chapter 20 p3 Flashcards
Chi-squared test
- The observed results from a genetic cross will almost always differ to some extent from the expected results and this will be due to chance.
- If you toss a coin 10 times you would be unlikely to get five heads and five tails.
- The observed ratio of heads to tails will probably be quite different from the expected ratio.
- This does not mean there is anything wrong with the coin.
- If the same coin were tossed a thousand times you would see less relative difference between the expected and observed ratios.
- The number of observations made, therefore, determines how chance affects the results.
- It is important when making comparisons between observed and expected results that it is known whether any differences are due to chance or if there is a reason for the differences (they are significant).
The chi-squared (x) test is a statistical test that
measures the size of the difference between the results you actually get (observe) and those you expected to get.
- It helps you determine whether differences in the expected and observed results are significant or not, by comparing the sizes of the differences and the numbers of observations.
- The chi-squared test is conventionally used to test the null hypothesis.
The null hypothesis is
that there is no significant difference between what we expect and what we observe - in other words any differences we do see are due to chance.
Calculated chi squared values are used to
find the probability of the difference being due to chance alone.
Large chi-squared values mean
there is a statistically significant difference between the observed and expected results and the probability that these differences are due to chance is low.
There must be a reason, other than chance, for the unexpected results.
The number of categories being compared in an investigation affects the size of the chi-squared value calculated.
The degrees of freedom
the number of comparisons being made and is calculated as n-1, where n is the number of categories or possible outcomes (phenotypes in the case of phenotypic ratios) present in the analysis.
For example, if you were looking at yellow and green peas there would be two categories and therefore one degree of freedom.
If the calculated x^2 value is less than the critical value found in a table at 5% significance (p=0.05)
we do not have sufficiently strong evidence to reject our null hypothesis. Therefore, we accept the null hypothesis - there is no significant difference between what we observed and what we expected.
However if the calculated X^2 value is greater than the critical value
we reject the null hypothesis - some other factor, outside our original expectation, is likely to be causing a significant difference between expectation and observation.
the critical value
The minimum x^2 value that gives a 5% probability
The critical value increases as the degrees of freedom increase.
If X^2 is less than the critical value
there is no significant difference
If X^2 is greater than or equal to the critical value
there is a significant difference
Corn and the chi-squared (x^2) test
- There will almost always be differences between expected and observed results because of the random nature of the processes involved.
- Statistical tests like the chi-squared test are performed to determine whether these differences are due to chance alone or caused by some other factor that may not have been considered.
- Maize plants have been used for many years to study genetic crosses.
- An ear of corn contains around 500 kernels, or seeds.
- The seeds are produced as the result of the cross-fertilisation of two maize plants.
- The colour of the seeds is controlled by one gene with a dominant (P, purple) allele and a recessive [p, yellow) allele.
- Another gene determines the texture of the seeds and there is again a dominant (R, round) allele and recessive (r, wrinkled) allele.
- A genetic study was carried out to determine if these two genes are linked.
- Two maize plants that were heterozygous for both colour and texture were cross-fertilised and an ear of corn produced as a result of this cross was analysed.
The results are shown in Table 2.
Epistasis:
- the interaction of genes at different loci.
- Gene regulation is a form of epistasis with regulatory genes controlling the activity of structural genes, for example, the lac operon.
- Gene interaction also occurs in biochemical pathways involving only structural genes.
- It was originally thought that all genes were expressed independently, and therefore their effects on the phenotype seen.
- Now it is known that many genes interact epistatically.
- It is the results of these interactions that we see in the phenotypes of living organisms.
- The characteristics of plants and animals that show continuous variation involve multiple genes and epistasis occurs frequently.