# Really Simple Statistics: Chi-Square #MRX

Welcome to Really Simple Statistics (RSS). There are lots of places online where you can ponder over the minute details of complicated equations but very few places that make statistics understandable to everyone. I won’t explain exceptions to the rule or special cases here. Let’s just get comfortable with the fundamentals.

If you haven’t had your morning cup of tea or coffee, may I be the first to disappoint you by saying this post has nothing to do with chai tea! Sorry. š¦

And my apologies again, it has nothing to with a traditional Chinese unit of length, or a dragon in Chinese mythology or a life-force.

### What is a chi-square

Chi-squares are all about percentages. They are a statistical test that is used to determine if the percentage for one group is significantly different than the percentage for another group. Is the percentage of men who play soccer different from the percentage of women who play soccer? Is the percentage of people who made a purchase on Saturday the same as the percentage of people who made a purchase on Sunday? Is the percentage of high-income people who buy Brand A the same as the percentage of low-income people who buy Brand A?

Like any statistic, chi-squares can be very simple.

• Compare the percentage of men who buy Brand A vs the percentage of women who buy Brand A

Chi-squares can also be more complicated.

• Compare the percentage of men who buy Brand A or Brand B or Brand C vs the percentage of women who buy Brand A or Brand B or Brand C

Most basic market research relies heavily on chi-square tests. All of those grid questions in a survey are usually analyzed with a chi-square – the percentage of people who chose “Strongly Agree” or the percentage of people who chose “Disagree.”

Usually, when a study is launched, one of the project deliverables is a set of data-tables, you know those 300 pages of tables? These tables are chock full of chi-square tests but you wouldn’t know it unless you read the tiny little print at the bottom of the tables.

The important thing to remember is that chi-squares all about percentages.

Really simple statistics!

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# A Box Score Lesson for Psychology Students

Image via Wikipedia

I was in school for a bunch of years, and took a bunch of research design courses and a bunch of statistical analysis courses. Easy ones, hard ones, and a few really interesting ones. Surprisingly, one thing I never learned about was box scores, a statistical staple in the market research world.

Box scores are a way of talking about and working with Likert scales or other types of categorical scales so that everyone knows whether you are talking about the positive end of the scale (top box, top 2 box), the middle of the scale (middle/neutral box), or the negative end of the scale (bottom box, bottom 2 box).

Instead of calculating average scores from the Likert scale responses, box scores are reported as the percentage out of the total number of people who answered the question.(If 10 out of 50 people chose strongly agree, top box score is 20%) Box scores let you clearly identify how many people fall into a subgroup – people who are happy, unhappy, or just don’t care about your product.

Why do box scores matter? In a sense, they do report the same type of information as average scores. But, unless standard deviations are near and dear to you, average scores often appear very similar between groups. It’s hard to explain to a client why scores of 3.6 and 3.9 are very different because there is no intuitive difference between those numbers.

But, let’s think about box scores now. Can you intuitively understand the difference between 30% of people liking your brand and 40% of people liking your brand? I’m pretty sure you can. And you don’t need to understand what a standard deviation is either. I’m not in favour of dumbing down statistics but I am in favour of people understanding them.

Here’s another reason box scores are good. The average score calculated for a result that is 10% top box, 10% bottom box and 80% middle box is exactly the same average score you would get for a result that is 40% top box, 40% bottom box, and 20% middle box. I’d certainly like to know if 10% or 40% of people hated my product. That’s a pretty important difference to be aware of and I wouldn’t want it getting lost because someone had a weak understanding of what a SD is.

So now, psychology/sociology/geography majors, go forth and prosper as market researchers!