Probabilities and Relationships

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Probabilities and Relationships
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What is probability?

• Probability statements provide descriptions about
  the relative power or the ability to repeat
  something. Sometimes these statements include
  chance. How much chance are you willing to
  accept?

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• Coin flipping
• Gambling
• Lifes oddities and chance

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Measures of Relationship
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Relationships among two variables

• Knowledge of relationships can assist decision
  making about training and performance, e.g., when
  wanting to train for the long jump a performer
  might focus on creating gastrocnemius strength.
• Knowledge of relationships can also help improve
  the efficiency of a test by determined the
  critical number of items contained in it.

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Graphing of Scores
Student Statistics Score Measurement Score
ABE 92 94
BARB 85 89
CAT 71 78
DEB 91 90
EM 94 95
FRAN 75 78
GER 82 80
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Graphing Technique
Student Statistics Score Measurement Score
ABE 92 94
BARB 85 89
CAT 71 78
DEB 91 90
EM 94 95
FRAN 75 78
GER 82 80
M E A S U R E M E N T
Statistics
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Scatter plots representing the relationship of
two variables
From Rothstein, A. L. (1985). Research
Design Statistics for Physical Education.
Prentice-Hall, Inc. Englewood Cliffs, NJ.
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From http//en.wikipedia.org/wiki/Scatter_plot
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Mathematical Technique

• Correlations range from a -1.00 to a 1.00
• Perfect positive correlation (1.00)
• Perfect negative correlation (-1.00)
• A correlation value (statistic) closer to 1.00 or
• -1.00 represents more related values than
  values closer
• to 0.

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Two Types of Correlations

• Pearson Correlation
• Assumes interval or ratio (continuous) scores
• Spearman Correlation
• Assumes ordinal (rank) scores

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Factors Affecting Measures of Relationship

• Scores that have low reliability
• Range of the scores
• Relationships shrink for more homogeneous scores