6.2.9

• chi-squared test - statistical test designed to find out if the difference between observed + expected data is significant or due to chance
• Chi-squared test

  Is the difference between observed and expected results significant?

  if we obtain results that are not quite as expected, we need to know whether the difference is just due to chance or whether the difference between what we observe + what we expect is significant. If it is significant, it may be that the inheritance pattern is different to what we thought + we need to rethink how to explain our observations
• we can use the chi-squared (X^2) test when:

  • the data are in categories (e.g. different phenotypes or discrete variables) + are not continuous
  • we have a strong biological theory to use to predict expected values
  • the sample size is large
  • the data are only raw counts (percentages or ratios cannot be used)
  • there are no zero counts in the raw count data
• the null hypothesis

  statistical tests cannot be used to directly test a hypothesis, instead they test a null hypothesis

  if the null hypothesis is not supported, then we can accept the original hypothesis

  the null hypothesis states:

  there is no statistically significant difference between the observed and expected data. Any difference is due to chance
• chi-squared test calculation

  1. calculate chi-squared test

  (use a table to calculate)

  χ2 = ∑(Oi – Ei)2/Ei

  2. find the number of degrees of freedom

  (number of categories - 1)

  3. if we look up the value of X^2 in a distribution table (see figure 2) , we can see that p values range from 0.01 (1%) to 0.99 (99%)

  4. reject or support null hypothesis with sentences