How to write a results section

 

 

Statistical Significance

 

In this section, you present the data in a straightforward manner with no analysis of the reasons the results occurred or the biological meaning of the data (these comments are reserved for the Discussion).  The results section contains a statistical analysis of the experimental data.  For your seed project the appropriate statistical test necessary to compare the treatments is a Chi-Square test.

            A significance test is performed to determine if an observed value of a statistic differs enough from a hypothesized value of a parameter to draw the inference that the hypothesized value of the parameter is not the true value. The hypothesized value of the parameter is called the "null hypothesis." A significance test consists of calculating the probability of obtaining a statistic as different or more different from the null hypothesis (given that the null hypothesis is correct) than the statistic obtained in the sample. If this probability is sufficiently low, then the difference between the parameter and the statistic is said to be "statistically significant."

Just how low is sufficiently low? The choice is somewhat arbitrary but by convention  the level of .05 is most commonly used.

For instance, an experimenter may have the “null hypothesis” that the humidity of a chamber does not affect the percent germination of a seed.  A group of seeds are placed into a chamber with humid conditions and another group of seeds are placed in a chamber with drier air conditions.   After running the experiment there are 60%  of the seeds in  humid chamber germinate and 25% of the seeds germinate in the drier chamber.  To determine if the difference in percent germination is significant the experimenter has to compare the results to expected values based on random chance.  If the number of seeds that germinated were random then we would expect 50% of the seeds to germinate in either chamber.   Therefore the expected calculation is:

                                Total number of seeds tested (in one chamber)  *  0 .5

                                        25 * .50  = 12.5 seeds

To test whether are observed choice ratio significantly deviated from random chance we have to calculate the chi-square values and the total chi-square value.

            (Observed number of seeds germinated -  expected number of seeds germinated) 2

                        The expected number of seeds germinated

            (15 – 12.5) 2    / 12.5       =      0.5                    calculations for the humid chamber

        ( 6.25 – 12.5) 2        /  12.5     =      3.12                  calculations for the dry chamber

The total chi-square value                   3.62                   The total is calculated by adding the                                                                                      chi square values for both treatments

 


To determine if the probability of the chi-square value is less than 0.05 you will need to use a chi-square table (If the probability of the chi-square value is less than .05 then you can conclude the difference between the two treatments is not due to random chance.)

 

The degrees of freedom are equal to (R-1)(C-1) where R is the number of rows and C is the number of columns. In this example, R = 2 and C = 2, so df = (2-1)(2-1) = 1. (……..in other words the degrees of freedom for a test is the number of categories compare minus 1).

 

A chi square table can be used to determine that for df = 1, a chi square of 3.62 has a probability value less than 0.10 and greater than 0.05.  Since there is a probability of greater than 0.05 of there is no significant difference between the pattern of isopod choice and random chance. 

 

If the total chi square value is greater than the critical value there is a significant difference between the pattern of percent germination observed and a random chance.

 

If the total chi square value is less than the critical value there is not a significant difference between the pattern of percent germination observed and a random chance.

 

Critical values for the Chi Square Distribution 

                        Significance Level
        df                                   0.10          0.05        0.025       0.01          0.005
 
         1                    2.705        3.841      5.023       6.634       7.879
         2                    4.605       5.9915      7.377       9.210       10.59
         3                    6.251       7.8147      9.348       11.34       12.83
         4                    7.779       9.4877      11.14       13.27       14.86
         5                    9.236       11.070      12.83       15.08       16.74
         6                    10.64       12.591      14.44       16.81       18.54

        

 

 

The results of a Chi-square test should be reported in table format within your results section. 

 

Table format

 

Data are organized into tables and or/figures (graphs).  This lab exercise will cover the proper format for the table and a figure required to be included in the results section of your lab report. 

 

Rules for using a Table within a scientific report:

 

1.  Tables within scientific reports contain summary information, not the raw data collected during an experiment. 

 

2.  The table caption is located at the top of the table.

 

3.  The table caption should define all abbreviations used in the table and the sample size of the data represented.

 

Example Table:

 

 

Table 1.  The number of germinated seeds within each chamber section at the end of the 5 day trial.  n= 25, df =1. 

                                                                                                                                               

                                                                                   

Treatment

Observed % germinated seeds

Expected % germinated seeds

Chi-square totals

Humid chamber

15

12.5

0.5

Dry chamber

6.25

12.5

3.12

 

 

 

 

Total

25

25

3.62

                                   

 


4. You will need to interpret the chi-square table within the text of the results section.  Below is an example of the correct way to refer to the results from a chi-square test.   If a table is included in a scientific report it must be referenced within the results section text.

 

            For example:

 

            The difference between the observed number of seeds germinated within the humid and dry chambers was not significant, p > 0.05 (Table 1). 

 

 

Your results section must include one table and one figure representing the results of your experimental data. 

1.  The results section must include a table (your report will be a table with the chi-

       square values).  The table must have a correct table caption.

2.  The results section must include a figure and have a correct figure caption.

3.  The Table and Figure must be referred to within the text of the results section.  

      You can not include a Table or Figure without referring to the Table or Figure

       within the text. 

 4.  The results section must contain more than the figure and table; there must be a

      paragraph describing the results.   Do not turn in a report with a results section  

      consisting of only a table and a figure.   If you have any questions about the

      format of the results paragraph consult the example that will be available in lab

      or ask the lab instructor.

 

 

Use the class data from your Petri dish experiment to test whether the number of colonies that were observed was greater than would be expected by random chance.

 

Table 1.  The raw Bio 100 class data of the number of colonies observed on petri dishes filled with nutrient agar after a 5 day experiment, n= 6.                                                                                                                                                                                

 

Sample number

Exposed for 30 min

Lab table surface

Human fingertips

Mouth or lips

No exposure to a surface

Table 1

 

 

 

 

 

 

Table 2

 

 

 

 

 

 

Table 3

 

 

 

 

 

 

Table 4

 

 

 

 

 

 

Table 5

 

 

 

 

 

 

Table 6

 

 

 

 

 

 

Totals

 

 

 

 

 

 

                                                                                                                                                                                               

 

How many colonies would have been expected for each treatment given random chance?

 

Expected number of colonies

Total * .50

 

 

 

 

 

 

 

 

Calculate the Chi- Square value for each category:

 

(Observed value  -  Expected value)2

                                                                                = Chi – Square value

         Expected value

 

Chi – Square  value for each category

 

 

 

 

 

 

 

 

 

                                                                                Sum all of the Chi-Square values =  ___________________

 

How many degrees of freedom are there for this Chi-Square test? ______________________

 

 

What is the Chi-Square critical value?                          ___________________________________

 

Is the total chi-square (sum of all chi-square values) greater or lesser than the critical value?  _________

 

Are the observed number of colonies for this experiment due to random chance? ___________________