# Statistical Analysis

"Skeptical scrutiny is the means by which deep thoughts can be winnowed from deep nonsense." Carl Sagan

#### Figure 1: What is the average size of the bacteria?

How would you determine the average size of the cocci bacteria in the population shown in the figure below. You could measure each coccus and then find the population's average size (mean) but this would be a large task to undertake. Another method would be to take a random sample of the population, measure the size of each coccus in the sample population then find the average size (mean) of the sample population. How confident are you that the sample mean is a good estimate of the population mean? Calculating the standard deviation will give you a measure of how reliable the sample mean is as an estimate of the population mean. #### How to calculate standard deviaton using a graphical calculator?

Table 1 shows the measured size of 20 coccus randomly selected from the population with the average size and standard deviation shown in Table 2. Standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean. A small standard deviation would indicate that the data are clustered closely around the sample mean and you would then assume that the sample mean is a good estimate of the population mean.

#### Placing your mouse pointer on the figure will reveal the procedure to calculate standard deviation with a graphical calculator. #### Use error bars in your graph!

The error bars in the graphs demonstrate the cocci that fall within one standard deviation of the mean.

#### Placing your mouse pointer on the figure will reveal a bar graph of the results. #### Sample problem: Can sleep affect SCAT test scores? #### How to perform a student t-test?

The procedure below outlines how to perform a student t-test. There are two procedures. Procedure A outlines a t-test using a t-value and t-table (you need to know this procedure) while Procedure B involves using p-values (which seems to be an easier method to use). You can use either procedure in your conclusion for lab write ups. Click on the link below to view a web page on how to perform a t-test if you do not have a graphical calculator. #### Placing your mouse pointer on the figure will reveal Procedure B.  #### Are the SCAT scores SIGNIFICANTLY different to support Sam's hypothesis?

The conclusion to Procedure A is shown below.

#### Placing your mouse pointer on the figure will reveal the conclusion to Procedure B. #### Correlation and Causation

Click on the figure below to open a webpage that explains that the existence of a correlation does not establish that there is a causal relationship between two variables.  