Year 13 1st March

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March 1, 2013, 11:49 pm

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Chi squared

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Chi Squared Test

This is a statistical test which is used to see if the results of an experiment support a theory.

First of all the theory is used to predict a result- the expected result.

Then an experiment is carried out and the actual result is recorded-this is the observed result.

To find out if the observed result supports the expected result you have to make a null hypothesis.

The null hypothesis is ALWAYS that there is NO SIGNIFICANT DIFFERENCE between the expected result and the observed result.

The x2 test is then carried out and the outcome of this will either support or reject the null hypothesis.

X2 = ∑▒((O-E))/E2

O= the observed result

E= the expected result

Work out X2 in stages:

work out the number of offspring expected for each phenotype

work out the actual number of offspring observed with each phenotype

Calculate O-E by subtracting the expected result from the observed result for each phenotype.

square the result

divide this number by the expected results

Do this for all the phenotypes individually

Add up all the numbers to give you the X2 value

To find out if there is no significant difference between the observed and expected results you have to compare the X2 value to a critical value.

The critical value is the value of X2 that corresponds to a 0.05 (5%) level of probability that the difference between the expected and observed value is due to chance

If your X2 value of smaller than the critical value then there is NO significant difference between the observed and expected results and the null hypothesis is accepted.

However, if your X2 value is higher than the critical value then there IS a significant difference between the expected and observed results and the null hypothesis is rejected.

Working out the critical value:

This is done from an X2 table which show a range of probabilities that correspond to different critical values for different degrees of freedom.

Work out the degrees of freedom- this is the number of classes (the number of phenotypes) minus 1.

Find the critical value corresponding to a probability of 0.05 (5%) at the right degree of freedom.

Comment by bethanysmith2012March 4, 2013 @ 11:25 amThe chi-squared Test

-It is a statistical test to work out if the difference between observed categorical data and expected data is small enough to be due to chance (5%)

– It tests the null hypothesis which is based on the assumption that there is no significant difference between the observed and expected results of an experiment.

– Chi-squared= the sum of [(observed values) – (expected values)]^2

Expected values

-This is best worked out using a table and the results of the test can then be compared against a table.

-If chi-squared is smaller than the critical value of probability of 0.05 the we can accept that the difference is insignificant.

– The degrees of freedom id the number of classes -1.

df P = 0.05 P = 0.01 P = 0.001

1 3.84 6.64 10.83

2 5.99 9.21 13.82

3 7.82 11.35 16.27

4 9.49 13.28 18.47

5 11.07 15.09 20.52

6 12.59 16.81 22.46

7 14.07 18.48 24.32

Comment by laurabriggs1March 4, 2013 @ 1:59 pmKey Definitions:

1. The chi-squared test- A statistical test to find out if the difference between the observed categorical data (data in categories) and expected data is small enough to be due to chance.

2. Degrees of freedom- In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

3. Null hypothesis- A type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations. The null hypothesis attempts to show that no variation exists between variables, or that a single variable is no different than zero.

4. Critical value- The value corresponding to a given significance level.

When can the chi-squared test be used?

The chi-squared test can be used for categorical data (data in categories) and where there is a strong biological theory that we can use to predict expected values. Other criteria that must be met include the fact that the sample size must be reasonably large, only raw counts are used and that there are no zero scores.

Formula:

The sum of the observed numbers (O)-expected numbers (E) squared. Divided by the expected numbers (E).

Comparison to critical value:

To find out if there is no significant difference between your observed and expected results a comparison needs to be made to a critical value.

The critical value equates to a 5% probability that the difference between your observed and expected results is due to chance.

If your result is smaller than the critical value then there is no significant difference and the null hypothecs is accepted.

If your result is greater than the critical value then there is a significant difference and the null hypothesis is rejected.

Comment by frankiebarrickMarch 4, 2013 @ 8:34 pmChi-Squared

Used on discontinuous data – how many individuals fit into a given category

Chi-squared is a statistical test to analyse the number of individuals with a certain characteristic and how this fits with the expected prevalence of this characteristic.

– If the expected and observed are similar, this is likely to be due to chance and the prediction holds true

– If the expected and observed are far apart it is likely our prediction is wrong

Ho: The null hypothesis – this assumes the prediction made from previous knowledge is correct; we test the observed number of individuals with a characteristic against the null hypothesis. Using a statistical measure – the chi-squared test – we can decide whether a number that is not the null hypothesis is caused due to chance, or because the prediction is wrong.

(Sum(Observed – Expected))^2/Expected

Degrees of Freedom (n-1) -> this is the number of categories, minus 1. When a number has been calculated using the formula above, we count how many categories were used to achieve this number and take one away. This number can be looked up on a statistical table. The table has a list of corresponding numbers each of which have a probability associated.

For example in a test with 4 classes, look up number 3 on the table, and find the corresponding value of chi-squared. This models onto a graph which shows the probability of that specific outcome.

If the probability associated with both the degree of freedom and value of chi-squared is more than 0.05 (or 5%) then we can consider H0 (the null hypothesis) to be correct. This means that the variance from the expected value has a 95% chance of being simply due to random mutation only, 95% being a high confidence. Any number which corresponds to a probability less than 0.05 is unlikely to be due to random variation alone and therefore our original hypothesis can be rejected in favour of a new one.

Essentially we are running a hypothesis test – how certain are we that variation is due to chance, and giving a probability (95%) that this is true.

Comment by rosiepattersonMarch 4, 2013 @ 8:45 pmWhat is Chi squared?

Statistical test that can be carried out on data that are in categories. It enables the person carrying out the statistical test to determine how close the data they have collected corresponds to the expected data for the variable. It can be also used where there is a strong biological theory that can be used to predict expected values.

Formula:

The sum of (observed numbers (O) – expected numbers (E)^2/expected numbers (E)

Null hypothesis:

The null hypothesis is a used as a starting point in examining results from a scientific investigation. The hypothesis is based upon an assumption that ‘there is no statistically significant difference between the observed and expected numbers, and any difference is due to chance’. It aims to show there is no variation between variables.

Degrees of freedom:

Given as (n-1) and in statistics it is used to calculate by how much numbers in a final calculation can vary by.

Critical value:

In order to find out if there is a statistical significant difference between observed and expected value, a critical value needs to be established to be compared to. This is normally taken as a 5% probability that the difference between the two results is to due by chance. If your result is smaller than this value then there is no significant difference and the null hypothesis proves to be true but if it is greater than the critical value there is significant difference and so there must be some error to the results.

Comment by erinmeredithhMarch 4, 2013 @ 10:54 pm