Many academic papers, theses, or research projects that contain quantitative findings can be enriched by the use of 95% confidence interval (CI) plots, which can be generated by statistical programs such as Stata, R, and SPSS.
Let’s discuss the underlying concept first. Assume you solicit income information for 30 people from New York City and 30 people from Denver. A 95% CI is the range of values that is 95% likely to contain a true population mean. We can generate some mock data to illustrate this concept, then place it into a 95% CI graph to show you how powerful this kind of illustration is.
set obs 60
gen subj = _n
label variable subj "Subject #"
gen city = .
replace city = 1 in 1/30
replace city = 2 in 31/60
label define city 1 "New York " 2 "Denver"
label variable city "City"
label value city city
drawnorm income1, mean(65000) sd(8000)
drawnorm income2, mean(40000) sd(5000)
replace income1 = . in 31/60
replace income2 = . in 1/30
egen income3 = rowmax(income1 income2)
drop income1 income2
gen income = round(income3)
label variable income "Income"
drop income3
Using descriptive statistics, we can calculate the 95% CI values for income levels among survey participants in both cities as follows:
There is a 95% likelihood that the true income level in Denver is between $37,599.46 and $41,392.60. There is also a 95% likelihood that the true income level in New York City is between $61,425.63 and $68,713.10. Here’s a 95% CI plot of these differences.
The reason we use 95% CIs in research papers that are quantitatively oriented is to assess overlaps between continuously distributed data. In this case, we see that Denver and New York City do not overlap at all in the 95% CIs of their income levels. Therefore, we can reliably expect that an independent samples t-test will find New York City to have a significantly higher mean income than Denver. A 95% CI plot, unlike a bar graph, lets you compare not merely point estimates (here, income averages) but the full distributional range of variables, which is statistically preferable.
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