1. Chi-squared Association Index

2. What does it do? Looks for “links” between two factors  Do dandelions and plantains tend to grow together?  Does the colour of a snail’s shell affect its habitat choice? Factors that are linked are said to be “associated”

3. Planning to use it? You are working with numbers of things, not, eg area, weight, length, %… You have an average of at least 5 things (people/plants/species…) in each category Make sure that…

4. How does it work? You assume (null hypothesis) there is no association – the two factors do not affect each other It compares  observed values the data you collected  expected values what you’d get if there was really no association

5. Doing the test These are the stages in doing the test: 1.Write down your hypotheseshypotheses 2.Work out the expected valuesexpected values 3.Use the chi-squared formula to get a chi- squared valuechi-squared formula 4.Work out your degrees of freedomdegrees of freedom 5.Look at the tablestables 6.Make a decisiondecision Click here Click here for an example

6. Hypotheses H 0: There is no association H 1: There is some association

7. Expected Values Your data here will be in a table. To work out the expected values: Add up the totals of all the rows, and the totals of all the columns. Also find the overall total of all the data Work out expected values using

8. Chi-Squared Formula For each cell in your table, work out O = Observed value – your data E = Expected value – which you’ve calculated Then add all your values up. This gives the chi-squared value  = “Sum of”

9. Degrees of freedom The formula here for degrees of freedom is degrees of freedom = (rows – 1)(columns – 1) You do not need to worry about what this means –just make sure you know the formula! But in case you’re interested – the larger your table, the more likely you are to get a “strange” result in one or more cells. The degrees of freedom is a way of allowing for this in the test.

10. Tables This is a chi-squared table These are your degrees of freedom (df) These are your significance levels eg 0.05 = 5%

11. Make a decision If the value you calculated is bigger than the tables, you reject your null hypothesis If the value you calculated is smaller than the tables, you accept your null hypothesis. Remember in each case to refer back to the actual example!

12. Example: Snail shell colour & habitat Samples were taken from limestone woodland and limestone pavement, and the numbers of light- and dark-shelled snails noted. Hypotheses: H 0: Shell colour and habitat preference are not associated H 1 Shell colour and habitat preference are associated

13. The data LightDark Pavement11576 Woodland 69106

14. Totals LightDarkTotals Pavement115 76191 Woodland 69106175 Totals184182366

15. Expected Values Expected value = Row Total  Column Total Overall Total Expected values: LightDark Pavement Woodland

16. The calculations: (O-E) 2 /E LightDark Pavement Woodland

17. The test  2 = 15.776 Degrees of freedom = (2 – 1)(2 – 1) = 1 Critical value (5%) = 3.841 Reject H 0 – there is some association between snail shell colour and habitat preference