Question

The article referenced in the previous exercise also described an experiment in which students at Columbia Business School were randomly assigned to one of two groups. Students in one group were shown a coffee mug and asked how much they would pay for that mug. Students in the second group were given a coffee mug identical to the one shown to the first group and asked how much someone would have to pay to buy it from them. It was reported that the mean value assigned to the mug for the second group was significantly higher than the mean value assigned to the same mug for the first group. In the context of this experiment, explain what it means to say that the mean value was significantly higher for the group that was given the mug.

Short answer

In statistics, 'significantly higher' means that the difference between the mean values of two groups is substantial and it's unlikely due to chance. In the context of this experiment, it means that the group who were given the mug (group 2), on average, placed a much higher value on the mug compared to the group who were just shown the mug (group 1). This difference isn't accidental but could indicate a psychological impact of ownership on value perception.

Step-by-step solution

Understand the Context

First, it is important to grasp the context of the experiment. There are two groups of students. Group 1 was shown a coffee mug and asked how much they would pay for it. Group 2 was given an identical mug and queried how much someone would have to pay to take it from them. The mean value that Group 2 assigned was 'significantly higher' than the mean value Group 1 assigned.

Evaluate the Mean Value

Each group has assigned a value to the mug, and these values have been used to calculate mean values for both groups. Meaning, these are the average amounts a student from each group would be willing to pay for or sell the mug for. The second group that owned the mug priced it 'significantly higher' which shows their valuation of the mug was higher on average compared to the first group that only viewed the mug.

Understand Significance in Statistics

In statistics, a 'significant' difference between two means is not just a simple acknowledgment that the means are different. Rather, it suggests the difference is meaningful, not likely due to chance, and represents a true value difference in the population. Saying the mean value was 'significantly higher' for group 2 suggests that the students in this group, on average, truly value the mug more when they personally own it, rather than when they do not. This isn't likely to have happened by chance.