Computing our example Step 1: compute sums of squares Recall our data… KNR 445 Statistics ANOVA...
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Computing our example Step 1: compute sums of squares Recall our data… KNR 445 Statistic s ANOVA (1w) Slide 1 TV Movie Soap Opera Infomercial 1 6 10 3 8 13 4 10 5 5 4 9 2 12 8 n = 5 n = 5 n = 5 = 3 = 8 = 9 N = 15 1 2 Movie X soap X sales X 67 . 6 T X
Computing our example Step 1: compute sums of squares Recall our data… KNR 445 Statistics ANOVA (1w) Slide 1 TV MovieSoap OperaInfomercial 1610 3813
Computing our example Step 1: compute sums of squares SS group
= 27.14 + 8.84 + 67.34= 103.32 KNR 445 Statistics ANOVA (1w) Slide
3 1 2
Slide 5
Computing our example Step 1: compute sums of squares SS error
=SS total -SS group = 187.33 103.32 = 84.01 So SS group = 103.32 SS
error = 84.01 Ss total = 187.33 KNR 445 Statistics ANOVA (1w) Slide
4 1
Slide 6
Computing our example Step 2: Compute df df group = k 1 = 3 1 =
2 df error = N k = 15 3 = 12 df total = N 1 = 15 1 = 14 KNR 445
Statistics ANOVA (1w) Slide 5 1
Slide 7
Computing our example Step 3: Compute Mean Squares (MS) KNR 445
Statistics ANOVA (1w) Slide 6 1
Slide 8
Computing our example Step 4: Put all the info in the ANOVA
table: KNR 445 Statistics ANOVA (1w) Slide 7 Source Sum of Squares
DFMSFsig. Between Groups 103.32251.66 MS B /MS W =51.66/7 =7.38
p-value Within Groups 84.01127 Total187.3314 1
Slide 9
Computing our example Step 5: Compare F obs to F critical : F
obs = 7.38 F critical = need to obtain F crit from tables for F df
will be (numerator, denominator) in F-ratio df = 2, 12 F (2,12,
=.05) = 3.89 Reject H 0 (F obs > F critical ) KNR 445 Statistics
ANOVA (1w) Slide 8 1 2
Slide 10
KNR 445 Statistics ANOVA (1w) Slide 9 1-way ANOVA in SPSS Data:
One column for the grouping variable (IV: group in this case), one
for the measure (DV: fitness in this case) Data: Note grouping
variable has 3 levels (goes from 1 to 3) 1
Slide 11
KNR 445 Statistics ANOVA (1w) Slide 10 1-way ANOVA in SPSS
Procedure: Choose the appropriate procedure, and 1
Slide 12
KNR 445 Statistics ANOVA (1w) Slide 11 1-way ANOVA in SPSS
Dialog box: slide the variables into the appropriate places 1
Slide 13
KNR 445 Statistics ANOVA (1w) Slide 12 1-way ANOVA in SPSS Here
we see the between and within sources of variance Here are the SDs
(here expressed as the mean square thats the average sum of
squares, which is after all a standardized deviation) k-1 = 3-1 =
2n k = 15 - 3 = 12n-1 = 15-1 = 14 Result! 1
Slide 14
KNR 445 Statistics ANOVA (1w) Slide 13 Significant resultnow
what? Follow-up tests ONLY compute after a significant ANOVA Like a
collection of little t-tests But they control overall type 1 error
comparatively well They do not have as much power as the omnibus
test (the ANOVA) so you might get a significant ANOVA & no sig.
Follow-up Purpose is to identify the locus of the effect (what
means are different, exactly?) 1 2
Slide 15
KNR 445 Statistics ANOVA (1w) Slide 14 Significant resultnow
what? Follow-up tests most common Tukeys HSD (honestly sig. diff.)
Formula: But its easier to use SPSS 1
Slide 16
KNR 445 Statistics ANOVA (1w) Slide 15 Follow-ups to ANOVA in
SPSS Choose post-hoc test (meaning after this) 1 2 Check the
appropriate box for the HSD (Tukey, not Tukeys b)
Slide 17
KNR 445 Statistics ANOVA (1w) Slide 16 Follow-ups to ANOVA in
SPSS Sig. levels between pairs of groups Groups that do not differ
And one that does (from the other 2) 1 2 3
Slide 18
KNR 445 Statistics ANOVA (1w) Slide 17 Follow-ups to ANOVA in
SPSS 1 So TV Movie differs from both Soap Opera and infomercial,
significantly Soap Operas and infomercials do not differ
significantly
Slide 19
KNR 445 Statistics ANOVA (1w) Slide 18 Assumptions to test in
One-Way 1. Samples should be independent (as with independent t-
test does not mean perfectly uncorrelated) 2. Each of the k
populations should be normal (important only when samples are
smallif theres a problem, can use Kruskal-Wallis test) 3. The k
samples should have equal variances (this is the homogeneity of
variance assumption, and well look at it shortlyviolations are
important mostly with small samples and unequal ns) 1
Slide 20
KNR 445 Statistics ANOVA (1w) Slide 19 Homogeneity of variance
- SPSS 1. Click on the options button 2. Choose homogeneity of
variance 3. Click continue
Slide 21
KNR 445 Statistics ANOVA (1w) Slide 20 Homogeneity of variance
- SPSS Homogeneity test output As you can see, no problems here.
The test has to be significant for there to be a violation
Slide 22
Interpret output The amount of aggression arising from watching
TV changed according to the type of program watched, F(2,12) =
7.38, p .05. Tukeys HSD follow-up tests showed that those watching
violent movies (M = 3) experienced less aggression than those
watching soap operas (M = 8) or infomercials (M = 9). There was no
difference in aggression level between those who watched soap
operas and those who watched infomercials. KNR 445 Statistics ANOVA
(1w) Slide 21 1