PSYC 243: Test 3
61 Cards in this Set
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Difference between a t-test and an Anova
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A t-test is for 2variables,
ANOVA for +2
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what are groups in ANOVAs called?
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factors
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levels of factors
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individual conditions
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two factorial design
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study that combines 2 factors
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single factor designs
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have 1 variable
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independent measures design
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studies that use separate group group of participants for each treatment condition
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ANOVA t statistic
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t=obtained difference between sample means/standard error
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f=
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variance between sample/variance expected with no treatment
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testwise alpha
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selected alpha level for hypothesis test that risks type 1 error
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Experimentwise alpha
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Total probability of type I error that is accumulated from all individual tests in the experiment
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if a test uses .05 alpha level, what is the % chance of error in each test?
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5%
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between treatment variance
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measuring difference between sample means
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within treatment variance
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measures difference inside each treatment condition; shows how big differences are
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k
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number of levels in a factor
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n
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number of scores in each treatment
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N, and equation
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number of scores in entire study
N=kn
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T
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sum of squares (∑X)
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G & equation
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grand total, sum of all scores, G=∑T or add all Ns
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variance treatments (within, between)
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ss/df (use within or b/w properly)
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ANOVA critical region
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df between, df within
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post hoc test
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done after ANOVA to determine which mean differences are significant
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when do you do a post hoc test?
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when rejecting H0 AND there's 3+ treatments
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types of post hoc tests
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Tukey & Scheffe
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how to get "q" in tukey's test
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use table ⇾k, df within & alpha level
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F ratio & t test relationship equation
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F ratio = t^2
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what happens to a t test when you square it for the f ratio?
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negative becomes positive, and moves to the other side of the graph
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When can ANOVAs be T tests? (3)
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1. observations are independent
2. samples are normal
3. populations must have equal variances
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if t= 3 and is converted to f ratio, what is the f ratio?
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9 (f=t^2)
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If an ANOVA has f ratio df= 1, 34, can it be a t test, and what is the t's df?
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yes, bc 2 treatments, and df=34
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if k=2, are post hocs necessary?
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no, must be at least k=3
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use tukey's test: T1= 16, T2= 32, T3= 40, n=8 and MSwithin= 2.5, and is it significant?
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q= 3.53, and HSD= 1.97; significant b/c 2 pt difference
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if M=35 changed to M=25, would the f ratio increase or decrease
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decrease, bc it would reduce the size of MSbetween & f ratio
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if SS=1005 changed to SS=1400, would the f ratio increase or decrease
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increase MSwithin & f ratio
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table on 374: if means & variances held constant buy n=20, would F increase/decrease
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increasing sample size increases f ratio
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Calculate 3 SS:
n1=5 T1=10 SS1=21
n2=5 T2=15 SS2=16
n3=5 T3=35 SS3=23
N=15 G=60 ∑X^2=370
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total=130
between=70
within=60
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df b/w=3
df w/i=28
How many treatment conditions?
If all treatments have same # of participants, how many are in each treatment?
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4 treatments, because df b/w=k-1
n=8 in each treatment, bc
df w/i=N-K
28= N-4,
N=32
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N (ch 13)
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refers to number of scores, NOT participants
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k=3, n=8. complete table:
SS df MS
b/w: x x x
w/i: x x 2
total: 62 x F ratio
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SS df MS
20 2 10
42 21 2
62 23 F=5
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difference between test wise alpha level and experiment wise alpha level
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when a single study has several tests, use testwise, experimentwise is total risk of type 1 error accumulated from all separate tests
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in anova, how is the total variability of scores separated?
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between treatments variability & within treatments variability
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if a treatment has no effect, what will F (usually) be in anova?
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When H0 is true, F=1.00
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what does it mean when the F ratio is a large value?
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indicates existence of treatment effect
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residual/error variance
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measures variances expected if there are treatment effects or ID
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P
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total number of individual score
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SS between subjects
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measures size of ID
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ƞ^2
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% of variance
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homogeneity of covariance
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relative stand of a subject should be maintained
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advantage of repeated measure design
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remove variance caused by ID
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disadvantage of repeated measure design
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creates opportunities for factors outside treatments to change effects
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main effect
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main differences among the levels of one factor
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interaction (3)
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1) occurs when mean differences b/w cells differ from prediction
2) when the effect of factor depends on another
3) non parallel lines on a 2 factor graph
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why is the within-treatment variability the appropriate denominator for the two-factor independent measures F ratios
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all individuals treated exactly the same
- within treatment variability measures the differences that exist between one score and another when there is no treatment effect causing the scores to be different
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Table on 424:
Calculate SS for factors A & B, and if SS b/w treatments=40, what is SS interaction?
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factor A: 30 & 30; SSa= 0
factor B: 10, 20, 30; SSb=20
SS axb= 20
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Fill in table (425)
SS df ms
b/w treat 75 x
factor A x x x F=x
Factor B x x 15 F=x
AxB x x x F=6
Within t…
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SS df ms
b/w treat 75 5
factor A 9 1 9 F=3
Factor B 30 2 15 F=5
AxB 36 2 18 F=6
Within treat. 90 …
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table on 417:
a) what is compared to evaluate main factor A
b) ^ same but B
c) is there an interaction & why
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a) M=25 & M=10
b) M=15 & M=25
c) yes, in A1 there is a 10 pt diff b/w levels of factor b, but none in A2. B depends on A
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T/F: It is impossible to have an interaction unless you also have main effects for at least 1 of 2 factors
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False. Interactions are independent of main effects
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A repeated measures study is used to eval the mean differences among 4 treatment conditions when n=10. What are the df values for the f ratio?
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df= 3, 27
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F ratio with df= 3, 24. How many conditions were compared and how many participated?
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4 conditions & 9 people
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table on 407
SS w/i treatments
SS b/w subjects
SS error
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SS w/i= 22
SS b/w= 8
SS error= 14
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Explain why individual differences are not part of b/w treatments variance in the numerator of F-ratio
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individuals in one treatment are the same as in others
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why individual differences are not part of the error variance in the denominator of f-ratio
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variance caused by ID is subtracted out to produce error variance w/o treatment effects or ID
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PSYC 243: Test 3