Discontinuous variation
- discrete - a characteristic that can only result in certain values
- determined by genetic factors only
- represented as a bar chart or pie chart
- e.g. sex, blood group, shape of bacteria
Continuous variation
- characteristic that can take any value within a range
- continuum = graduation in values
- controlled by a number of genes (polygenes) + environmental factors
- represented in a frequency table + histogram with curve drawn
- e.g. height, mass
Normal distribution
- continuous distribution usually produces a bell-shaped curve - normal distribution curve
- mean, mode, median = same
- Bell-shape = symmetrical distribution about the mean
- 50% of values are < mean, 50% of values > mean
- most values lie close to the mean - individuals at extremes are low
- 68% of the data are 1SD away from the mean, 95% of the data are 2SD away from the mean
What is Spearman’s rank correlation coefficient?
- a statistical test for the correlation between 2 sets of data - to consider the relationship
- measures strength in correlation - positive or negative or none
- need at least 8 pairs of data
- Rs values are always between -1 and +1
- 1 indicates a perfect relationship; -1 = perfect inverse relationship; 0 = no relationship
Null hypothesis for Spearman’s rank
H₀: no statistically significant correlation
When to reject or accept H₀ - Rs
- if Rs is less than the critical value, we accept the null hypothesis = >5% probability that any association is due to chance and <95% certain of a statistically significant correlation
- if Rs is greater than the critical value, we reject the null hypothesis = <5% probability that any association is due to chance and >95% certain of a statistically significant correlation
How to calculate Rs
- Each of the data needs to be put into order of rank
- 2 or more tied data share the no. of ranks (average them)
- Find the difference between the ranks and square them
- Apply the formula
- Compare Rs to critical value
Conclusion for Spearman’s rank test
The calculated Rs of ___ is greater/less than the critical value of ___ for ___ pairs of data. Therefore accept/reject H₀ at the 5% significance level. There is/is not a statistically significant correlation at the 5% significance level.
What is the students T-test?
- test for comparing the means of data values of 2 populations
- can only be used on normally distributed data
- t-score/value is a ratio between the difference between 2 groups and the difference within the groups. The larger the t-score, the more difference between groups; small t-score = more similarity between groups
Difference between paired and unpaired t-tests
- paired - both sets of data from the same individual: df = number of pairs - 1
- unpaired - sets of data come from different samples: df = number of samples - 2
Differences between the tails
- 1 tailed - H₁ considers only 1 alternative: < or>
- 2 tailed - H₁ considers either alternative: /=
When to accept and reject H₀ - t-test
- if the t-value exceeds the critical value at p=0.05, then we reject the null hypothesis
Null hypothesis for t-test
H₀: there is no statistically significant difference between the means of the data
