informal confidence intervals
(ICI)
In year 9 and 10 we could make the "call" that one group was larger than the other simply by stating which median was larger. In year 11 we could make the "call" as long as the distance between the medians compared to the overall visible spread was greater than 1/3. Alternatively, we could use the bottom 3/4 top 1/2 rule to make the call.
the iCI
In year 12 we use another method for determining if we can make the call that a parameter of one group is greater than that of another group. This is called the Informal Confidence Interval (ICF), or "blue line" that you will notice attached to the median bar in the box plots.
From the sample, the informal confidence interval is an approximation of the population median, a calculation done inside NZGrapher which produces blue symmetrical lines around the median. For the sample to be representative, the sample size needs to be at least 30. The sample is taken using NZGrapher, sample and more. For kiwi we select a good sample size of 100, that's about 50 samples of female and male kiwi.
Why do we need informal confidence intervals and why are they not called formal confidence intervals?
Recall that when we carried out an investigation of the kiwi population data set everyone in the class got a slightly different median. I think everyone got box plots that generally showed that the female kiwi were heavier than male kiwi. This is called the variability of estimates. The variability depends on sample size. The blue bar on your graph tells you that the population median is likely to be within that blue bar...with a confidence of 95%. So as long as the two blue bars don't overlap we can make the call that one is lager than the other. The greater the sample size, the thinner the blue bar gets and the more accurate your estimate will be. But 30 is the minimum and we use 100 samples for the kiwi investigation.
In year 13 we use a more formal approach called boot strapping.
In summary, confidence intervals tell us how good an estimate is and that we can be 95% pretty sure that the true population median will fall between the limits indicated by the blue bars on the graph. If the blue bars overlap, we cant say which group is larger and if the blue don't overlap we can.
Recall that when we carried out an investigation of the kiwi population data set everyone in the class got a slightly different median. I think everyone got box plots that generally showed that the female kiwi were heavier than male kiwi. This is called the variability of estimates. The variability depends on sample size. The blue bar on your graph tells you that the population median is likely to be within that blue bar...with a confidence of 95%. So as long as the two blue bars don't overlap we can make the call that one is lager than the other. The greater the sample size, the thinner the blue bar gets and the more accurate your estimate will be. But 30 is the minimum and we use 100 samples for the kiwi investigation.
In year 13 we use a more formal approach called boot strapping.
In summary, confidence intervals tell us how good an estimate is and that we can be 95% pretty sure that the true population median will fall between the limits indicated by the blue bars on the graph. If the blue bars overlap, we cant say which group is larger and if the blue don't overlap we can.
But what happens if the box plots get closer together...To be continued