How to Analyze DataAPES

Part of any good research project is analyzing and presenting data properly. Raw data is never presented. The author needs to prepare and present the data in a way that helps make their point. To this extent there should always be triplicate of each treatment, so that means can be generated. Mean data is always preferable to singular data.

How you present your data, depends upon the researched hypothesis. The following are suggested ways to present data.

Compare results to expected:

Chi Square test. Useful when there is a ONE predictable outcome. For example this is used for Mendel genetic crosses, because the expected outcome is predictable and very reliable.

X2 = (o-e)2o= observed e= expected

e

As with the T-test, you can compare this x2 value to .05. If x2 < α, and α=.05 than any difference in the data is due to chance, so your results are statistically significant.

Compare is two set of data are different

T-Test. This test shows if two sets of data are statistically different. This test is useful when the hypothesis demonstrates an “if and then” relationship. For example, “If nitrogen is added to lake water, algal population density will increase.” If this situation you can compare algal density from the nitrogen added treatment to the control treatment.

To do a t-test in Excel:

  • Enter your data for control, the other for the treatment.
  • Calculate the standard deviations of each treatment before starting to do the t-test. Choose the “Formulas” tab at the top of the screen, then select “More Functions” and then “Statistical”. Select “STDEV” in the list that appears. Follow directions, highlight data. You will need the standard deviation later, but not to during the t-test.
  • Choose the “Formulas” tab at the top of the screen, then select “More Functions” and then “Statistical”. Select “TTEST” in the list that appears.
  • In the window that opens, click in the box next to “Array1” and select the data for one of the two treatments. Then click in the box for “Array2” and select the data for the other treatment.
  • Click in the third box – “Tails” – and pick the appropriate t-test you want to do. If you are testing if one treatment is bigger than the other (a directionaltest), choose a one-tailed distribution. If you are just testing if there is any difference between the two treatments (a nondirectional test), then choose a two-tailed distribution.
  • Click in the fourth and final box – “Type” and select the type of t-test you want to run. There are three options: Paired data, Not Paired equal variance or Not pair unequal variance. Your data is Paired if the two treatments are not independent, one depends on other. If your data are independent of each other, then look at the standard deviations for the two treatments. Is the larger one more than twice as large as the smaller one? If not, then you can consider this to be a “two-sample equal variance (homoscedastic)” test. If it is, then choose the “two-sample unequal variance” test.
  • Click ok. Excel will give you the p-value in the spreadsheet cell you originally clicked in.
  • Compare this p-value to =0.05. If p < , then you can say that the data is significantly different.
  • If you did a one-tailed t-test: “The algal density is significantly higher in the control than in treatment A”. You’ll have to be careful of which set of data are selected first and second. This is directional, one set of data is larger than the other.
  • If you did a two-tailed t-test: “The number of stomata per m2 is significantly different on trees growing in the sun and trees growing in the shade”

Other Statistical Tests

These tests so not demonstrate statistical significance. The can be used to make general assumptions. Many are used for observational biology.

Species Richness (R)

The species richness is based solely on the number of species found in the given area and does not reflect the relative dominance of species. The formula is:

R = s

s = the number of species

Shannon-Wiener Index (H)

This index is determined by both the number of species and the even distribution of individuals among those species (relative dominance). It indicates the degree of uncertainty of predicting the species of a given individual picked at random from the community. In other words, if the diversity is high, you have a poor chance of correctly predicting the species of the next individual picked at random. The formula is:

H = - sum(Pi • ln[Pi])

Pi (relative abundance) = ni/N

ni = number of individuals in species i

N = total number of individuals in all species

H = (the uncertainty of predicting the species) will range from 0 for a community with a single species, to over 7 for a very diverse community.

Species Evenness (E)

Using species richness (R) and the Shannon-Wiener index (H), you can also compute a measure of evenness. The formula is:

E = H/ln(R)

Evenness (E) is a measure of the similarity of the abundance of different species. When there are similar proportions of all species then evenness is one, but when the abundance is very dissimilar (some rare and some common species) then the value increases.