Chapter 9

Descriptive Statistics, Significance Levels,

and Hypothesis Testing

 

The Impact of the Standard Deviation on the Normal Curve 

A great interactive website lets you see what happens when the value of a standard deviation changes for a data set. It also lets you see what happens to the normalcy of the data distribution as the number of cases increases. Point your mouse to the black dot at the bottom of the first standards (+1 and –1). When you enter the site, they are set at a standard deviation of 1.25; move the standards closer together to reflect a smaller standard deviation. Notice how this change affects the steepness and slope of the normal curve. Now slide the bin (interval) bar to its lowest value (.05). Click on the button “Create New Histogram.” This feature randomly selects data points and distributes them on the normal curve. Look at the difference between histograms with 100 data points and 500 data points. Using these interactive features you should be see the value of having a greater number of cases in the data set. You should also see how the +1 and –1 standards have a relative position to one another and the mean despite their value.  

 

Mean, Median or Mode? 

This website provides a good review of measures of central tendency.  

The Scientific Tradition of p Values

In spring 2019, physical scientists have made the case that researchers are inappropriately making decisions about hypothesis on the basis of p  values. Why is this important? The social sciences generally follow the statistical practices of the physical scientists. The Communication discipline has not yet responded or made any announcements. So I'll post links here as I find them. If you are a student, please check with your professor about his/her preferences of making decisions based on the value of the p value.

Scientists rise up against statistical significance (March 2019)

Statisticians' Call To Arms: Reject Significance And Embrace Uncertainty! (March 2019)

 

American Psychological Association's statement on p values  (March 2016)

Updated March 24, 2019