# May I interpret confidence levels as confidence intervals in r?

If I got values of lower .CL (confidence level) and upper .CL for a category of A factor, each o.206, 0.245 and

for b category of A factor, each 0.215 and 0.256 in R, can/may I so interpret?

: confidence Interval of a is [0.206, 0.245] and of b is [0.215, 0.256]?

• Edited
A emmean SE df lower.CL upper.CL
a 0.21 0.0009 52 0.206 0.245
b 0.205 0.0009 52 0.215 0.256
• Please try to explain your question and provide a code sample. Also, not that a CI should be noted along its confidence level. Aug 2, 2021 at 12:36
• I agree with @Spätzle on the suggestion to provide a code sample. However, to my best knowledge, the values in your example refer to confidence intervals. Confidence levels refer to the probability with which the estimation of the location of a effect estimate is also true for the population i.e., usually set at 90%, 95%, or 99%. HTH Aug 2, 2021 at 13:25
• Thanks then lower & upper. CL is confidence interval? I thought CL means confidence level!! and what is the code sample? I thought the table examples is a code sample... Aug 2, 2021 at 13:45
• Lower CL and upper CL are the confidence limits, i.e the limits of the confidence interval. Aug 2, 2021 at 14:00
• Thank you so much!! Aug 2, 2021 at 14:14

To be explicit: Suppose you have the (fictitious) data sampled using R below:

set.seed(2021)
x = rnorm(20, 50, 7)
summary(x);  length(x);  sd(x)
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
36.54   49.86   52.48   52.76   60.42   62.11
 20        # sample size
 7.621391  # sample standard deviation


A boxplot and a stripchart (dotplot) of the data are shown below:

par(mfrow = c(2,1))
boxplot(x, col="skyblue2", horizontal=T)
stripchart(x, pch=20)
abline(v=mean(x), col="red")
par(mfrow = c(1,1)) t.test(x, mu = 55)

One Sample t-test

data:  x
t = -1.3151, df = 19, p-value = 0.2041
alternative hypothesis: true mean is not equal to 55
95 percent confidence interval:
49.19194 56.32578
sample estimates:
mean of x
52.75886


Then (because this is simulated data) we know population mean is $$\mu = 50,$$ sample mean is $$52.76,$$ which is not significantly different from hypothetical mean $$\mu_0 = 55.$$ A 95% CI for $$\mu$$ is $$(49.19, 56.33).$$ which is centered at $$\bar X = 52.76$$ and contains $$\mu_0 = 55.$$

In a real application you would never know that $$\mu =50,$$ exactly. The best point estimate is $$\hat \mu = \bar X = 52.76$$ and we can be 95% confident that $$\mu$$ is in interval $$(49.19, 56.33).$$

A narrower 90% confidence interval is $$(49.81, 55.71).$$

t.test(x, conf.lev=.90)$conf.int  49.81208 55.70564 attr(,"conf.level")  0.9 And a wider 99% CI is $$(47.88, 57,63).$$ t.test(x, conf.lev=.99)$conf.int
 47.88327 57.63445
attr(,"conf.level")
 0.99


To consolidate these relationships, you should look at the formula in your text or class notes for a one-sample t.test and use the summary information printed above for $$n, \bar X, S_x$$ to make all three confidence intervals, 90%, 95%, and 00%. Then check your hand computations with the results above from R.

• Wow thank your for your detailed explanation and time :D confidence levels are just the number 90, 95 and 99? Aug 2, 2021 at 14:15
• Yes 90%,, 95%, 99%. Aug 2, 2021 at 14:20
• Super thanks!!! Aug 2, 2021 at 17:01
• Maybe you need to talk to a statistical consultant. There is more to statistics than running programs. You need to understand what it is you have. Aug 2, 2021 at 23:54