# Chi-Square Test

**Topics:**Variance, Statistical significance, Errors and residuals in statistics, Null hypothesis, Analysis of variance /

**Pages:**4 (869 words) /

**Published:**Jul 22nd, 2011

Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences between observed and expected) the result of chance, or were they due to other factors. How much deviation can occur before you, the investigator, must conclude that something other than chance is at work, causing the observed to differ from the expected. The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result.

The formula for calculating chi-square (χ²) is: 2= (o-e) ²/e

That is, chi-square is the sum of the squared difference between observed (o) and the expected (e) data (or the deviation, d), divided by the expected data in all possible categories.

INTERPRETATION OF CHI-SQUARE TEST

1. Determine degrees of freedom (DF). Degrees of freedom can be calculated as the number of categories in the problem minus 1.

2. Determine a relative standard to serve as the basis for accepting or rejecting the hypothesis. The relative standard commonly used in biological research is p > 0.05. The p value is the probability that the deviation of the observed from that expected is due to chance alone (no other forces acting). In this case, using p > 0.05, you would expect any deviation to be due to chance alone 5% of the time or less.

3. Refer to a chi-square distribution table Using the appropriate degrees of 'freedom, locate the value closest to your calculated chi-square in the table. Determine the closest probability(p) value associated with your chi-square and degrees of freedom.

Step-by-Step Procedure for Testing