6.2.9 - Using the Chi Squared Test

• We know what the ratios should be with a large sample, however with a small sample, the observed ratio may be different due to the 'genetic lottery', i.e. which gametes happen to fuse together and other variables such as some ovules not being fertilised.
• If we obtain results which are not quite as expected, we need to know whether the difference is just due to chance and is not significantly different.

  • If the observed numbers of offspring in a cross are similar to the expected number, our predicted inheritance pattern is correct.
  • If the observed and expected numbers are significantly different, our predicted inheritance pattern may be incorrect, or there is a reason the pattern was not shown (e.g unfertilised offspring).
• The Chi Squared Test can be used when:

  • the data are in categories and 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
  • There are no zero counts in the raw data.
• The Null Hypothesis:

  • Statistical tests can not be used to directly test a hypothesis, instead they test a null hypothesis
  • If the null hypothesis states: "There is no statistically significant difference between the observed and expected data. Any difference is due to chance".
• $x^2 =$$Σ (O-E)^2 /E$
• Σ = sum of

  O = observed results

  E = expected results
• In the equation:

  • The differences may be positive or negative, so they are squared to prevent any negative values cancelling any positive values
  • Dividing the E takes into account the size of the numbers
  • The 'sum of' sign takes into account the number of comparisons being made.
• The procedure is:

  1. Calculate the value of X^2
  2. Determine the number of degrees of freedom (number of categories - 1)
  3. Determine the critical value in a distribution table, using 0.05 (5%)
  4. If Chi Squared is larger than or equal to the critical value, we can reject the null hypothesis as there is a significant difference between the observed and expected results.