Exercise 23 questions to be graded

Correlation Analysis - Graded On Exercise 23 And 24 Plus Bonus Question - TOTORIAL

21 Questions of type below:

1. What is the r value for the relationship between Hamstring strength index 60°/s and the Shuttle run test? Is this r value significant? Provide a rationale for your answer.

6. Which of the following sets of variables has the strongest relationship?

a. Hamstring strength index 120°/s and the Hop index

b. Quadriceps strength index 60°/s and the Carioca test

c. Quadriceps strength index 120°/s and the Side step test

d. Quadriceps strength index 60°/s and the Triple hop index

10. Consider the relationship reported for the Quadriceps strength index 120°/s and the Hop index (r = 0.744**, p= 0.000). What do these r and p values indicate related to statistical significance and clinical importance?

STATISTICAL TECHNIQUE IN REVIEW

Review the statistical information regarding Pearson's Product-Moment Correlation Coefficient presented in Exercise 23. In this exercise, you will need to apply that information to gain an understanding of interpreting Pearson r results presented in a mirror-image table. A mirror-image table, as the name implies, has the same labels in the same order for both the x- and y-axes. Frequently, letters or numbers are assigned to each label, and only the letter or number designator is used to label one of the axes. To find the r value for a pair of variables, look both along the labeled or y-axis in the table below and then along the x-axis, using the letter designator assigned to the variable you want to know the relationship for, and find the cell in the table with the r value. Below is an example of a mirror-image table that compares hours of class attended, hours studying, and final grade as a percentage. The results in the table are intended as an example of a mirror-image table and are not based on research. If you were asked to identify the r value for the relationship between hours of class attended and the final grade as a percentage, the answer would be r = 0.72, and between hours studying and final grade as a percentage, the answer would be r = 0.78. The dash (–) marks located on the diagonal line of the table represent the variable's correlation with itself, which is always a perfect positive correlation or r = +1.00.

VARIABLES A B C

A. Hours of class attended – 0.44 0.72

B. Hours studying 0.44 – 0.78

C. Final grade as a percentage 0.72 0.78 –

Effect Size of an r Value

In determining the strength of a relationship, remember that a weak relationship is r < 0.3 or r < −0.3, a moderate relationship is r = 0.3 to 0.5 or −0.3 to −0.5, and a strong relationship is r > 0.5 or > −0.5. The r value is equal to the effect size or the strength of a relationship. In the table above, the relationship between hours of class attended and hours of studying is r = 0.44 and the effect size = 0.44. The effect size is used in power analysis to determine sample size for future studies. The strength of the effect size is the same as that for the r values, with a weak effect size < 0.3 or < −0.3, a moderate effect size 0.3 to 0.5 or −0.3 to −0.5, and a strong effect size > 0.5 or > −0.5. The smaller the effect size, the greater the sample size needed to detect significant relationships in future studies. Thus the larger the effect size, the smaller the sample size that

is needed to determine significant relationships. The determination of study sample sizes with power analysis is presented in Exercise 12.

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Percentage of Variance Explained in a Relationship

Percentage of variance explained is a calculation based on a Pearson's r value. The purpose for calculating the percentage of variance explained is to understand further the relationship or correlation between two variables in terms of clinical importance. To calculate the percentage of variance explained, square the r value then multiply by 100 to determine a percentage.

Formula: r2 × 100 = % variance explained

Example: r = 0.78 (correlation between hours studying and final grade as a percentage)

(0.78)2 × 100 = 0.6084 × 100 = 60.84% variance explained

The example above indicates that the hours studying can be used to predict 60.84% of the variance in the final course grade. Calculating the percentage of variance explained helps the researchers and consumers of research better understand the practical implications of reported results. The stronger the r value, the greater the percentage of variance explained. For example if r = 0.5, then 25% of the variance in one variable is explained by an another variable and if r = 0.6, then 36% of the variance is explained. Any Pearson's r ≥ 0.3, which yields a 9% variance explained, is considered clinically important. Keep in mind that a result may be statistically significant (p < 0.05), but it may not represent a clinically important finding (Burns & Grove, 2005).

RESEARCH ARTICLE

Source: Hatchett, G. T., & Park, H. L. (2004). Relationships among optimism, coping styles, psychopathology, and counseling outcome. Personality and Individual Differences, 36 (8), 1755–69.

Introduction

Hatchett and Park (2004) conducted a study consisting of 96 college students to determine the relationships between optimism, coping styles,

psychopathology, and counseling outcomes. Each participant filled out three questionnaires before beginning counseling: the Outcome Questionnnaire-45 (OQ-45) (measures psychopathology), the Life Orientation Test-Revised (LOT-R) (measures optimism and pessimism), and the Coping Inventory for Stressful Situations (CISS) (measures coping styles). At the termination of treatment, the OQ-45 was re-administered. The researchers reported that optimism “was negatively correlated with psychopathology, emotion-oriented coping, and the avoidance-distraction subscale from the CISS” (Hatchett & Park, 2004, p. 1762). Conversely, they report optimism to be positively correlated with task-oriented coping and the avoidance–social diversion subscales. Pessimism reportedly had the opposite or negative relationships with these same variables. The researchers reported no statistically significant correlation between optimism and counseling outcomes. “Future research might be directed at determining whether the early assessment and subsequent remediation of pessimistic thoughts leads to better outcomes. Furthermore research might ascertain whether optimists and pessimists respond differently to certain types of clinical interventions. [One] might advocate matching clinical interventions to clients’ unique personality characteristics. For example, optimists, who rely more on problem-focused coping strategies, might respond better to more active intervention strategies (e.g., problem-solving skills). On the other hand, pessimists, who report greater use of emotion-oriented coping, might respond better to more expressive and supportive therapeutic techniques” (Hatchett & Park, 2004, pp. 1766–7).

Relevant Study Results

In Table 2 in p. 175, Hatchett and Park (2004) presented the correlations among optimism (LOT-R Total and Positive Items); pessimism (Negative Items); psychopathology (OQ-45); and coping styles (Task, Emotion, Avoidance, Avoidance–Distraction, and Avoidance–Social Diversion). Table 2 is a mirror-image table with the variables numbered and labeled on the y-axis and the numbers of the variables on the x-axis. The blank spaces in the table are where the variable is correlated with itself and would be a +1.00 correlation.

TABLE 2 Intercorrelations among Optimism, Psychopathology, and Coping Styles

Variable 1 2 3 4 5 6 7 8 9

1. OQ-45 (psychopathology) – -0.72** -0.59** 0.74** -0.43** 0.76** -0.22* 0.09 -0.45**

2. LOT-R Total (optimism) – 0.92** -0.94** 0.54** -0.58** 0.11 -0.20* 0.38**

3. Positive Items (from LOT-R) – -0.72** 0.53** -0.48** 0.15 -0.16 0.38**

4. Negative Items (from LOT-R) – -0.47** 0.58** -0.06 0.21* -0.32**

5. Task (coping style) – -0.42** 0.08 -0.09 0.22*

6. Emotion (coping style) – -0.02 0.21* -0.24*

7. Avoidance (coping style) – 0.83** 0.78**

8. Avoidance-Distraction (coping style) – 0.36**

9. Avoidance-Social Diversion (coping style) –

* p < 0.05.

** p <0.01.

Hatchett, G. T., & Park, H. L. (2003). Relationships among optimism, coping styles, psychopathology, and counseling outcome. Personality and Individual Differences, 36(8), p. 1762. Copyright © 2003, with permission from Elsevier.