Computing our example

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# Computing our example - PowerPoint PPT Presentation

Computing our example. Step 1: compute sums of squares Recall our data…. 1. 2. N = 15. Computing our example. Step 1: compute sums of squares SS total = [10 2 + 13 2 + 5 2 + 9 2 + 8 2 + 6 2 + 8 2 + 10 2 + 4 2 +12 2 + 1 2 + 3 2 + 4 2 + 5 2 + 2 2 ] -

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## Computing our example

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Presentation Transcript
Computing our example
• Step 1: compute sums of squares
• Recall our data…

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N = 15

Computing our example
• Step 1: compute sums of squares
• SStotal

= [102 + 132 + 52 + 92 + 82 + 62 + 82 + 102 + 42 +122 + 12 + 32 + 42 + 52 + 22] -

= 854 – 666.67 = 187.33

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Computing our example
• Step 1: compute sums of squares
• SSgroup

= 27.14 + 8.84 + 67.34= 103.32

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Computing our example
• Step 1: compute sums of squares
• SSerror
• =SStotal-SSgroup

= 187.33 – 103.32 = 84.01

• So…
• SSgroup = 103.32
• SSerror = 84.01
• Sstotal = 187.33

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Computing our example
• Step 2: Compute df
• df group = k – 1 = 3 – 1 = 2
• dferror = N – k = 15 – 3 = 12
• df total = N – 1 = 15 – 1 = 14

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Computing our example
• Step 3: Compute Mean Squares (MS)

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Computing our example
• Step 4: Put all the info in the ANOVA table:

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Computing our example
• Step 5: Compare Fobs to Fcritical:
• Fobs = 7.38
• Fcritical = …need to obtain Fcrit from tables for F
• df will be (numerator, denominator) in F-ratio
• df = 2, 12
• F (2,12, α = .05) = 3.89
• Reject H0 (Fobs > Fcritical)

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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)

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1-way ANOVA in SPSS

Procedure: Choose the appropriate procedure, and…

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1-way ANOVA in SPSS

Dialog box: slide the variables…

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…into the appropriate places

n – k = 15 - 3 = 12

k-1 = 3-1 = 2

n-1 = 15-1 = 14

Here we see the between and within sources of variance

Here are the SD’s (here expressed as the “mean square” – that’s the average sum of squares, which is after all a ‘standardized’ deviation)

1-way ANOVA in SPSS

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Result!

Significant result…now what?

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• 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?)

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Significant result…now what?
• Follow-up tests – most common…
• Tukey’s HSD (honestly sig. diff.)
• Formula:
• But it’s easier to use SPSS…

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Follow-ups to ANOVA in SPSS

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Choose “post-hoc” test (meaning ‘after this’)

Check the appropriate box for the HSD (Tukey, not Tukey’s b)

Sig. levels between pairs of groups

Groups that do not differ

Follow-ups to ANOVA in SPSS

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And one that does (from the other 2)

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Follow-ups to ANOVA in SPSS

So “TV Movie” differs from both “Soap Opera” and “infomercial” , significantly

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“Soap Operas” and “infomercials” do not differ significantly

Assumptions to test in One-Way
• Samples should be independent (as with independent t-test – does not mean perfectly uncorrelated)
• Each of the k populations should be normal (important only when samples are small…if there’s a problem, can use Kruskal-Wallis test)
• The k samples should have equal variances (this is the homogeneity of variance assumption, and we’ll look at it shortly…violations are important mostly with small samples and unequal n’s)

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Homogeneity of variance - SPSS

1. Click on the ‘options’ button

2. Choose homogeneity of variance

3. Click continue

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

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. Tukey’s 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.”

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