The Chi-squared test Flashcards
What is the Chi-squared test?
A statistical test to find out whether the difference between observed and expected data is due to chance or a real effect.
What are the criteria for the the Chi-squared test?
- Data placed in discrete categories
- Large sample size
- Only raw data allowed i.e not %s
- No data values equal zero
How is the chi-squared test performed?
The formula results in a number, which is then compared to a critical value (for the corresponding degrees of freedom). If the number is greater than or equal to to the critical value, we conclude there is a significant difference between the observed data and the expected data and that the results did not occur due to chance.
How can we use the chi-squared test in relation to the content of this topic?
We can compare the expected phenotypic ratios with the observed ratios to test our understanding of how different genes and alleles are inherited.
What is a null hypothesis?
a hypothesis that proposes that no statistical significance exists in a set of given observations.
Suggest a null hypothesis for the following:
Light makes animals in a zoo more aggressive.
Taking a vitamin B supplement will increase nail growth
There are more owls found in deciduous woods compared to coniferous woods.
light has no difference on whether animals are aggressive in a zoo.
Taking a vitamin B supplement will make difference in finger nail growth compared to when no no vitamin B supplement is taken.
There is no difference in the number of owls found in deciduous woods compared to coniferous woods.
What is the equation for the Chi sqaured test?
In an investigation, cyanogenic and acyanogenic plants were grown together in pots. Slugs were placed in each pot and records were kept of the number of leaves damaged by the feeding of the slugs over a period of 7 days. The results are shown in Table 1.
A x² test was carried out on the results.
(i) Suggest the null hypothesis that was tested.
(ii) x² was calculated. When this value was looked up in a table, it was found to correspond to a probability of less than 0.05. What conclusion can you draw from this?
I) the variety of plant makes no difference on the number of leaves eaten.
II)
- there was less than a 5% probability the difference in the results is due to chance.
- reject the null hypothesis
- being cyanogenic does protect plants from slugs.
The inheritance of body colour in fruit flies was investigated. Two fruit flies with grey bodies were crossed. Of the offspring, 152 had grey bodies and 48 had black bodies.
(b) Explain why a statistical test should be applied to the data obtained in this investigation.
To obtain the probability of the results being due to chance.
In many families where the parents could have produced children of all four blood groups the total number of children in each blood group was:
I) The x² test can be used to test the hypothesis that there is no significant difference between these results and the expected 1: 1: 1:1 ratio. Complete a table to calculate the value for x² for there results.
II) The critical value for x² with the three degrees of freedom at the 0.05 probability level is 7.82. Explain what the calculated value of x² tells us about the results.
II) degrees of freedom:
4 - 1=3
3 and 0.05 = 7.82
x² is lower than the critical value.
Therefore, there is more than a 5% probability the difference is dur to chance.
So, accept the null hypothesis.
A student investigated whether the abundance of the orange star lichen on the walls of a building was influenced by the direction the wall faced. The student recorded the number of colonies within a 50 cm³ quadrat, placed one metre above the ground on each of three walls.
A X-test was applied to the results.
(a) Give a null hypothesis for this investigation.
(b) Complete the following table.
(c) how many degrees of freedom were in this x² test.
(d) A x² value of 15.5 was calculated from these results. This X value has a probability of less than 0.001. Explain what this means when applied to this investigation.
(a) The direction of the wall had no effect on the number of lichen there that will grow.
(b) pic
(c) 3-2=1
(d) There is less than a 0.2% probability the difference in the results was due to chance.
Reject the null hypothesis.
The direction the wall faced does affect the number of lichen growing on different parts of the wall.
Algae are green protoctists. Lichens consist of a fungus and an alga living together in a relationship where both organisms benefit. Suggest how the relationship between the alga and the fungus allows the lichen to survive on an inorganic surface such as a wall.
Mutualistic
Lichen made of algae and fungus.
Algae photosynthesize to produce organic molecules
Fungus helps to cling to wall or absorb water.
