So far. . .

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Conceptual Understanding
Complete the above table for an ANOVA having 3
levels of the independent variable and n 20.
Test for significant at .05.
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Conceptual Understanding
Fcrit 3.18 Complete the above table for an
ANOVA having 3 levels of the independent variable
and n 20. Test for significant at .05.
Fcrit (2, 57) 3.15
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Conceptual Understanding

• Under what circumstance will the F ratio, over
  the long run, approach 1.00? Under what
  circumstances will the F ratio be greater than
  1.00?

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Conceptual Understanding

• Under what circumstance will the F ratio, over
  the long run, approach 1.00? Under what
  circumstances will the F ratio be greater than
  1.00?
• F ratio will approach 1.00 when the null
  hypothesis is true
• F ratio will be greater than 1.00 when the null
  hypothesis is not true

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Conceptual Understanding
Without computing the SS within, what must its
value be? Why?
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Conceptual Understanding
The SS within is 0. All the scores within a
group are the same (i.e., there is NO variability
within groups)
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Practice

• You are interested in comparing the taste
  preference of four sodas. Subjects drank one of
  four sodas and asked to rank it on a 1-10 scale
  of how much they liked the taste.

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Results
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Practice

• Is there a significant (.01) difference in how
  much these sodas were liked?

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Step 1 State the Hypothesis

• H0 ?P ?C ?R ?M
• H1 The four population means are not all equal

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Step 2 Find F-Critical

• Step 2.1
• Need to first find dfbetween and dfwithin
• Dfbetween 3 (k number of groups)
• dfwithin 12 (N total number of
  observations)
• dftotal 15
• Check yourself
• 15 3 12

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Step 2 Find F-Critical

• Step 2.2
• Look up F-critical using table F on pages 370 -
  373.
• F (3,12) 5.95

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Step 3.1 Ingredients

• ?X 121
• ?X2 937
• ?Tj2 3671
• N 16
• n 4

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Step 3.2 Calculate SS
?X 121 ?X2 937 ?Tj2 3671 N 16 n 4

• SStotal

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Step 3.2 Calculate SS
?X 121 ?X2 937 ?Tj2 3671 N 16 n 4

• SStotal

121
937
21.94
16
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Step 3.2 Calculate SS
?X 121 ?X2 937 ?Tj2 3671 N 16 n 4

• SSWithin

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Step 3.2 Calculate SS
?X 121 ?X2 937 ?Tj2 3671 N 16 n 4

• SSWithin

3671
19.25
937
4
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Step 3.2 Calculate SS
?X 121 ?X2 937 ?Tj2 3671 N 16 n 4

• SSBetween

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Step 3.2 Calculate SS
?X 121 ?X2 937 ?Tj2 3671 N 16 n 4

• SSBetween

2.69
3671
121
4
16
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Step 3.2 Calculate SS

• Check!
• SStotal SSBetween SSWithin

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Step 3.2 Calculate SS

• Check!
• 21.94 2.69 19.25

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Step 3.3 Calculate MS
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Step 3.3 Calculate MS
2.69
.90
3
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Calculating this Variance Ratio
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Step 3.3 Calculate MS
19.25
1.60
12
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Step 3.4 Calculate the F value
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Step 3.4 Calculate the F value
.90
.56
1.60
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Step 4 Decision

• If F value gt than F critical
• Reject H0, and accept H1
• If F value lt or to F critical
• Fail to reject H0

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Step 4 Decision
F value .56 F crit 5.95

• If F value gt than F critical
• Reject H0, and accept H1
• If F value lt or to F critical
• Fail to reject H0

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Step 5 Create the Summary Table
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Step 6 Put answer into words

• Question Is there a significant (.01) difference
  in how much these sodas were liked?
• H0 ?P ?C ?R ?M
• There was not a significant difference in how
  much these sodas were liked. On average, they
  were all liked equally as well.

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Practice

• Odometers measure automobile mileage. Suppose 12
  cars drove exactly 10 miles and the following
  mileage figures were recorded. Determine if, on
  average, the odometers were accurate (Alpha
  .05).
• 9.8, 10.1, 10.3, 10.2, 9.9, 10.4, 10.0, 9.9,
  10.3, 10.0, 10.1, 10.2

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One-sample t-test

• H1 Mean not equal to 10
• H0 Mean 10
• t critical (11) 2.201
• t obs 1.86
• The odometers did not record a siginficantly
  different distance than what was driven.

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Practice

• A research study was conducted to examine the
  differences between older and younger adults on
  perceived life satisfaction. A pilot study was
  conducted to examine this hypothesis. Ten older
  adults (over the age of 70) and ten younger
  adults (between 20 and 30) were given a life
  satisfaction test with high scores indicative of
  high life satisfaction. Determine if age has an
  affect (.05) on life satisfaction.

Older Adults Younger Adults
Mean 44.5 Mean 28.1
S 8.68 S 8.54
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• tobs  4.257
• tcrit  2.101
• Age does seem to affect life satisfaction.

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Review

• Compare one sample to another value
• One sample t-test
• Compare two independent samples to each other
• Two sample independent t-test (equal or unequal
  n)
• Compare two dependent samples to each other
• Two sample dependent t-test
• Compare two or more independent samples to each
  other
• One-way ANOVA