EXERSICE24: UNDERSTANDING PEARSONS r, EFFECT SIZE, AND PERCENTAGE OF VARIANCEEXPLAINED
Nursing
(Date)

What is the r value listed for the relationship between variables 4 and 9?
r=0.32, p<0.01 It is an effective positive size. Percentage ofvariance =(0.32)^{2}x100=10.24.This is considered a good relationship with good variance

Describe the correlation r=0.32** using words. Is this a statistically significant correlation? Provide a rationale for your answer
r= 0.32** represents a moderate (0.5 < r < 0.3) negativerelationship between the two variables therefore the variables changein opposite directions as one variable increases, the other variabledecreases. This value has ** next to it, so it is statisticallysignificant at p < 0.01, as indicated by the key below the table

Calculate the percentage of variance explained for r=0.53. Is this correlation clinically important? Provide a rationale for your answer
Percentageof variance = r^{2}x100Percentage of variance = (0.53)^{2}x100 = 28.09% (0.53)^{2}x100=28.09%.This is clinically important cause it is significantly greaterthan9%. Since any variance over 9% is considered clinicallyimportant.

According to Table 2, r=0.15 is listed as the correlation between which two items? Describe this relationship. What is the effect size for this relationship, and what size sample would be needed to detect this relationship in future studies?
Thisvalue is indicated for variables 3 and 7.  It representscorrelation between Positive Items and Avoidance.   There is aweak correlation here because r < 0.3.   The effect size is0.15.   The sample size required in this case would be 273(given a power of 0.8).

Calculate the percentage of variable explained for r =0.15. Describe the clinical importance of this relationship.
(0.15)^{2}x100=2.25%,which is less than 9% so it is not an important relationshipclinically.

Which two variables in Table 2 have the weakest correlation, or r value? Which relationship is the closest to this r value? Provide a rationale for your answer.
Variables6 and 7 have r= 0.02 which is considered the weakest correlationbecause it is the furthest from 1 or 1 and closest to 0.0. This isthe relationship between emotion and avoidance, which are copingstyles.

Is the correlation between LOTR Total score and AvoidanceDistraction coping style statistically significant? Is this relationship relevant to practice? Provide rationales for your answer
Therelationship between LOTR Total scores and Avoidance – Distractioncoping style has an rvalue = 0.2* as listed in Table 2. Thisrepresents a weak positive relationship between the two variablesindicating that the LOTR Total scores and Avoidance –Distractioncoping styles will either increase or decrease together. The r valuehas a* next to it, so it is statistically significant at P < 0.05as indicated by the key below the table.
r=0.20,p<0.05, (.20)^{2}x100=4%. These indicate a negative relationship with larger p value to thisis not a significant result with a low variance.

Is the correlation between variables 9 and 4 significant? Is this correlation relevant to practice? Provide a rationale for your answer
Thecorrelation between variables 9 and 4 has an r value = 0.32**. Thisrepresents a moderate (0.5 < r < 0.3) negative relationshipbetween the two variables therefore the variables change in oppositedirections as one variable increases, the other variable decreases.This value has **next to it, so it is statistically significant at p< 0.01, as indicated by the key below the table. The percentage ofvariance explained for r = 0.32** is (0.32)^{2}x100 = 10.24%. This relationship is clinically important as it isgreater than the 9% variance explained threshold for clinicalimportance. Therefore, this relationship is very relevant topractice.

Consider two values, r=0.08 and r= 0.58. Describe them in relationship to each other. Describe the clinical importance of both r values.
r= 0.58 is a strong negative relationship and is the stronger of thetwo, as r = 0.08 is a weak positive relationship. The r value closerto 0.00 is considered the weakest relationship. Also, r = 0.58** ismore significant at p<0.01, whereas r = 0.08 is not consideredsignificant. The percentage of variance explained for r = 0.58** is(0.58)^{2}x100 = 33.64%. This relationship is clinically important as it isgreater than the 9% variance explained threshold for clinicalimportance. Therefore, this relationship is very relevant topractice.
Thepercentage of variance explained for r = 0.08 is (0.08)^{2}x100 = 0.64%. This relationship is not clinically important as it islower than the 9% variance explained threshold for clinicalimportance. Therefore, this relationship is not very relevant topractice.

Examine the Pearson r values for LOTR total, which measured Optimism with the Task and Emotion Coping Styles. What do these results indicate? How might you use this information in your practice?
Therelationship between LOTR Total which measured optimism with theTask Coping styles is listed with an r value of 0.54**. This shows astrong positive relationship between the variables which means thatthe variables will either increase or decrease together. The r valuehas ** next to it, so it is statistically significant at p < 0.01,as indicated by the key below the table. The percentage of varianceexplained for r = 0.54** is (0.54)^{2}x100 = 29.16%. This means that the LOTR Total which measured optimismcan be used to predict 29.16% of the variance in the Emotion copingstyle scores. This relationship is clinically important as it isgreater than the 9%variance explained threshold for clinicalimportance. Therefore, this relationship is very relevant topractice.
Therelationship between LOTR Total which measured optimism with theEmotion Coping styles is listed with an r value of 0.58**. Looking atthis score as r=0.58 p<0.01 and a percentage of varianceexplained for r = 0.54** is (0.58)^{2}x100 = 33.64%. I could conclude there is a strong correlation in thetwo even if negative. It indicates that emotional coping is down. Icould use this in my practice when taking into considerationpatient’s Coping skills and that even when they attempt to bepositive they can still be difficult to cope with and can come outnegative.
BONUSQUESTION
Oneof the study goals was to examine the relationship between optimismand psychopathology. Using the data in Table 2, formulate an opinionregarding the overall correlation between optimism andpsychopathology. Provide a rationale for your answer.
Inthis case, r = 0.72** reveling that optimism and psychopathologycomprise negative powerful relationship as well as negative powerfuleffect size. This reveals that, the effect size broadens the littlesamples size required to determine important correlations.
REFERENCE
DavidW. Stockburger, 2015: IntroductoryStatistics: Concepts, Models, and Applications.
Retrievedfrom http://www.psychstat.missouristate.edu/introbook/sbk17.htm