BIO MATHS

• Standard Deviation


  A measure of how spread out all of your repeats are from your mean
• Advantages of using the S.D instead of the range

  • S.D shows the spread of data around the mean, whereas the range is only the difference between the highest and lowest value
  • S.D reduces the effect of anomalies, whereas the range includes anomalies
  • S.D can be used to indicate whether a difference between results is significant
• Using Standard Deviation for a conclusion

  • If the S.D overlaps = likely no significant difference between x and y
  • If the S.D does not overlap = likely to be a significant difference between x and y
• Example of using Standard Deviation

  • The standard deviation of the upper end of B overlaps with the lower end of A, therefore there is likely no significant difference between the species richness in habitat A and B
  • The standard deviation for habitat C does not overlap with either A or B, and is therefore likely to be significantly different
• Correlation Coefficient


  Used to investigate an association between two measurements
• How to decide which statistical test should be used

  • Correlation coefficient is used to investigate an association between two measurements
• Null hypothesis


  A statement that there is no relationship between two variables
• The student concluded that the more glucose you add, the more bacteria there will be, but this conclusion is not supported by the data
• Student T-test


  Used to investigate a difference between two means
• How to use the Student T-test

  • Justify the use of the Student T test
  • Write a null hypothesis
  • Write a conclusion
• Worked examples of Student T-test

  • Calculated T-test value exceeds critical value, so can reject null hypothesis and conclude difference is significant
  • Calculated T-test value does not meet or exceed critical value, so must accept null hypothesis and conclude difference is not significant
• The scientists concluded that the communities did change, but this conclusion is not fully supported by the data
• Chi-squared test


  Used to determine whether there is a significant difference between the observed and expected results in an experiment
• How to use the Chi-squared test

  • Justify the use of the Chi-squared test
  • Write a null hypothesis
  • Write a conclusion
• Index of Diversity


  A measurement that describes the relationship between the number of species present and how each species contributes to the total number of organisms in a community
• Calculating Index of Diversity

  1. Calculate N(N-1) to find value A

  2. Calculate n(n-1) for each species and add to find value B

  3. Calculate A / B
• Worked example of calculating Index of Diversity

  • N = 25, ∑n(n-1) = 180, D = N(N-1)/∑n(n-1) = 3.3
• Assumptions of Hardy-Weinberg Theorem

  • No natural selection
  • Random mating
  • No mutations
  • Closed population
  • Large population size
• Hardy-Weinberg Theorem


  Can determine the allele frequency and the genotype frequency
• Determining allele frequency


  Use equation p + q = 1 where p is frequency of dominant allele and q is frequency of recessive allele
• Determining genotype frequencies


  Use equation p^2 + 2pq + q^2 = 1 where p^2 is frequency of homozygous dominant, 2pq is frequency of heterozygous, and q^2 is frequency of homozygous recessive
• Worked examples of using Hardy-Weinberg Theorem

  • Calculating allele frequency of recessive allele
  • Calculating genotype frequency of homozygous dominant allele