• The?difference between expected and observed results?in experiments can be statistically significant or insignificant (happened by chance)
• If the difference between results is statistically significant it can suggest that?something else is happening?in the experiment that isn’t being accounted for
  • For example linkage between genes

   

• A statistical test called the?chi-squared test?determines whether there is a significant difference between the observed and expected results in an experiment
• The chi-squared test is completed when the data is categorical (data that can be grouped)

Calculating chi-squared values

• Obtain the expected and observed results for the experiment
• Calculate the difference between each set of results
• Square each difference (as it is irrelevant whether the difference is positive or negative)
• Divide each squared difference by the expected value and get a sum of these answers to obtain the chi-squared value

Analysing chi-squared values

• To work out what the chi-squared value means, a table that relates chi-squared values to probabilities is used
• If the chi-squared value represents a larger probability?than the?critical?probability?then it can be stated that the differences between the expected and observed results are?due to chance
• If it represents a?smaller probability?than the critical probability then the differences in results are?significant?and something else may be causing the differences
• To determine the critical probability biologists generally use a probability of?0.05?(they allow that chance will cause five out of every 100 experiments to be different)
• The number of comparisons made must also be taken into account when determining the critical probability. This is known as the?degrees of freedom

Chi-squared worked example table

The expected ratio is calculated by multiplying the total number of organisms ( 128 rabbits) with each expected ratio:

• In order to understand what this chi-squared value of 0.56 says about the data, a table relating chi-squared values to probability is needed

• The chi-squared table displays the probabilities that the differences between expected and observed are?due to chance
• The?degrees of freedom?can be worked out from the results. It is calculated by?subtracting one from the number of classes
  • In this example there are four phenotypes which means four classes, 4 - 1 = 3
  • This means that the values in the third row are important for comparison

   

• For this experiment, there is a?critical probability of 0.05
  • This means that 7.82 is the value used for comparison

   

• The chi-squared value from the results (0.56) is much smaller than 7.82
• 0.56 would be located somewhere to the left-hand side of the table, representing a probability much?greater than 0.1
• This means that there is?no significant difference?between the expected and observed results, any differences that do occur are?due to chance