The chi-squared** **(c^{2}) test is a measure of expected frequency versus observed frequency to determine how closely aligned they are; whether what is observed would be expected or whether it is different to what would be expected.

The default expectation is the **null hypothesis** which states that *no difference* exists between the things we are experimenting with, observing or comparing and their default, or control state.

The chi-squared value we obtain from the chi-squared test is put against a **probability** scale. The probability refers to the probability that for a given chi-squared value (which is defined by how different our observation is from what we would expect), what we observe *really is* different to what we expect to a significant extent that enables us to **reject** the null hypothesis.

For example, our expected values for the eye colour of 154 flies in a population would be…