UCL = min ( 1, p + z *StdErr) /* UCL can't be less than 0 */ label p = "Proportion" LCL= "Lower 95% CL" UCL= "Upper 95% CL" LCL = max ( 0, p - z *StdErr) /* LCL can't be less than 0 */ P = Grads / Total /* empirical proportion */ StdErr = sqrt (p *(1-p)/Total) /* standard error */ /* use Wald 95% CIs */ The following SAS DATA step defines the number of students who graduated in four years (Grads) and the number of students in each cohort (Total). Suppose a college has six majors, labeled as A, B, C, D, E, and F.
I don't want to embarrass any small college, so the following data are fake but are typical of the group sizes that you might see in real data. Because most colleges have fewer Hispanic, Asian, and Native American students, it is important to indicate the sample size or the uncertainty in the empirical estimates.
You can also find the graduation rate by race (five groups) for any individual college. You can find the average graduation rate by states (50 groups) or by college (hundreds of groups). The Chronicle of Higher Education web site enables you to find the graduation rates for US colleges and universities. As I've explained, I prefer to display the confidence interval. When you have a smaller number of groups, a simple alternative is a dot plot with error bars that indicate either the standard error or a 95% confidence interval for the estimate. Therefore, it is a good idea to incorporate some visual aspect of the uncertainty into any graph of proportions and rates.įor analyses that involve dozens or hundreds of groups, you can use a funnel plot of proportions, which I have used to analyze adoption rates for children and immunization rates for kindergartens in North Carolina. Thus for the physics students, the standard error is sqrt(0.6*0.4/8) = 0.17, whereas for the English majors, the standard error is sqrt(0.6*0.4/80) = 0.05.
Specifically, if the estimate of a binomial proportion is p, the standard error of the estimate is sqrt( p(1– p)/ n), where n is the sample size. However, because of the small sample size, the uncertainty in that estimate is much greater than for a larger group, such as if the English department graduates 50 out of 80 students. If a small college has 8 physics majors and 5 of them graduate in four years, the graduation rate in physics is 0.6. The first two examples are somewhat depressing, so I will use graduation rates for this article.Īn important fact to remember is that the uncertainty in an estimate depends on the sample size. Four-year graduation rates by academic major.Mortality rates for various types of cancers.Examples of proportions that depend on subgroups include: When you are computing several proportions, it is helpful to visualize how the rates vary among subgroups of the population. Computing rates and proportions is a common task in data analysis.
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