Question

Each of the following statements contains a blunder. Explain in each case what is wrong. (a) There is a high correlation between the age of American workers and their occupation. The relationship between age and American workers' occupation has a curved relationship and correlation measures the strength of only the linear relationship between two variables. Because occupation has a categorical (nominal) scale, we cannot compute the correlation between occupation and anything. Occupation of American workers can not be correlated with other variables because it is too complex. Age would not have any association with American workers' occupation. (b) We found a high correlation (r = 1.18) between students' ratings of faculty teaching and ratings made by other faculty members. The relationship between students' ratings of faculty teaching and ratings made by other faculty members would have more of a curved relationship and correlation measures the strength of only the linear relationship between two variables. The correlation between students' ratings of faculty teaching and ratings made by other faculty members would not be this high. A correlation r = 1.18 is impossible because −1 ≤ r ≤ 1 always. Because students' ratings of faculty teaching has a categorical (nominal) scale, we cannot compute the correlation between these ratings and anything. (c) The correlation between the sex of a group of students and the color of their cell phone was r = 0.26. Because neither variable (sex and cell phone color) is quantitative, we cannot compute the correlation between them. There is no correlation between sex and cell phone color. The correlation between sex and cell phone color would be much higher. The relationship between sex and cell phone color has a curved relationship and correlation measures the strength of only the linear relationship between two variables.

Answer 1

(a) There is a high correlation between the age of American workers and their occupation.

Blunder : Correlation is measured between two quantitative variables (Contineous values)

Accupation is Qualitative so no correlation between them.

(b) We found a high correlation (r = 1.18) between students' ratings of faculty teaching and ratings made by other faculty members as Correlation is measured between two quantitative variables

Blunder : Correlation always lies between -1 to 1. It cant 1.19 so it is Blunder.

(c) The correlation between the sex of a group of students and the color of their cell phone was r = 0.26.

Blunder: Variable Gender and color are qualitative variables.Correlation is measured between two quantitative variables. So there is no correlation between Gender and color.

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