Question

Assuming, I'm correct that sex and yes/no questions are nominal data, then the best source of testing from my reading and research is mode. However in my question/answers, the only options are mean, SD, range, or median. My reading and research says you can't use median, SD, or median. But range wouldn't really be relavent data either? The question does say "relative data". So my best guess is range; but I'm a bit confused by this? Can you shed any light into this question?  

Answer 1

Yes, sex and yes/no questions are nominal data. Classifying the data into different categories such as male/female in case of sex; blue, white, yellow or red in case of color, etc,. without ranking the categories and labelling each category with alphabet or number is the nominal data. For example, you can label M for male and F for female or you can label 1 for male and 2 for female. These number have no numerical meaning. They are just labels. One cannot perform mathematical calculations for these numbers that are actually not numerical but are labels for qualitative data(nominal data). Mean, median, range and std. deviation are not appropriate measures for nominal data. Even though the data is relative, one cannot perform relative measures such as coefficient of range, coefficient of variation for nominal data because for relative measures to perform one needs absolute measures.

The mode is one measure of central tendency that can be used for nominal data. Frequencies and percentages are used for nominal data.

For example: color frequency

Red 5

Yellow 7

Black 3

Green 10

That is the frequency distribution of preference colors of 25 participants. Here, the mode is Green as it is preferred by more number of people.

If you take another class of 25 participants with the same colors to choose, then you can find mode and compare it with the previous one. Let's say, here, the color Red is preferred by many participants and so, mode is Red.

If the number of participants in both classes are not same, then you have to find percentage of members of a color to its total participants and then compare them.

One can also find association of two nominal variables of different categories/classes(independent nominal variable of one class, say, gender and dependent nominal variable of another class, say, color preference) by using chi-square tests of association that uses expected and observed frequencies.