Question

Nicole is studying a two-way table. She has computed the relative frequencies by column for each cell. What characteristic of the data will imply an association between the two variables?
The relative frequencies are nearly the same in each row.
The relative frequencies are significantly different each row.
The relative frequencies add to 100% for each column.
The relative frequencies add to 100% for each row.

Answer 1

'characteristic of the data?

Answer 2

Let's use an example to illustrate

If I survey students on their:
1. eye color
and
2. GPA

and I plot the results in a two way table, I would not expect to see any significant association between these two variables. I would expect the relative frequencies for % blue eyes, % brown eyes, % green eyes, etc. to be roughly the same, regardless of GPA. Likewise, comparing between eye colors, I would expect the % high GPA, % average GPA, % low GPA to be relatively equal as well.

However, if I surveyed students on their:
1. hours spent studying per week
2. GPA

I would expect a significant association between the two variables. I would expect the relative frequency of high GPA, high-studiers to be significantly higher than low GPA, high-studiers.

Therefore, significant differences in relative frequencies in a row will indicate that there is an association between the variables.