Why do the widths of the confidence intervals differ

We'll begin by defining a procedure to calculate intervals for various confidence levels; the procedure will print these out as a table:. Next we'll declare the distribution object we'll need, note that the degrees of freedom parameter is the sample size less one:. Most of what follows in the program is pretty printing, so let's focus on the calculation of the interval. First we need the t-statistic, computed using the quantile function and our significance level.

Note that since the significance levels are the complement of the probability, we have to wrap the arguments in a call to complement Note that alpha was divided by two, since we'll be calculating both the upper and lower bounds: had we been interested in a single sided interval then we would have omitted this step. Now to complete the picture, we'll get the one-sided width of the interval from the t-statistic by multiplying by the standard deviation, and dividing by the square root of the sample size:.

The two-sided interval is then the sample mean plus and minus this width. The corresponding dataplot output for this test can be found in section 3. As you can see the large sample size and small standard deviation 0. Leave a Reply Cancel reply Your email address will not be published. The Analysis Factor uses cookies to ensure that we give you the best experience of our website.

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Here the number 7 is your margin of error. For confidence intervals around the mean, the margin of error is just half of your total confidence interval width. The precision of your statistics depends on your sample size and variability. A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error.

A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error. The level of confidence also affects the interval width.

If you want a higher level of confidence, that interval will not be as tight. Search Campus:. Confidence Intervals Remember that there is variability associated with your outcomes and statistics. Let's Look at an Example: Suppose that you want to compare the mean age for those with and without an IV in the prehospital setting.