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How inferential Statistical Decisions Operate 
An additional tutorial which develops this example in more detail is available by clicking here.
Simple Visual Reaction Time (SVRT) tells the length of time it takes to start a response (a key press, for instance) after a visual stimulus appears. The typical reaction time is about 1/5 second (200 milliseconds; 200 ms).
It is well documented that females have a slightly longer SVRT than males.
Use the 9 males and 9 females in our Experimental Psychology course to check the validity of the assertion that males have shorter reaction times than females. Assume we discover then 9 females have an average SVRT of 190 ms and the males have an average of 180. The difference in average reaction times is 10 ms (female Mn  male Mn). This difference is plotted as an orange square in the card image shown below.
Descriptive Statistics is the term used to indicate I am telling you what the subjects of the research didwhat the results of the study are. I am not generalizing or predicting what the results might be if the research were repeated with another set of subjects.
If I were to repeat the research with another 18 subjects (9 males and 9 females)? Would these descriptive statistical results be repeated? Would I find again (and again) that the female reaction time was longer? When I make predictions about the results of research with another group of subjects I am asking an Inferential Statistics question.
Descriptive Statistics of the Original Study  Results that might happen in the future with different subjects  
Females have a longer reaction time than the males.  The descriptive statistics of the repeated study shows that females have longer reaction times then males.
Confirms the original study: Females have shorter reaction times. 

The descriptive statistics of the replicated studies do not support the notion that females have longer reaction times than males.
No evidence females have shorter reaction times. 
Another possibility is to think outside the box. Let's reverse the question: What would data "look like" if females and males had the same average reaction time?
So, let's run a simulation where we draw repeatedly draw two samples of 9 observations from one populationwhich is what is meant when we assume males and females have the same reaction time.
The Process: Draw two samples of 9 (pretend the first sample is the measurement of female SVRT). Calculate the means of the two samples and find the difference in the two means. Plot the result in the image below as a black triangle. Repeat the sampling procedure many times (100 times in this instance). The orange square indicates the results of the result measuring 9 males and females in class.

When a researcher analyzes the data of an experiment with a statistical test, she is wanting to know whether or not the results are reliablewould she get similar results if the experiment were repeated with different subjects.
When the researcher calculates the value of statistic for an inferential statistical test and then compares that value to tabled values, she is asking, "Are the results I actually obtained similar to what I might have gotten if there NO real difference between the groups of subjects.
If you look at the simulation screen you'll notice there are a number of settings that can be changed. When these values are changed, you might end up making a different decision about whether or not the results of the empirical research are reliable.
These settings (aka "parameters") are assumptions that are made when inferential statistical tests are performed.
Here are some examples of the impact changes in parameters can have on the decisions based on simulation. The first 3 examples are based on a 10 ms difference in reaction time and change the sample size (4, 16, or 25). The second three examples are based on a 5 ms difference and have sample sizes of 9, 16, and 36.
© 2005 by Burrton Woodruff. All Rights Reserved. Modified