10. The point-biserial correlation Aa Aa Suppose a counseling psychologist sets

Question

10. The point-biserial correlation Aa Aa Suppose a counseling psychologist sets out to see whether having children is related to relationship longevity. She decides to measure relationship satisfaction in a group of couples with children and a group of childless couples. She chooses the Marital Satisfaction Inventory because it refers to "partner" and "relationship" rather than "spouse" and "marriage," which makes it useful for research with both traditional and nontraditional couples. Higher scores on the Marital Satisfaction Inventory indicate greater relationship satisfaction The psychologist administers the Marital Satisfaction Inventory to 58 couples-30 are couples with children and 28 are childless couples. She wants to calculate the correlation between a couple's relationship satisfaction and whether use? they have children. Which of the following types of correlations would be most appropriate for the psychologist to A Pearson correlation O A phi-coefficient O A Spearman correlation O A point-biserial correlation To calculate the correlation, the psychologist converts "having children" to a dichotomous variable. Suppose the data for the first 5 couples she surveys are shown in the table that follows. By assigning one (1) to couples with children and zero (0) to childless couples, complete the table Marital Satisfaction Children Children Inventory Score (Converted) no no yes 20 41 18 46 32 Suppose the psychologist calculates the correlation using the data as coded in the previous table. Then, she recalculates the correlation, but this time, instead of assigning one (1) to couples with children and zero (0) to childless couples, she reverses the codes and assigns zero (0) to couples with children and one (1) to childless couples. Which of the following statements is true regarding her two calculations of the correlation? The absolute values of the two correlations are different The signs of the two correlations are opposite, but their absolute values are the same O The two correlations are the same Before calculating the correlation, the psychologist does an independent-measures t test comparing the Marital Satisfaction Inventory scores of couples with children and childless couples. The value of the t statistic is 4.26 with 56 degrees of freedom. Using this information, the square of the point-biserial correlation is r2 =

Explanation / Answer

Here we are considering two variables,

having children or no children. As they are binary variables since both can not be true at the same time. Phi -Coefficient deals with binary variables and that will here.

Now Psychologist converts having children to a dichtomous variable. That implies children(yes)=1 and Children(no)=0. The table becomes,

Marital Satisfaction

Inventory Score  

Children

Converted

Interchaning 1 and 0 will have the same value for ?2. So value of ? will be same but sign will be different.

r2 = t2 / (t2 + df) = (4.26)2 /(4.262 +56) = 18.1476/ 74.1476 = 0.244

where t = 4.26 and df =56

Children  

Marital Satisfaction

Inventory Score  

Children

Converted

yes 20 1 yes 41 1 no 18 0 no 46 0 yes 32 1

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