Reporting the results of statistical tests
In the scientific literature, there are standardized ways of reporting the results of statistical tests. The following items should always be included in reporting the results of a test: the calculated value of the statistic (which varies depending on the test - for example in a t-test the calculated value of t would be reported), the number of degrees of freedom (i.e. df) if appropriate for the test, and an indication of the value of P. In some cases, the actual value of P as calculated by statistical software is reported. In other cases, symbols are used to indicate that a particular quantity in a table is significant at a certain P level. For example, an asterisk (*) is often used to indicate that P<0.05 and two asterisks (**) is often used to indicate that P<0.01. "NS" is used to indicate "not significant". When such symbols are used in a table, it is expected that a key will explain the symbols. Other quantities are included as appropriate. (From the Stats manual)
Specific examples for tests we have used
t-test of means or paired t-test: t=0.709, df=26, P=0.485
chi-squared contingency test: χ2=7.4, df=1, P=0.007
chi-squared goodness of fit test: χ2=6.65, df=2, P=0.036
regression: slope= -7.25 mW/h, N=15, R2=0.894, P=0.029 The slope should be expressed with the correct units. Alternatively, the entire equation of best fit can be stated rather than just the slope.
ANOVA: The results are typically reported in the form of a table with a row for each source of variability (the experimental factor(s) and the error term) and the totals.
|
Source |
Degrees of freedom |
Sum of squares |
Mean square |
F ratio |
P |
|
Soap |
1 |
4704500 |
4704500 |
7.1 |
0.0164 |
|
Triclosan |
1 |
264500 |
264500 |
0.40 |
0.536 |
|
Error |
17 |
11280500 |
663559 |
|
|
|
Total |
19 |
16249500 |
|
|
|
Note: since it is possible to calculate some values in the table from others, sometimes the totals or the mean square may be omitted.
t-test practice data (NOT required for the problem set)
- Viero egg mass dataTen vireo eggs from Ontario were weighed and ten vireo eggs from the southeastern US were weighed. Type of data: continuous. Comparison: group means. Appropriate test: t-test of means. Null hypothesis: the mean of Ontario eggs is the same as the mean of SE US eggs.
General notes on importing text files
If you need to import a text file into Excel: Use the Open dialog to navagate to the place where you saved the file. Change the file type from "All Excel Files" to "All files". Then double-click on the text file you want to import. The Text Import Wizard will open. Click "next" to the first dialog. In the next dialog, if Comma is not checked as a delimiter, check it and then click "Finish".
If you need to import a text file into JMP: Import the file into the JMP software by clicking the "Open Data Table" button. Under the "Look In:" drop down list, select the Desktop. In the "Files of Type:" drop down list, select "Text Import Files". Select the data file and click the "Open" button.
Paquette Data
You can download the file (right click on the link and select “Save link as..” in Firefox or “Save target as…” in IE). Save the file on the Desktop.
Lobo Data
You can download the file (right click on the link and select “Save link as..” in Firefox or “Save target as…” in IE). Save the file on the Desktop.
Abbas et al. data
Abbas et al. (1975) examined the distribution of surface immunoglobulins on lymphocytes (Fig. 5, above) by counting the number of sites in small areas of a grid and comparing the distribution of sites per area to that which would be predicted in a random distribution (Fig. 6, above). A simplified summary of their data for Fig. 5B would be as follows:
|
Dots per square |
Observed distribution |
Expected random distribution |
|
0 to 2 |
100 |
68 |
|
3 to 5 |
94 |
151 |
|
6 to 8 |
63 |
57 |
|
9 to 13 |
26 |
7 |
Is the distribution of surface immunoglobulins random? If not, are they too clumped or too uniform?
