## Some Basic Statistical Procedures

These allow simple statistical evalation of results for students with no statistical background. The statistical calcuations are treated as "black boxes" so the students can focus on the reasoning behind the calculations and the need for statistical analysis of data.

There are many possible statistical procedures. These will not be appropriate for everything. More advanced students doing serious research should use other resources, such as:

• Ambrose, Harrison W. and Katherine Peckham Ambrose 2002. A Handbook of Biological Investigation, 6th edition. Hunter Textbooks. This is an easy to understand paperback.
• University of Leicester's Introduction to Statistical Analysis. This is a very good web site for determining appropriate statistical procedures to use.
• VassarStats: Website for Statistical Computation. This excellent site allows on-line data entry for many different statistical tests (including nonparametrics). It is quite easy to use. It does assume some statistical knowledge, including what tests are appropriate. So one might first consult the University of Leicester site or the BioStats Basics Online site. This site does include an on-line companion textbook.
• Also, new versions of Excel have an easy to use statistical analysis package. You first have to add it to your Excel features as follows: Open the Tools menu, click on "Add -Ins...", then select "Analysis ToolPak." From then on you can enter your data in a spreadsheet, select "Data Analysis" from the Tools menu and select the kind of statistics you wish.

### Standard Error Bars

Error bars allow comparison of means of different populations.  The independent variable is qualitative (such as categories like men vs. women; woods vs. meadow) and the dependent variable is quantitative (e.g. height, weight, number of grasshoppers). Comparing + and - one standard error bars around sample means serves as a very rough approximation of a t-test. Using error bars has two advantages over a t-test.  First, it gives novices in statistics a more easily grasped visual way to test for significant differences, showing variability of data.  Second, it can be used to compare more than two means.  However, this simplicity comes with a greater risk of false positive results -- that is, concluding that two populations are different when they really are not.  For that reason, biology majors should follow up with a t-test or ANOVA.

### Chi-square

For data where both independent and dependent variables are quantitative (such as categories like men vs. women and favoring vs. opposing something). The data is the number of individuals in those categories (such as number of men favoring, number of men opposed, number of women favoring, number of women opposed).

### Correlation

For data where both independent and dependent variables are quantitative, such as weight vs. height, number of insects vs. temperature. Both variables are measured for each sample (e.g. each individual's height and weight it measured, or in each 1m plot you record the number of insects and the temperature. NOTE: Presence of a correlation does not necessarily mean one variable caused the other to change.