1. Chi square Test

2. Chi squared tests are used to determine whether the difference between an observed and expected frequency distribution is statistically significant. X 2 = (oberseved – Expected) 2 Expected For the beans this would be: X 2 = (ob. grass – Exp. grass) 2 + (ob. concrete – exp. concrete) 2 Exp. grassExp. concrete

3. X 2 = 1.33 To understand what this number means, you need to know the degree of freedom (one less than the total number of classes – in this case, 2 classes (white & orange), degree of freedom = 1 (AKA DoF). In biology we always use a p value (significance level) of 0.05 (5%) and the degree of freedom to determine the critical value. Compare the calculated X 2 value to the critical value. If the X 2 is between theses (i.e. in the critical region) the result is statistically significant – there will be a biological explanation e.g. linked genes. If the calculated value is outside of the critical region the result is not significantly significant, the result is due to chance. Use the chart provided to determine whether the number of albino offspring is due to chance or not.

4. T HE T ERMINOLOGY Null Hypothesis (H o ) In science, we assume that the observed data WILL match the specified pattern. For example, in the coin example above, we will assume that the coin is fair until it is shown not to be fair by the Chi- Square test. Our initial assumption, that the observed data will fit the expected pattern, is called the null hypothesis. That said, the null hypothesis is a statement indicating that the observed data fits the specified pattern. Alternative Hypothesis (H 1 ) The alternative hypothesis is a statement indicating that the observed data do not fit the pattern or distribution indicated in the null hypothesis (it is the alternative to the null hypothesis). In the coin example, the alternative hypothesis would be that the coin is not fair.