb="" ssw="" dfw="" f="MS" b="" ms="" w="SS" b="" df="" b="" ss="" w="" df="" w="" qobt="X" 1="" −="" x="" 2="" msw="" n="" q="" obt="X" 1="" -x="" 2="" ms="" w="" n="" qobt="X" 1="" −="" x="" 2="" msw="" 2="" 1="" n1="" +="" 1="" n2="" ⎛="" ⎝="" ⎜="" ⎞="" ⎠="" ⎟="" q="" obt="X" 1="" -x="" 2="" ms="" w="" 2="" 1="" n="" 1="" +="" 1="" n="" 2="" æ="" è="" ç="" ö="" ø="" ÷="" microsoft="" word="" -="" spss_lab4_instructions.docx="" lab="" assignment="" #4="" to="" test="" whether="" memory="" changes="" with="" age,="" a="" researcher="" conducts="" an="" experiment="" in="" which="" there="" are="" four="" groups="" of="" 6="" subjects="" each.="" the="" groups="" differ="" according="" to="" age.="" in="" group="" 1,="" the="" subjects="" are="" 30="" years="" old;="" group="" 2,="" 40="" years="" old;="" group="" 3,="" 50="" years="" old;="" and="" group="" 4,="" 60="" years="" old.="" each="" subject="" is="" shown="" a="" series="" of="" nonsense="" words="" at="" a="" rate="" of="" one="" word="" every="" 4="" seconds.="" the="" series="" is="" shown="" twice,="" after="" which="" the="" subjects="" are="" asked="" to="" write="" down="" as="" many="" of="" the="" words="" as="" they="" can="" remember.="" the="" number="" of="" words="" remembered="" by="" each="" subject="" is="" shown="" below.="" 30="" years="" 40="" years="" 50="" years="" 60="" years="" 15="" 12="" 17="" 12="" 18="" 15="" 14="" 9="" 16="" 16="" 14="" 7="" 18="" 11="" 9="" 8="" 13="" 12="" 13="" 6="" 11="" 18="" 15="" 9="" a.="" conduct="" the="" anova="" (include="" descriptive="" statistics="" and="" effect="" size).="" use="" a="" tukey="" test="" for="" your="" post-hoc="" test.="" remember="" to="" test="" for="" homogeneity="" of="" variance.="">