2Chi Square is a test used to see if two pieces of data are significantly different or due to chance In Biology, we use this test a lot to see if our data is significant. In a population lab, we would see if 2 species found are associated with each other
3Quadrant SamplingThis method is only suitable for plants and other organisms that are not motile.Choose a random number to determine the length and width of your areaIf the absence or presence of more than one species is recorded in every quadrat during sampling of a habitat, it is possible to test for an association between species.
6A quadrat is a wire shaped into a square of a known size , such as 10x10 meters or 100m2. If you want to know the population size of two plant species, take random samples of this area by throwing down the quadrat and recording the population numbers in each subunit of the quadrat.
7Setting up quadrats Setting up quadrats This is a grid of 100 quadrats, each 10 m on a side. Dr.RodrigueEnvironmental Systems
8Count how many individuals there are inside the quadrat of the plant population being studied. Repeat steps 2 and 3 as many times as possible.Measure the total size of the area occupied by the population, in square meters.Survey of native and exotic species
9Calculate the mean number of plants per quadrat Calculate the mean number of plants per quadrat. Then calculate the estimated population size using the following equation:Population size = mean number per quadrat X total areaarea of each quadrat
10Populations are often unevenly distributed because some parts of the habitat are more suitable for a species than others.If two species occur in the same parts of a habitat, they will tend to be found in the same quadrats.This is known as a Positive association
11H0 -Two species are distributed independently There are 2 hypotheses:H0 -Two species are distributed independentlyThe Null HypothesisH1 – Two species are associated (either positively so they tend to occur together or negatively so they tend to occur apart)We can test these hypotheses using a statistical procedure – the chi square test
12Method for Chi SquareDraw up a contingency table of observed frequencies.Species A presentSpecies A absentRow totalsSpecies B presentSpecies B absentColumn totals
13Calculate the row and column totals. Adding the row and column totals should give the same grand total in the lower right cell.
14Calculate the expected frequencies, assuming the independent distribution for each of the four species combinations.Each expected frequency is calculated from values on the contingency table using this equation.Expected frequency = row total x column totalgrand total
15Calculate the degree’s of freedom using this equation: DF = (m-1)(n-1) Where m and n are the number of rows and columns in the contingency table
16Find the critical region for chi-squared from a table of chi-square values, using the degrees of freedom that you calculated. It should have a significance level (p) of 0.05 (5%)
17X2 = Σ 𝑜−𝑒 2 e O – observed e- expected Σ- the sum of Calculate the chi-squared using this equation:X2 = Σ 𝑜−𝑒 2eO – observede- expectedΣ- the sum of
18What is statistically significant H0 - the null hypothesis with the belief that there is no relationship between the twoH1 – There is a relationshipThe usual procedure is to test the null hypothesis with the expectation of showing that it is false.If you say that the results were statistically significant, it means that if the null hypothesis was true, the probability of getting results as extreme as the oberved results would be very small.
20exampleIn a certain town, there are about one million eligible voters. A simple random sample of 10,000 eligible voters were chosen to study the relationship between sex and participation in the last election. The results are summarized in the following 2x2 contingency table:MenWomenVoted27923591Didn’t vote14862131
21We want to check whether being a man or a woman (columns) is independent of having voted in the last election (rows). In other words is ‘sex and voting independent’?Null – sex is independent of votingAlternative – sex and voting are dependent
22We now need to complete our contingency table. MenWomenTotalvoted279235916383Didn’t vote148657223617427810000
23Expected Table Men Women Total Voted 2731 3652 6383 Didn’t vote 1547 20703617Totals4278572210000Remember: expected frequencies = row totals x column totalsgrand totalSo: 6383 x 4278 / = 27316383 x 5722 / = 3652
24Now we have the observed table and the expected table under the null hypothesis of independence. Now we need to compute X2(O – e)2e