In an article about anti-tobacco campaigns, Siegel and Biener (1997) discuss the results of a survey of tobacco usage and attitudes, conducted in Massachusetts in 1993 and 1995; Table 4-4 shows the results of this survey. Focusing on just the first line (the percentage smoking 25 cigarettes daily), explain what this result means to a person who has never had a course in statistics. (Focus on the meaning of this result in terms of the general logic of hypothesis testing and statistical significance.)
Table 4-4 (Selected Indicators of Change in Tobacco Use, ETS Exposure, and Public Attitudestoward Tobacco Control Policies?Massachusetts, 1993-1995)
Adult Smoking Behavior
Percentage smoking 25 cigarettes daily 24 10*
Percentage smoking _15 cigarettes daily 31 49*
Percentage smoking within 30 minutes of waking 54 41
Environmental Tobacco Smoke Exposure
Percentage of workers reporting a smoke free worksite 53 65*
Mean hours of ETS exposure at work during prior week 4.2 2.3*
Percentage of homes in which smoking is banned 41 51*
Attitudes Toward Tobacco Control Policies
Percentage supporting further increase in tax on
Tobacco with funds earmarked for tobacco control 78 81
Percentage believing ETS is harmful 90 84
Percentage supporting ban on vending machines 54 64*
Percentage supporting ban on support of sports and cultural
events by tobacco companies 59 53*
* p < .05
What we see in that first line of the table is evidence that the percentage of people smoking 25 cigarettes daily has decreased SIGNIFICANTLY between 1993 and 1995. We know this is a decrease by the numbers themselves (10% is smaller than 24%) and we know it's a statistically significant decrease because of the star beside the 1995 value, which as you can see from the legend at the bottom indicates that that change has a p value that is smaller than .05.
Let's think about what it actually means to have a p value smaller than .05. When we're testing hypotheses, we're always comparing our data to a null distribution. That null distribution is the distribution we would expect to see if our experiment or treatment didn't work. Let's imagine that in this case, the state has implemented a program that ran throughout 1994 and 1995 and was designed to decrease smoking rates. In this case, our null hypothesis might be that the program doesn't affect smoking rates (and our alternative ...
Hypothesis testing an statistical significance is examined.