Each of the following statements contain a blunder. Explain in each case what is wrong.
a) There is a high correlation between the age of American workers and their occupation.
b) we found a high correlation (r=1.19) between students rating of faculty teaching and ratings made by other faculty members.
c) The correlation between the gender of a group of students and the color of their cell phones was r=0.23.
a. Each occupation has varying ages; occupation is not a continuous variable.
b. r cannot be > 1.00.
c. They are not continuous variables.
a) The blunder in this statement is that correlation does not imply causation. Just because there is a high correlation between the age of American workers and their occupation does not mean that one causes the other. It could simply be a coincidence or influenced by other factors.
b) The blunder here is that the correlation coefficient (r) should range from -1 to +1. A correlation coefficient of 1.19 is not valid, as it exceeds the maximum value of 1. Perhaps the statement meant to say that there was a strong positive correlation, but the exact correlation coefficient would need to be adjusted.
c) The blunder in this statement is that the correlation coefficient (r) of 0.23 suggests a relatively weak correlation. This implies that the gender of students and the color of their cell phones have only a minimal relationship. The statement could have been phrased differently if the intention was to highlight a stronger correlation.
a) The blunder in this statement is the use of the term "correlation" to describe the relationship between the age of American workers and their occupation. The correct term to use here would be "association" or "relationship" because occupation is not a numerical variable that can be correlated with age. Correlation is a statistical measure that is used to quantify the relationship between two numerical variables.
b) The blunder in this statement is the reported correlation value of 1.19, which exceeds the range of possible correlation values (-1 to 1). Correlation coefficients can only range from -1 to 1, where 1 represents a perfect positive correlation and -1 represents a perfect negative correlation. Any value outside of this range is not possible and indicates an error in measurement or calculation.
c) The blunder in this statement is the incorrect interpretation of the correlation value of 0.23. A correlation value of 0.23 indicates a weak or low correlation, not a moderate or high correlation. The strength of a correlation is typically classified as weak (0.1 to 0.3), moderate (0.3 to 0.5), or strong (above 0.5). Therefore, it would be more accurate to state that there is a weak correlation between the gender of a group of students and the color of their cell phones.
a) The blunder in this statement is that correlation measures the strength and direction of the linear relationship between two variables on a scale from -1 to 1. However, age and occupation are not necessarily linearly related. It would be more appropriate to say that there might be a relationship or association between the age of American workers and their occupation, but the term "correlation" is not accurate in this context.
b) The blunder in this statement is that a correlation coefficient of 1.19 is not possible. A correlation coefficient ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. Any correlation coefficient outside of this range suggests an error or miscalculation.
c) The blunder in this statement is that a correlation coefficient of 0.23 does not indicate a strong correlation between the gender of students and the color of their cell phones. Typically, a correlation coefficient between 0.1 and 0.3 is considered a weak or low correlation. Therefore, describing the correlation as "high" is not accurate.