WHAT IS THE CHI-SQUARED TEST?
This is an inferential test created by Karl Pearson (left). It is used when:
(* it’s possible to turn interval/ratio level data into ordinal data: you just put the scores into a frequency table)
The Edexcel exam might ask you about the appropriateness of the Chi-Squared test – when you would use it. But you could be asked to calculate the test. The equation and tables are provided at the front of the exam booklet.
If you are using a interval/ratio data, use one of the other inferential tests instead.
MAKING THE CALCULATIONS
Of course, most researchers use computers to do their statistical tests. There are lots of websites that will let you input your data from an experiment and carry out the Chi-Squared test for you.
The Exam expects you to be able to work out the Chi-Squared test "by hand" and, although it's fiddly, it's not that difficult. However, it would be best to bring a calculator!
There are two formulae up above and they look pretty simple, but they take a while to do. The simplest way is to draw some tables (and if this question comes up in the Exam, the question paper will probably draw the table for you to fill in).
You are trying to work out the value of Chi-Squared (X2) and to do this you need to calculate O (the frequencies you observed) and E (the frequencies you expected to observe). Let’s imagine the results of a survey to find out how many men and women own smartphones.
O is easy enough. Imagine you have researched whether women are more likely to own a smartphone than men. Draw a table of your observed frequencies.
To work out E, you need to add up your rows and columns.
Now you need to label each box in your table going down each column in turn:
Once this is done, you can create your Chi-Squared table of Expected Frequencies:
The only tricky thing to work out here is E and if you’re lucky an Exam question will do that for you too. You work out E for each box (A, B, C, etc) like this:
So box A has a row that adds up to (30+30) 60 and a column that adds up to (30+25) 55; the sum of all the rows/columns is 100.
Here it is in full:
The rest is straightforward. You deduct each value of E from the value of O above it:
Then you square (multiply by itself) each number you just arrived at:
Lastly you divide each number you produced by the value of E up above:
Nearly there. You work out X2 by adding all the numbers in the bottom row together:
You will compare X2 to the critical value and you are looking for X2 to be lower than the critical value.
Before you can look up the critical value, you need to know three things:
Degrees of freedom is a number that represents the complexity of your data. You work it out from the second formula given in the Exam Booklet:
This means taking the number of rows on your original table of frequencies (minus 1) and multiplying it by the number of columns (minus 1). So a simple 2x2 table like the one above is described as “1 degree of freedom”.
Look at the table of critical values below. If your value of X2 is greater than the critical value, you can refute your null hypothesis (and cautiously accept your hypothesis).
If X2 is less than the critical value, you must accept your null hypothesis and refute your experimental hypothesis.
WHAT'S THIS???!!!?!?! Yes, it's a misprint. Edexcel's sample papers all (WRONGLY) say you're looking for X2 to be lower than the critical value. No. You want it to be HIGHER. Hopefully, the Exam Board will correct this in future.
A STATEMENT OF STATISTICAL SIGNIFICANCE
You can sum up your statistical test with a statement of statistical significance. This will include:
The results were subjected to a Chi-Squared test
The observed value (X2) was 1.5, which is lower than the critical value of 4.6 for a 1-tailed test where p≤0.05 at 1df
Therefore, the null hypothesis can be accepted
APPLYING CHI-SQUARED TEST IN PSYCHOLOGY