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T13-03 Line Plot & Bar Graph (by XY Category)

Purpose Allows the analyst to visually analyze the difference in data samples by 6 X-categories and 10 Y-categories. Most often used to visually analyze two-factor experimental design interaction.

Inputs X & Y LabelsX & Y Data

Outputs Line Plot (by XY Category)Bar Graph (by XY Category)

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The USGA (United States Golf Association) regularly tests golf equipment to ensure that it conforms to USGA standards. It wishes to compare the distance used by 3 different brands of golf ball when hit by a driver and a 5 iron. 6 balls from each brand are chosen and hit with the USGA robot called the Iron Byron. Is there a factor interaction?

Example: ANOVA 2 Factor w/ Replication

BrandClub A B CDriver 226.4 238.3 240.5

232.6 231.4 246.9234.0 227.7 240.3

5 Iron 163.8 184.4 179.0179.4 180.6 168.0168.6 179.5 162.5

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ANOVA

Source of Variation SS df MS F P-value F crit

Sample 16946.41 1 16946.41 507.30 0.0000 4.75

Columns 136.01 2 68.01 2.04 0.1733 3.89

Interaction 357.44 2 178.72 5.35 0.0218 3.89

Within 400.86 12 33.40

Total 17840.72 17

Key Information (refer to EXCEL Basics Lesson 20)

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Anova: Two-Factor With Replication

SUMMARY A B C TotalDriver

Count 3 3 3 9Sum 693.00 697.40 727.70 2118.10Average 231.00 232.47 242.57 235.34Variance 16.36 28.94 14.09 44.59

5 Iron

Count 3 3 3 9Sum 511.80 544.50 509.50 1565.80Average 170.60 181.50 169.83 173.98Variance 63.84 6.61 70.58 67.20

Total

Count 6 6 6Sum 1204.80 1241.90 1237.20Average 200.80 206.98 206.20Variance 1126.53 793.50 1620.91

Key Information (refer to EXCEL Basics Lesson 20)

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Hypothesis Test Facts: F - statistic = 5.35

p-value = .0218.05

null hypothesis is falsealternative is true

Business Conclusion:

The statistical evidence shows that there is an interaction between the club and the brand of the ball (ie: the ball flight by brand is different when struck with a 5 iron and a driver).

Hypothesis Test ANOVA Single Factor

0 F

p-value

F-statistic = 5.35

H no interaction

H interactiono

a

:

:

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Input the factor averages, with the labels in the bright green cells and the averages in the light green cells

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A line plot shows a graphical representation of the interaction between the factors.

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A bar graph shows a graphical representation of the interaction between the factors (however, it is not as easy to interpret as the line plot).