Week 5: Correlations

Question 1

Describe correlation (6 points)

Answer 1

• Statistical technique used to express the relationship between two variables within the one sample.
• How the variables relate to each other = correlate.
• Examples:
  
  • Athletic participation and academic achievement.
  • Arm strength and golf drive distance.
  • Percentage of body fat and the ability to run 4km.

Question 2

Linear Correlation (2 points)

Answer 2

• The degree to which a straight line best describes the relationship between two variables.
• Simplest and most common correlation

Question 3

Correlation Coefficient (6 points)

Answer 3

• The number that represents the correlation is called the correlation coefficient
• Regardless of the technique, correlation coefficients have several common characteristics:
• Values will always range from +1.00 to -1.00
• A positive coefficient indicates a direct relationship
• A negative coefficient indicates an inverse relationship
• A correlation coefficient near .00 indicates no relationship

Question 4

Describe the common characteristics of all correlation coefficients (2 points)

Answer 4

• The number indicates the degree of the relationship, and the sign indicates the type of relationship.
• A correlation coefficient indicates relationship. But, does not predict which is the cause/effect.

Question 5

Describe the different types of correlations (10 points)

Answer 5

1. Spearman Rho Rank-Order Correlation
   - Ordinal data
   - Difference between the ranks of two sets is scores is used
   - Spearman Rho
2. Pearson Product-Moment Correlation
   - Pearson r
   - Interval or ratio data
   - More precise estimate of relationship
   - 30 or more subjects are desirable
   - The symbol for the product-moment correlation coefficient is r

Question 6

How do you interpret a correlation coefficient? (10 points)

Answer 6

• 1.00 - perfect positive correlation
• 0.00 - no correlation/ no relationship
• -1.00 - perfect negative correlation
• -.75 is just as strong a correlation as .75
• -.50 is a stronger correlation than .49
• • or - .80 – 1.00 High
• • or - .60 - .79 Moderately high
• • or - .40 - .59 Moderate
• • or - .20 - .39 Low
• • or - .01 - .20 Very low

Question 7

Describe shared variance (4 points)

Answer 7

• Correlation coefficient^2 = r2 = shared variance between the 2 sets of variables
• For example: correlation coefficient between contested marks & goals scored for forwards in the AFL is .54
• Shared variance = .54^2 = .2916
• The 2 sets of data have 29.16% shared variance or overlap due to common factors

Question 8

Describe Degrees of Freedom (5 points)

Answer 8

• Concept used in all statistical tests
• df = the number of scores in a distribution that are free to vary:
• Working with 1 variable df = N – 1
• Working with 2 variables df = N – 2
• Relevant when calculating significance of correlation.

Question 9

List the factors that need to be considered when reporting correlations (9 points)

Answer 9

• Must include the variables considered
• Whether or not it was significant
• Strength of relationship
• Correct statistical values (r, df, p)
• Shared variance
• All presented in sentence format
• Scatterplot with trend line to support
• Refer to figure before it is included
• Title is below the figure