Edexcel A (SNAB) A Level Biology:复习笔记2.4.6 Chi-squared Test

• 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)
• It is important to formulate a null hypothesis - this states that there is no significant difference between the observed and expected results

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 the results support the null hypothesis that there is no significant difference between the expected and observed results, any differences that do occur are due to chance